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Fraction word prob.

Fraction word problems

Here you will learn about fraction word problems, including solving math word problems within a real-world context involving adding fractions, subtracting fractions, multiplying fractions, and dividing fractions.

Students will first learn about fraction word problems as part of number and operations—fractions in 4 th grade.

What are fraction word problems?

Fraction word problems are math word problems involving fractions that require students to use problem-solving skills within the context of a real-world situation.

To solve a fraction word problem, you must understand the context of the word problem, what the unknown information is, and what operation is needed to solve it. Fraction word problems may require addition, subtraction, multiplication, or division of fractions.

After determining what operation is needed to solve the problem, you can apply the rules of adding, subtracting, multiplying, or dividing fractions to find the solution.

For example,

Natalie is baking 2 different batches of cookies. One batch needs \cfrac{3}{4} cup of sugar and the other batch needs \cfrac{2}{4} cup of sugar. How much sugar is needed to bake both batches of cookies?

You can follow these steps to solve the problem:

Step-by-step guide: Adding and subtracting fractions

Step-by-step guide: Adding fractions

Step-by-step guide: Subtracting fractions

Step-by-step guide: Multiplying and dividing fractions

Step-by-step guide: Multiplying fractions

Step-by-step guide: Dividing fractions

Common Core State Standards

How does this relate to 4 th grade math to 6 th grade math?

• Grade 4: Number and Operations—Fractions (4.NF.B.3d) Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.
• Grade 4: Number and Operations—Fractions (4.NF.B.4c) Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat \cfrac{3}{8} of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?
• Grade 5: Number and Operations—Fractions (5.NF.A.2) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result \cfrac{2}{5}+\cfrac{1}{2}=\cfrac{3}{7} by observing that \cfrac{3}{7}<\cfrac{1}{2} .
• Grade 5: Number and Operations—Fractions (5.NF.B.6) Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
• Grade 5: Number and Operations—Fractions (5.NF.B.7c) Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share \cfrac{1}{2} \: lb of chocolate equally? How many \cfrac{1}{3} cup servings are in 2 cups of raisins?
• Grade 6: The Number System (6.NS.A.1) Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for \cfrac{2}{3} \div \cfrac{4}{5} and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that \cfrac{2}{3} \div \cfrac{4}{5}=\cfrac{8}{9} because \cfrac{3}{4} of \cfrac{8}{9} is \cfrac{2}{3}. (In general, \cfrac{a}{b} \div \cfrac{c}{d}=\cfrac{a d}{b c} \, ) How much chocolate will each person get if 3 people share \cfrac{1}{2} \: lb of chocolate equally? How many \cfrac{3}{4} cup servings are in \cfrac{2}{3} of a cup of yogurt? How wide is a rectangular strip of land with length \cfrac{3}{4} \: m and area \cfrac{1}{2} \: m^2?

[FREE] Fraction Operations Worksheet (Grade 4 to 6)

Use this quiz to check your grade 4 to 6 students’ understanding of fraction operations. 10+ questions with answers covering a range of 4th to 6th grade fraction operations topics to identify areas of strength and support!

How to solve fraction word problems

In order to solve fraction word problems:

Determine what operation is needed to solve.

Write an equation.

Solve the equation.

State your answer in a sentence.

Fraction word problem examples

Example 1: adding fractions (like denominators).

Julia ate \cfrac{3}{8} of a pizza and her brother ate \cfrac{2}{8} of the same pizza. How much of the pizza did they eat altogether?

The problem states how much pizza Julia ate and how much her brother ate. You need to find how much pizza Julia and her brother ate altogether , which means you need to add.

2 Write an equation.

3 Solve the equation.

To add fractions with like denominators, add the numerators and keep the denominators the same.

4 State your answer in a sentence.

The last step is to go back to the word problem and write a sentence to clearly say what the solution represents in the context of the problem.

Julia and her brother ate \cfrac{5}{8} of the pizza altogether.

Example 2: adding fractions (unlike denominators)

Tim ran \cfrac{5}{6} of a mile in the morning and \cfrac{1}{3} of a mile in the afternoon. How far did Tim run in total?

The problem states how far Tim ran in the morning and how far he ran in the afternoon. You need to find how far Tim ran in total , which means you need to add.

To add fractions with unlike denominators, first find a common denominator and then change the fractions accordingly before adding.

\cfrac{5}{6}+\cfrac{1}{3}= \, ?

The least common multiple of 6 and 3 is 6, so 6 can be the common denominator.

That means \cfrac{1}{3} will need to be changed so that its denominator is 6. To do this, multiply the numerator and the denominator by 2.

\cfrac{1 \times 2}{3 \times 2}=\cfrac{2}{6}

Now you can add the fractions and simplify the answer.

\cfrac{5}{6}+\cfrac{2}{6}=\cfrac{7}{6}=1 \cfrac{1}{6}

Tim ran a total of 1 \cfrac{1}{6} miles.

Example 3: subtracting fractions (like denominators)

Pia walked \cfrac{4}{7} of a mile to the park and \cfrac{3}{7} of a mile back home. How much farther did she walk to the park than back home?

The problem states how far Pia walked to the park and how far she walked home. Since you need to find the difference ( how much farther ) between the two distances, you need to subtract.

To subtract fractions with like denominators, subtract the numerators and keep the denominators the same.

\cfrac{4}{7}-\cfrac{3}{7}=\cfrac{1}{7}

Pia walked \cfrac{1}{7} of a mile farther to the park than back home.

Example 4: subtracting fractions (unlike denominators)

Henry bought \cfrac{7}{8} pound of beef from the grocery store. He used \cfrac{1}{3} of a pound of beef to make a hamburger. How much of the beef does he have left?

The problem states how much beef Henry started with and how much he used. Since you need to find how much he has left , you need to subtract.

To subtract fractions with unlike denominators, first find a common denominator and then change the fractions accordingly before subtracting.

\cfrac{7}{8}-\cfrac{1}{3}= \, ?

The least common multiple of 8 and 3 is 24, so 24 can be the common denominator.

That means both fractions will need to be changed so that their denominator is 24.

To do this, multiply the numerator and the denominator of each fraction by the same number so that it results in a denominator of 24. This will give you an equivalent fraction for each fraction in the problem.

\begin{aligned}&\cfrac{7 \times 3}{8 \times 3}=\cfrac{21}{24} \\\\ &\cfrac{1 \times 8}{3 \times 8}=\cfrac{8}{24} \end{aligned}

Now you can subtract the fractions.

\cfrac{21}{24}-\cfrac{8}{24}=\cfrac{13}{24}

Henry has \cfrac{13}{24} of a pound of beef left.

Example 5: multiplying fractions

Andre has \cfrac{3}{4} of a candy bar left. He gives \cfrac{1}{2} of the remaining bit of the candy bar to his sister. What fraction of the whole candy bar does Andre have left now?

It could be challenging to determine the operation needed for this problem; many students may automatically assume it is subtraction since you need to find how much of the candy bar is left.

However, since you know Andre started with a fraction of the candy bar and you need to find a fraction OF a fraction, you need to multiply.

The difference here is that Andre did NOT give his sister \cfrac{1}{2} of the candy bar, but he gave her \cfrac{1}{2} of \cfrac{3}{4} of a candy bar.

To solve the word problem, you can ask, “What is \cfrac{1}{2} of \cfrac{3}{4}? ” and set up the equation accordingly. Think of the multiplication sign as meaning “of.”

\cfrac{1}{2} \times \cfrac{3}{4}= \, ?

To multiply fractions, multiply the numerators and multiply the denominators.

\cfrac{1}{2} \times \cfrac{3}{4}=\cfrac{3}{8}

Andre gave \cfrac{1}{2} of \cfrac{3}{4} of a candy bar to his sister, which means he has \cfrac{1}{2} of \cfrac{3}{4} left. Therefore, Andre has \cfrac{3}{8} of the whole candy bar left.

Example 6: dividing fractions

Nia has \cfrac{7}{8} cup of trail mix. How many \cfrac{1}{4} cup servings can she make?

The problem states the total amount of trail mix Nia has and asks how many servings can be made from it.

To solve, you need to divide the total amount of trail mix (which is \cfrac{7}{8} cup) by the amount in each serving ( \cfrac{1}{4} cup) to find out how many servings she can make.

To divide fractions, multiply the dividend by the reciprocal of the divisor.

\begin{aligned}& \cfrac{7}{8} \div \cfrac{1}{4}= \, ? \\\\ & \downarrow \downarrow \downarrow \\\\ &\cfrac{7}{8} \times \cfrac{4}{1}=\cfrac{28}{8} \end{aligned}

You can simplify \cfrac{28}{8} to \cfrac{7}{2} and then 3 \cfrac{1}{2}.

Nia can make 3 \cfrac{1}{2} cup servings.

Teaching tips for fraction word problems

• Encourage students to look for key words to help determine the operation needed to solve the problem. For example, subtracting fractions word problems might ask students to find “how much is left” or “how much more” one fraction is than another.
• Provide students with an answer key to word problem worksheets to allow them to obtain immediate feedback on their solutions. Encourage students to attempt the problems independently first, then check their answers against the key to identify any mistakes and learn from them. This helps reinforce problem-solving skills and confidence.
• Be sure to incorporate real-world situations into your math lessons. Doing so allows students to better understand the relevance of fractions in everyday life.
• As students progress and build a strong foundational understanding of one-step fraction word problems, provide them with multi-step word problems that involve more than one operation to solve.
• Take note that students will not divide a fraction by a fraction as shown above until 6 th grade (middle school), but they will divide a unit fraction by a whole number and a whole number by a fraction in 5 th grade (elementary school), where the same mathematical rules apply to solving.
• There are many alternatives you can use in place of printable math worksheets to make practicing fraction word problems more engaging. Some examples are online math games and digital workbooks.

Easy mistakes to make

• Misinterpreting the problem Misreading or misunderstanding the word problem can lead to solving for the wrong quantity or using the wrong operation.
• Not finding common denominators When adding or subtracting fractions with unlike denominators, students may forget to find a common denominator, leading to an incorrect answer.
• Forgetting to simplify Unless a problem specifically says not to simplify, fractional answers should always be written in simplest form.

Related fractions operations lessons

• Fractions operations
• Multiplicative inverse
• Reciprocal math
• Fractions as divisions

Practice fraction word problem questions

1. Malia spent \cfrac{5}{6} of an hour studying for a math test. Then she spent \cfrac{1}{3} of an hour reading. How much longer did she spend studying for her math test than reading?

Malia spent \cfrac{1}{2} of an hour longer studying for her math test than reading.

Malia spent \cfrac{5}{18} of an hour longer studying for her math test than reading.

Malia spent \cfrac{1}{2} of an hour longer reading than studying for her math test.

Malia spent 1 \cfrac{1}{6} of an hour longer studying for her math test than reading.

To find the difference between the amount of time Malia spent studying for her math test than reading, you need to subtract. Since the fractions have unlike denominators, you need to find a common denominator first.

You can use 6 as the common denominator, so \cfrac{1}{3} becomes \cfrac{3}{6}. Then you can subtract.

\cfrac{3}{6} can then be simplified to \cfrac{1}{2}.

Finally, you need to choose the answer that correctly answers the question within the context of the situation. Therefore, the correct answer is “Malia spent \cfrac{1}{2} of an hour longer studying for her math test than reading.”

2. A square garden is \cfrac{3}{4} of a meter wide and \cfrac{8}{9} of a meter long. What is its area?

The area of the garden is 1\cfrac{23}{36} square meters.

The area of the garden is \cfrac{27}{32} square meters.

The area of the garden is \cfrac{2}{3} square meters.

The perimeter of the garden is \cfrac{2}{3} meters.

To find the area of a square, you multiply the length and width. So to solve, you multiply the fractional lengths by mulitplying the numerators and multiplying the denominators.

\cfrac{24}{36} can be simplified to \cfrac{2}{3}. 

Therefore, the correct answer is “The area of the garden is \cfrac{2}{3} square meters.”

3. Zoe ate \cfrac{3}{8} of a small cake. Liam ate \cfrac{1}{8} of the same cake. How much more of the cake did Zoe eat than Liam?

Zoe ate \cfrac{3}{64} more of the cake than Liam.

Zoe ate \cfrac{1}{4} more of the cake than Liam.

Zoe ate \cfrac{1}{8} more of the cake than Liam.

Liam ate \cfrac{1}{4} more of the cake than Zoe.

To find how much more cake Zoe ate than Liam, you subtract. Since the fractions have the same denominator, you subtract the numerators and keep the denominator the same.

\cfrac{2}{8} can be simplified to \cfrac{1}{4}. 

Therefore, the correct answer is “Zoe ate \cfrac{1}{4} more of the cake than Liam.”

4. Lila poured \cfrac{11}{12} cup of pineapple and \cfrac{2}{3} cup of mango juice in a bottle. How many cups of juice did she pour into the bottle altogether?

Lila poured 1 \cfrac{7}{12} cups of juice in the bottle altogether.

Lila poured \cfrac{1}{4} cups of juice in the bottle altogether.

Lila poured \cfrac{11}{18} cups of juice in the bottle altogether.

Lila poured 1 \cfrac{3}{8} cups of juice in the bottle altogether.

To find the total amount of juice that Lila poured into the bottle, you need to add. Since the fractions have unlike denominators, you need to find a common denominator first.

You can use 12 as the common denominator, so \cfrac{2}{3} becomes \cfrac{8}{12}.  Then you can add.

\cfrac{19}{12} can be simplified to 1 \cfrac{7}{12}. 

Therefore, the correct answer is “Lila poured 1 \cfrac{7}{12} cups of juice in the bottle altogether.”

5. Killian used \cfrac{9}{10} of a gallon of paint to paint his living room and \cfrac{7}{10} of a gallon to paint his bedroom. How much paint did Killian use in all?

Killian used \cfrac{2}{10} gallons of paint in all.

Killian used \cfrac{1}{5} gallons of paint in all.

Killian used \cfrac{63}{100} gallons of paint in all.

Killian used 1 \cfrac{3}{5} gallons of paint in all.

To find the total amount of paint Killian used, you add the amount he used for the living room and the amount he used for the kitchen. Since the fractions have the same denominator, you add the numerators and keep the denominators the same.

\cfrac{16}{10} can be simplified to 1 \cfrac{6}{10} and then further simplified to 1 \cfrac{3}{5}.

Therefore, the correct answer is “Killian used 1 \cfrac{3}{5} gallons of paint in all.”

6. Evan pours \cfrac{4}{5} of a liter of orange juice evenly among some cups.

He put \cfrac{1}{10} of a liter into each cup. How many cups did Evan fill?

Evan filled \cfrac{2}{25} cups.

Evan filled 8 cups.

Evan filled \cfrac{9}{10} cups.

Evan filled 7 cups.

To find the number of cups Evan filled, you need to divide the total amount of orange juice by the amount being poured into each cup. To divide fractions, you mulitply the first fraction (the dividend) by the reciprocal of the second fraction (the divisor).

\cfrac{40}{5} can be simplifed to 8.

Therefore, the correct answer is “Evan filled 8 cups.”

Fraction word problems FAQs

Fraction word problems are math word problems involving fractions that require students to use problem-solving skills within the context of a real-world situation. Fraction word problems may involve addition, subtraction, multiplication, or division of fractions.

To solve fraction word problems, first you need to determine the operation. Then you can write an equation and solve the equation based on the arithmetic rules for that operation.

Fraction word problems and decimal word problems are similar because they both involve solving math problems within real-world contexts. Both types of problems require understanding the problem, determining the operation needed to solve it (addition, subtraction, multiplication, division), and solving it based on the arithmetic rules for that operation.

The next lessons are

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Strategies for Solving Word Problems – Math

It’s one thing to solve a math equation when all of the numbers are given to you but with word problems, when you start adding reading to the mix, that’s when it gets especially tricky.

The simple addition of those words ramps up the difficulty (and sometimes the math anxiety) by about 100!

How can you help your students become confident word problem solvers? By teaching your students to solve word problems in a step by step, organized way, you will give them the tools they need to solve word problems in a much more effective way.

Here are the seven strategies I use to help students solve word problems.

1. read the entire word problem.

Before students look for keywords and try to figure out what to do, they need to slow down a bit and read the whole word problem once (and even better, twice). This helps kids get the bigger picture to be able to understand it a little better too.

2. Think About the Word Problem

Students need to ask themselves three questions every time they are faced with a word problem. These questions will help them to set up a plan for solving the problem.

Here are the questions:

A. what exactly is the question.

What is the problem asking? Often times, curriculum writers include extra information in the problem for seemingly no good reason, except maybe to train kids to ignore that extraneous information (grrrr!). Students need to be able to stay focused, ignore those extra details, and find out what the real question is in a particular problem.

B. What do I need in order to find the answer?

Students need to narrow it down, even more, to figure out what is needed to solve the problem, whether it’s adding, subtracting, multiplying, dividing, or some combination of those. They’ll need a general idea of which information will be used (or not used) and what they’ll be doing.

This is where key words become very helpful. When students learn to recognize that certain words mean to add (like in all, altogether, combined ), while others mean to subtract, multiply, or to divide, it helps them decide how to proceed a little better

Here’s a Key Words Chart I like to use for teaching word problems. The handout could be copied at a smaller size and glued into interactive math notebooks. It could be placed in math folders or in binders under the math section if your students use binders.

One year I made huge math signs (addition, subtraction, multiplication, and divide symbols) and wrote the keywords around the symbols. These served as a permanent reminder of keywords for word problems in the classroom.

If you’d like to download this FREE Key Words handout, click here:

C. What information do I already have?

This is where students will focus in on the numbers which will be used to solve the problem.

3. Write on the Word Problem

This step reinforces the thinking which took place in step number two. Students use a pencil or colored pencils to notate information on worksheets (not books of course, unless they’re consumable). There are lots of ways to do this, but here’s what I like to do:

• Circle any numbers you’ll use.
• Lightly cross out any information you don’t need.
• Underline the phrase or sentence which tells exactly what you’ll need to find.

4. Draw a Simple Picture and Label It

Drawing pictures using simple shapes like squares, circles, and rectangles help students visualize problems. Adding numbers or names as labels help too.

For example, if the word problem says that there were five boxes and each box had 4 apples in it, kids can draw five squares with the number four in each square. Instantly, kids can see the answer so much more easily!

5. Estimate the Answer Before Solving

Having a general idea of a ballpark answer for the problem lets students know if their actual answer is reasonable or not. This quick, rough estimate is a good math habit to get into. It helps students really think about their answer’s accuracy when the problem is finally solved.

6. Check Your Work When Done

This strategy goes along with the fifth strategy. One of the phrases I constantly use during math time is, Is your answer reasonable ? I want students to do more than to be number crunchers but to really think about what those numbers mean.

Also, when students get into the habit of checking work, they are more apt to catch careless mistakes, which are often the root of incorrect answers.

7. Practice Word Problems Often

Just like it takes practice to learn to play the clarinet, to dribble a ball in soccer, and to draw realistically, it takes practice to become a master word problem solver.

When students practice word problems, often several things happen. Word problems become less scary (no, really).

They start to notice similarities in types of problems and are able to more quickly understand how to solve them. They will gain confidence even when dealing with new types of word problems, knowing that they have successfully solved many word problems in the past.

If you’re looking for some word problem task cards, I have quite a few of them for 3rd – 5th graders.

This 3rd grade math task cards bundle has word problems in almost every one of its 30 task card sets..

There are also specific sets that are dedicated to word problems and two-step word problems too. I love these because there’s a task card set for every standard.

CLICK HERE to take a look at 3rd grade:

This 4th Grade Math Task Cards Bundle also has lots of word problems in almost every single of its 30 task card sets. These cards are perfect for centers, whole class, and for one on one.

CLICK HERE to see 4th grade:

This 5th Grade Math Task Cards Bundle is also loaded with word problems to give your students focused practice.

CLICK HERE to take a look at 5th grade:

Want to try a FREE set of math task cards to see what you think?

3rd Grade: Rounding Whole Numbers Task Cards

4th Grade: Convert Fractions and Decimals Task Cards

5th Grade: Read, Write, and Compare Decimals Task Cards

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Objective 2

Translating sentences and define a process for problem solving, learning objectives.

• Translate words into algebraic expressions and equations
• Define a process for solving word problems

Word problems can be tricky. Often it takes a bit of practice to convert an English sentence into a mathematical sentence, which is one of the first steps to solving word problems. In the table below, words or phrases commonly associated with mathematical operators are categorized. Word problems often contain these or similar words, so it’s good to see what mathematical operators are associated with them.

How much will it cost?

Some examples follow:

• [latex]x\text{ is }5[/latex]  becomes [latex]x=5[/latex]
• Three more than a number becomes [latex]x+3[/latex]
• Four less than a number becomes [latex]x-4[/latex]
• Double the cost becomes [latex]2\cdot\text{ cost }[/latex]
• Groceries and gas together for the week cost $250 means [latex]\text{ groceries }+\text{ gas }=250[/latex]
• The difference of 9 and a number becomes [latex]9-x[/latex]. Notice how 9 is first in the sentence and the expression

Let’s practice translating a few more English phrases into algebraic expressions.

Translate the table into algebraic expressions:

In this example video, we show how to translate more words into mathematical expressions.

The power of algebra is how it can help you model real situations in order to answer questions about them.

Here are some steps to translate problem situations into algebraic equations you can solve. Not every word problem fits perfectly into these steps, but they will help you get started.

• Read and understand the problem.
• Determine the constants and variables in the problem.
• Translate words into algebraic expressions and equations.
• Write an equation to represent the problem.
• Solve the equation.
• Check and interpret your answer. Sometimes writing a sentence helps.

Twenty-eight less than five times a certain number is 232. What is the number?

Following the steps provided:

• Read and understand: we are looking for a number.
• Constants and variables: 28 and 232 are constants, “a certain number” is our variable because we don’t know its value, and we are asked to find it. We will call it x.
• Translate:  five times a certain number translates to [latex]5x[/latex] Twenty-eight less than five times a certain number translates to [latex]5x-28[/latex] because subtraction is built backward. is 232 translates to [latex]=232[/latex] because “is” is associated with equals.
• Write an equation:  [latex]5x-28=232[/latex]

[latex]\begin{array}{r}5x-28=232\\5x=260\\x=52\,\,\,\end{array}[/latex]

[latex]\begin{array}{r}5\left(52\right)-28=232\\5\left(52\right)=260\\260=260\end{array}[/latex].

In the video that follows, we show another example of how to translate a sentence into a mathematical expression using a problem solving method.

Another type of number problem involves consecutive numbers. Consecutive numbers are numbers that come one after the other, such as 3, 4, 5. If we are looking for several consecutive numbers it is important to first identify what they look like with variables before we set up the equation.

For example, let’s say I want to know the next consecutive integer after 4. In mathematical terms, we would add 1 to 4 to get 5. We can generalize this idea as follows: the consecutive integer of any number, x , is [latex]x+1[/latex]. If we continue this pattern we can define any number of consecutive integers from any starting point. The following table shows how to describe four consecutive integers using algebraic notation.

We apply the idea of consecutive integers to solving a word problem in the following example.

The sum of three consecutive integers is 93. What are the integers?

• Read and understand:  We are looking for three numbers, and we know they are consecutive integers.
• Constants and Variables:  93 is a constant. The first integer we will call x . Second: [latex]x+1[/latex] Third: [latex]x+2[/latex]
• Translate:  The sum of three consecutive integers translates to [latex]x+\left(x+1\right)+\left(x+2\right)[/latex], based on how we defined the first, second, and third integers. Notice how we placed parentheses around the second and third integers. This is just to make each integer more distinct. is 93 translates to [latex]=93[/latex] because is is associated with equals.
• Write an equation:  [latex]x+\left(x+1\right)+\left(x+2\right)=93[/latex]

[latex]x+x+1+x+2=93[/latex]

Combine like terms, simplify, and solve.

[latex]\begin{array}{r}x+x+1+x+2=93\\3x+3 = 93\\\underline{-3\,\,\,\,\,-3}\\3x=90\\\frac{3x}{3}=\frac{90}{3}\\x=30\end{array}[/latex]

• Check and Interpret: Okay, we have found a value for x . We were asked to find the value of three consecutive integers, so we need to do a couple more steps. Remember how we defined our variables: The first integer we will call [latex]x[/latex], [latex]x=30[/latex] Second: [latex]x+1[/latex] so [latex]30+1=31[/latex] Third: [latex]x+2[/latex] so [latex]30+2=32[/latex] The three consecutive integers whose sum is [latex]93[/latex] are [latex]30\text{, }31\text{, and }32[/latex]

• Writing Algebraic Expressions. Authored by : James Sousa (Mathispower4u.com) for Lumen Learning. Located at : https://youtu.be/uD_V5t-6Kzs . License : CC BY: Attribution
• Write and Solve a Linear Equations to Solve a Number Problem (1). Authored by : James Sousa (Mathispower4u.com) for Lumen Learning. Located at : https://youtu.be/izIIqOztUyI . License : CC BY: Attribution
• Write and Solve a Linear Equations to Solve a Number Problem (Consecutive Integers). Authored by : James Sousa (Mathispower4u.com) for Lumen Learning. Located at : https://youtu.be/S5HZy3jKodg . License : CC BY: Attribution

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Adapting Math Word Problems for ELLs

To make word problems less confusing, especially for English language learners, change the language, not the math. Here are some ideas.

All students have a right to rigorous and challenging math classes, and word problems are a ubiquitous part of elementary and middle school math. Complex language structures or overly challenging vocabulary, however, can sometimes create barriers for students that impede access to a rigorous and challenging math curriculum. This is particularly true for English language learners (ELLs).

As teachers, we strive to cultivate mathematical reasoning and help students apply math to real-world contexts. When designing instruction for our English language learners, we have to ensure that they are afforded access to rich math tasks but also attend to the unique challenges of students working to acquire an understanding of the language. Fortunately, by attending to our vocabulary choices and sentence structure, we can adapt word problems and ensure that all students have access to rich mathematical content.

Certain linguistic features commonly found in middle school math classes are especially  problematic. Passive voice, complex sentences, and long noun phrases or clauses can be very difficult for all learners, but especially multilingual students developing English proficiency. Unfamiliar vocabulary, novel context, and poorly worded or vague questions can also create barriers to understanding. Small changes that simplify language, however, can significantly improve accessibility and ensure that more students can tackle rich math tasks.

Adapting the Math Language

Use the active voice: The passive voice can obscure what is actually happening in a word problem. Use the active voice to show people engaging with the world. For instance, rather than “The ball was thrown by the girl,” revise the sentence structure to “The girl threw the ball.”

Separate complex sentences: Break up long, convoluted, and meandering sentences to express key ideas. Consider the difference between “A hot dog costs $3.75 and a side salad costs $1.65. If a group of 5 students ordered 6 hot dogs and 4 side salads, and they left an 18% tip, how much did they pay in total, including the tip?” and the revised problem, “A group of friends ordered 6 cheeseburgers at $6.50 each and 4 side salads at $1.65 each. They left an 18% tip on the total bill. How much did they pay in total, including the tip?”

Both versions require the same mathematical understanding, but the language of the second is clearer and more accessible.

Simplify verb tense: Lean toward simple present tense. “The maintenance crew repairs the AC unit” rather than “has been repairing.”

Center people in the problem: Humanize problems with people rather than impersonal subjects. “85% of parents supported the schedule,” not “85% of the votes supported....”

Use familiar vocabulary: Swap challenging terminology for more recognizable vocabulary. “The school is hosting a fundraiser by selling concessions during the basketball tournament. If they sold 322 hamburgers at $3 each and 211 hot dogs at $2 each, what was the total revenue from the concession stand sales?”

Here’s a suggested alternative: “The school wants to raise money by selling food at a basketball game. They sold 322 hamburgers for $3 each and 211 hot dogs for $2 each. How much did the school make from selling the food?” Of course, some students will require additional supports, such as pictures and labels for key vocabulary found in word problems.

Shorten clauses: Trim unnecessary clauses. Instead of “The math tutor, who has taught for 10 years, helps students,” use “The math tutor helps students. She taught for 10 years.”

Replace obscure questions: Be sure to look for vague questions that distract from the math and substitute clear, direct questions. Change “What was the resulting amount after the chef used 16½ cups of milk?” to “The chef used 16½ cups of milk to make ice cream. Calculate how much ice cream the chef made yesterday.” Is something missing here?

Consider the big idea: Notice that in the previous example, students do not have enough information to solve the problem. When adapting math word problems for English language learners, revise the construction of your questions to clarify the task at hand, but also be mindful to simultaneously help students to think like mathematicians. To paraphrase what math education innovator Dan Meyer notes in his TED Talk on math instruction , real-world problems do not contain a simple list of all the required information.

As you adapt math instruction for English language learners, be sure to design rich experiences and help them to develop a mathematical mindset. What additional information do I need to solve this problem? What can I do to find the missing information? English language learners need accessible English, but they also need experiences that help them develop habits of inquiry, problem-solving, and self-efficacy.

The key is to adapt language without watering down rich mathematical thinking and problem-solving. Be sure to maintain high expectations while providing appropriate linguistic support. With slight modifications to ensure comprehensible and accessible language, your English language learners can tackle the same meaningful math as their peers.

Equity in math education means meeting each student where they are and helping them reach meaningful goals. Adjusting language is one path toward creating a math community that works for everyone.

Remember, context matters: Real-world contexts allow students to see math as a meaningful tool, rather than an abstract set of rules. However, take care not to introduce obscure, unfamiliar contexts that overwhelm ELLs with new vocabulary. Similarly, jumping between many different contexts in short succession can impede understanding.

When selecting contexts for word problems and examples, opt for familiar situations from students’ everyday lives that clearly illuminate the mathematical concepts. Additionally, aim to consistently revisit and reinforce the same contexts when teaching specific concepts, math models, or problem types. Repeated exposure across similar situations allows ELLs to digest both the linguistic and mathematical nuances. As comfort builds, you can broaden into new contexts, always taking care to explain unfamiliar vocabulary or scenarios that are essential to the problem.

The goal is to have students see math as meaningful while preventing contexts from distracting from the essential mathematical reasoning. Familiar, consistent contextualization keeps the focus on math concepts and problem-solving strategies.

The Power of Mathematical Models and Manipulatives

In addition to thoughtful verbal and written language adaptations, mathematical models and manipulatives provide critical visual and tactile scaffolds that support deeper understanding and reasoning for English language learners. Charts, ratio tables, coordinate planes, fraction models, graphs, algebra tiles , base-ten blocks, and more make concepts concrete while mitigating vocabulary barriers.

Leveraging models and manipulatives moves learning toward mathematical action. Students demonstrate conceptual connections nonverbally, allowing alternative pathways to develop understandings. All students access deeper thinking as teachers elevate mathematical visualization alongside precision in academic language.

When planning for math instruction and adapting for our multilingual learners, I’ve found these resources to be particularly helpful:

• Teaching Math to Multilingual Students, Grades K–8: Positioning English Learners for Success ,
• “ Mathematical mindsets: Unleashing students’ potential through creative math, inspiring messages and innovative teaching ,” and
• Math Workshop: Five Steps to Implementing Guided Math, Learning Stations, Reflection, and More .

Ultimately, we want students to develop a deep conceptual understanding of mathematics and to grow their English language proficiency. Slight adaptations to language, the use of familiar real-world contexts, and deliberately incorporating mathematical models and manipulatives can help students to access the math curriculum and to acquire English.

We’d like to know—what strategies have you successfully used to help improve math accessibility for ELL students? Please comment and share.

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Maneuvering the Middle

Student-Centered Math Lessons

3 Types of Word Problems to Teach

Problem solving is a multifaceted process! While I’ve written about Math Problem Solving Strategies and How to Teach Word Problems and Problem Solving , there is still so much more to cover.

Noelle presented an amazing math training this summer on Practical Problem Solving Strategies. I was truly amazed at just how much I learned. I will be breaking down the training into 3 blog posts over the course of this month, so if you missed the training, be sure to check back here for more updates.

If you want to learn more, check out this book, Mathematize It! , that covers the topic of teaching how to solve word problems in much more detail.

Today we are going to talk about the 3 types or categories of word problems that you teach and your students may face: action, relationship, and comparison. The purpose of identifying word problem types is to force students to slow down and analyze what is happening in the word problem before jumping to computation.

You can also grab our problem solving posters freebie below!

Action Word Problems

Here is an example of an action word problem: 

How do we know that this is an action? Ask yourself:

• Did something occur?
• Was there some kind of change?

If yes, the word problem likely falls into the action category.

Relationship Word Problems

Here is an example of a relationship word problem: 

How do we know this is a relationship? Ask yourself:

• Are parts being described or referred to in relation to a whole? 
• Is a whole being described or referred to in relation to a part?

If yes, the word problem is a relationship. Here we can see the parts of the marching band relate to the total number of marching band members. 

Comparison Word Problems

And lastly, here is an example of a comparison word problem: 

How do we know this is a comparison?

Ask yourself:

• Is something in the word problem being described in comparison to something else?

In this word problem, we can see that the cost of popcorn is being described by the cost of the candy. 

Why is this helpful to know?

Why do students need to know this? Well, by observing and “making meaning” from the words and scenarios they are processing, students are less likely to rush to determine a path to the solution. 

Does this sound familiar? Students quickly perform some operations with the values given. In this first step of the problem-solving process, we want to take the focus off the values and direct students to notice what is being described in the problem.

The goal is not for them to be able to identify and put the word problem into the correct category. We simply want students to notice what is happening, and over time they will start to recognize patterns in word problems. 

Next week, I will dive deeper into how we take these word problem types and use them to help students with the first part of the problem solving process: restating the problem .

Grab our problem solving posters freebie!

In the meantime, can you identify the category these sample problems belong in?

• Ricky buys a package of chicken to use throughout the week. On Monday, he uses 28 ounces to make chicken salad for lunch. On Thursday, he grills 53 ounces of chicken for dinner. If Ricky determines he has 37 ounces of chicken remaining to cook, how many ounces of chicken did he buy at the beginning of the week?
• Gavin has two pet turtles, a red-eared slider and a map turtle. His red-eared slider weighs 2,680 grams and his map turtle weighs 670 grams. How many times bigger is the red-eared slider than the map turtle?
• Ivory created a paper chain of her school colors, blue, green, and white, as a decoration for a pep rally. The blue section measured 5.5  feet long, the green section measured 4.25  feet long, and the white section measured 3.75  feet long. What is the total length of the paper chain?
• A king-sized chocolate bar has a mass of 2.6 ounces. A regular-sized chocolate bar has a mass of 1.55 ounces. How many more ounces is the king-sized chocolate bar than the regular-sized chocolate bar?
• A nature center has a stocked pond with an automatic fish feeder. The fish feeder has 70.5 pounds of fish food and releases food into the pond twice a day. If the feeder releases 2.6 pounds of food in the morning and 1.2 pounds of food in the evening, how many pounds of food are remaining in the feeder at the end of the day? 
• The San Francisco Bay Area is hosting a triathlon, a race consisting of swimming, biking, and running. The athletes will swim for 0.75  miles and bike for 15.5  miles. If the total distance of the triathlon is 20.5  miles, how many miles is the running portion of the race?

Problem Solving Posters (Represent It! Bulletin Board)

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What Is Problem-Solving Therapy?

Arlin Cuncic, MA, is the author of The Anxiety Workbook and founder of the website About Social Anxiety. She has a Master's degree in clinical psychology.

Daniel B. Block, MD, is an award-winning, board-certified psychiatrist who operates a private practice in Pennsylvania.

Verywell / Madelyn Goodnight

Problem-Solving Therapy Techniques

How effective is problem-solving therapy, things to consider, how to get started.

Problem-solving therapy is a brief intervention that provides people with the tools they need to identify and solve problems that arise from big and small life stressors. It aims to improve your overall quality of life and reduce the negative impact of psychological and physical illness.

Problem-solving therapy can be used to treat depression , among other conditions. It can be administered by a doctor or mental health professional and may be combined with other treatment approaches.

At a Glance

Problem-solving therapy is a short-term treatment used to help people who are experiencing depression, stress, PTSD, self-harm, suicidal ideation, and other mental health problems develop the tools they need to deal with challenges. This approach teaches people to identify problems, generate solutions, and implement those solutions. Let's take a closer look at how problem-solving therapy can help people be more resilient and adaptive in the face of stress.

Problem-solving therapy is based on a model that takes into account the importance of real-life problem-solving. In other words, the key to managing the impact of stressful life events is to know how to address issues as they arise. Problem-solving therapy is very practical in its approach and is only concerned with the present, rather than delving into your past.

This form of therapy can take place one-on-one or in a group format and may be offered in person or online via telehealth . Sessions can be anywhere from 30 minutes to two hours long. 

Key Components

There are two major components that make up the problem-solving therapy framework:

• Applying a positive problem-solving orientation to your life
• Using problem-solving skills

A positive problem-solving orientation means viewing things in an optimistic light, embracing self-efficacy , and accepting the idea that problems are a normal part of life. Problem-solving skills are behaviors that you can rely on to help you navigate conflict, even during times of stress. This includes skills like:

• Knowing how to identify a problem
• Defining the problem in a helpful way
• Trying to understand the problem more deeply
• Setting goals related to the problem
• Generating alternative, creative solutions to the problem
• Choosing the best course of action
• Implementing the choice you have made
• Evaluating the outcome to determine next steps

Problem-solving therapy is all about training you to become adaptive in your life so that you will start to see problems as challenges to be solved instead of insurmountable obstacles. It also means that you will recognize the action that is required to engage in effective problem-solving techniques.

Planful Problem-Solving

One problem-solving technique, called planful problem-solving, involves following a series of steps to fix issues in a healthy, constructive way:

• Problem definition and formulation : This step involves identifying the real-life problem that needs to be solved and formulating it in a way that allows you to generate potential solutions.
• Generation of alternative solutions : This stage involves coming up with various potential solutions to the problem at hand. The goal in this step is to brainstorm options to creatively address the life stressor in ways that you may not have previously considered.
• Decision-making strategies : This stage involves discussing different strategies for making decisions as well as identifying obstacles that may get in the way of solving the problem at hand.
• Solution implementation and verification : This stage involves implementing a chosen solution and then verifying whether it was effective in addressing the problem.

Other Techniques

Other techniques your therapist may go over include:

• Problem-solving multitasking , which helps you learn to think clearly and solve problems effectively even during times of stress
• Stop, slow down, think, and act (SSTA) , which is meant to encourage you to become more emotionally mindful when faced with conflict
• Healthy thinking and imagery , which teaches you how to embrace more positive self-talk while problem-solving

What Problem-Solving Therapy Can Help With

Problem-solving therapy addresses life stress issues and focuses on helping you find solutions to concrete issues. This approach can be applied to problems associated with various psychological and physiological symptoms.

Mental Health Issues

Problem-solving therapy may help address mental health issues, like:

• Chronic stress due to accumulating minor issues
• Complications associated with traumatic brain injury (TBI)
• Emotional distress
• Post-traumatic stress disorder (PTSD)
• Problems associated with a chronic disease like cancer, heart disease, or diabetes
• Self-harm and feelings of hopelessness
• Substance use
• Suicidal ideation

Specific Life Challenges

This form of therapy is also helpful for dealing with specific life problems, such as:

• Death of a loved one
• Dissatisfaction at work
• Everyday life stressors
• Family problems
• Financial difficulties
• Relationship conflicts

Your doctor or mental healthcare professional will be able to advise whether problem-solving therapy could be helpful for your particular issue. In general, if you are struggling with specific, concrete problems that you are having trouble finding solutions for, problem-solving therapy could be helpful for you.

Benefits of Problem-Solving Therapy

The skills learned in problem-solving therapy can be helpful for managing all areas of your life. These can include:

• Being able to identify which stressors trigger your negative emotions (e.g., sadness, anger)
• Confidence that you can handle problems that you face
• Having a systematic approach on how to deal with life's problems
• Having a toolbox of strategies to solve the issues you face
• Increased confidence to find creative solutions
• Knowing how to identify which barriers will impede your progress
• Knowing how to manage emotions when they arise
• Reduced avoidance and increased action-taking
• The ability to accept life problems that can't be solved
• The ability to make effective decisions
• The development of patience (realizing that not all problems have a "quick fix")

Problem-solving therapy can help people feel more empowered to deal with the problems they face in their lives. Rather than feeling overwhelmed when stressors begin to take a toll, this therapy introduces new coping skills that can boost self-efficacy and resilience .

Other Types of Therapy

Other similar types of therapy include cognitive-behavioral therapy (CBT) and solution-focused brief therapy (SFBT) . While these therapies work to change thinking and behaviors, they work a bit differently. Both CBT and SFBT are less structured than problem-solving therapy and may focus on broader issues. CBT focuses on identifying and changing maladaptive thoughts, and SFBT works to help people look for solutions and build self-efficacy based on strengths.

This form of therapy was initially developed to help people combat stress through effective problem-solving, and it was later adapted to address clinical depression specifically. Today, much of the research on problem-solving therapy deals with its effectiveness in treating depression.

Problem-solving therapy has been shown to help depression in: 

• Older adults
• People coping with serious illnesses like cancer

Problem-solving therapy also appears to be effective as a brief treatment for depression, offering benefits in as little as six to eight sessions with a therapist or another healthcare professional. This may make it a good option for someone unable to commit to a lengthier treatment for depression.

Problem-solving therapy is not a good fit for everyone. It may not be effective at addressing issues that don't have clear solutions, like seeking meaning or purpose in life. Problem-solving therapy is also intended to treat specific problems, not general habits or thought patterns .

In general, it's also important to remember that problem-solving therapy is not a primary treatment for mental disorders. If you are living with the symptoms of a serious mental illness such as bipolar disorder or schizophrenia , you may need additional treatment with evidence-based approaches for your particular concern.

Problem-solving therapy is best aimed at someone who has a mental or physical issue that is being treated separately, but who also has life issues that go along with that problem that has yet to be addressed.

For example, it could help if you can't clean your house or pay your bills because of your depression, or if a cancer diagnosis is interfering with your quality of life.

Your doctor may be able to recommend therapists in your area who utilize this approach, or they may offer it themselves as part of their practice. You can also search for a problem-solving therapist with help from the American Psychological Association’s (APA) Society of Clinical Psychology .

If receiving problem-solving therapy from a doctor or mental healthcare professional is not an option for you, you could also consider implementing it as a self-help strategy using a workbook designed to help you learn problem-solving skills on your own.

During your first session, your therapist may spend some time explaining their process and approach. They may ask you to identify the problem you’re currently facing, and they’ll likely discuss your goals for therapy .

Keep In Mind

Problem-solving therapy may be a short-term intervention that's focused on solving a specific issue in your life. If you need further help with something more pervasive, it can also become a longer-term treatment option.

Get Help Now

We've tried, tested, and written unbiased reviews of the best online therapy programs including Talkspace, BetterHelp, and ReGain. Find out which option is the best for you.

Shang P, Cao X, You S, Feng X, Li N, Jia Y. Problem-solving therapy for major depressive disorders in older adults: an updated systematic review and meta-analysis of randomized controlled trials .  Aging Clin Exp Res . 2021;33(6):1465-1475. doi:10.1007/s40520-020-01672-3

Cuijpers P, Wit L de, Kleiboer A, Karyotaki E, Ebert DD. Problem-solving therapy for adult depression: An updated meta-analysis . Eur Psychiatry . 2018;48(1):27-37. doi:10.1016/j.eurpsy.2017.11.006

Nezu AM, Nezu CM, D'Zurilla TJ. Problem-Solving Therapy: A Treatment Manual . New York; 2013. doi:10.1891/9780826109415.0001

Owens D, Wright-Hughes A, Graham L, et al. Problem-solving therapy rather than treatment as usual for adults after self-harm: a pragmatic, feasibility, randomised controlled trial (the MIDSHIPS trial) .  Pilot Feasibility Stud . 2020;6:119. doi:10.1186/s40814-020-00668-0

Sorsdahl K, Stein DJ, Corrigall J, et al. The efficacy of a blended motivational interviewing and problem solving therapy intervention to reduce substance use among patients presenting for emergency services in South Africa: A randomized controlled trial . Subst Abuse Treat Prev Policy . 2015;10(1):46. doi:doi.org/10.1186/s13011-015-0042-1

Margolis SA, Osborne P, Gonzalez JS. Problem solving . In: Gellman MD, ed. Encyclopedia of Behavioral Medicine . Springer International Publishing; 2020:1745-1747. doi:10.1007/978-3-030-39903-0_208

Kirkham JG, Choi N, Seitz DP. Meta-analysis of problem solving therapy for the treatment of major depressive disorder in older adults . Int J Geriatr Psychiatry . 2016;31(5):526-535. doi:10.1002/gps.4358

Garand L, Rinaldo DE, Alberth MM, et al. Effects of problem solving therapy on mental health outcomes in family caregivers of persons with a new diagnosis of mild cognitive impairment or early dementia: A randomized controlled trial . Am J Geriatr Psychiatry . 2014;22(8):771-781. doi:10.1016/j.jagp.2013.07.007

Noyes K, Zapf AL, Depner RM, et al. Problem-solving skills training in adult cancer survivors: Bright IDEAS-AC pilot study .  Cancer Treat Res Commun . 2022;31:100552. doi:10.1016/j.ctarc.2022.100552

Albert SM, King J, Anderson S, et al. Depression agency-based collaborative: effect of problem-solving therapy on risk of common mental disorders in older adults with home care needs . The American Journal of Geriatric Psychiatry . 2019;27(6):619-624. doi:10.1016/j.jagp.2019.01.002

By Arlin Cuncic, MA Arlin Cuncic, MA, is the author of The Anxiety Workbook and founder of the website About Social Anxiety. She has a Master's degree in clinical psychology.

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Definition of problem

 (Entry 1 of 2)

Definition of problem  (Entry 2 of 2)

mystery , problem , enigma , riddle , puzzle mean something which baffles or perplexes.

mystery applies to what cannot be fully understood by reason or less strictly to whatever resists or defies explanation.

problem applies to a question or difficulty calling for a solution or causing concern.

enigma applies to utterance or behavior that is very difficult to interpret.

riddle suggests an enigma or problem involving paradox or apparent contradiction.

puzzle applies to an enigma or problem that challenges ingenuity for its solution.

Examples of problem in a Sentence

These examples are programmatically compiled from various online sources to illustrate current usage of the word 'problem.' Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Send us feedback about these examples.

Word History

Middle English probleme , from Latin problema , from Greek problēma , literally, obstacle, from proballein to throw forward, from pro- forward + ballein to throw — more at pro- , devil

14th century, in the meaning defined at sense 1a

1894, in the meaning defined at sense 1

Phrases Containing problem

• attitude problem
• drinking problem
• drink problem
• first world problem
• have a problem with
• not a problem
• not someone's problem
• problem - solving
• therein lies the problem
• what's someone's problem
• word problem

Articles Related to problem

11 "Problems" Inspired by Animal Names

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Dictionary Entries Near problem

problematic

Cite this Entry

“Problem.” Merriam-Webster.com Dictionary , Merriam-Webster, https://www.merriam-webster.com/dictionary/problem. Accessed 23 Apr. 2024.

Kids Definition

Kids definition of problem.

Kids Definition of problem  (Entry 2 of 2)

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Nglish: Translation of problem for Spanish Speakers

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Britannica.com: Encyclopedia article about problem

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Definition of problem noun from the Oxford Advanced Learner's Dictionary

• big/serious/major problems
• She has a lot of health problems .
• financial/social/technical problems
• Let me know if you have any problems .
• The government must address the problem of child poverty.
• We cannot tackle this problem effectively on our own.
• We are dealing with a serious problem here.
• Money isn't going to solve the problem .
• (especially North American English) to fix a problem
• If he chooses Mary it's bound to cause problems .
• to pose/create a problem
• The problem first arose in 2018.
• problem with something There is a problem with this argument.
• problem of something the problem of drug abuse
• problem of doing something Most students face the problem of funding themselves while they are studying.
• problem for somebody Unemployment is a very real problem for graduates now.
• It’s a nice table! The only problem is (that) it’s too big for our room.
• Part of the problem is the shape of the room.
• Stop worrying about their marriage—it isn't your problem.
• There's no history of heart problems (= disease connected with the heart) in our family.
• the magazine’s problem page (= containing letters about readers’ problems and advice about how to solve them)
• All the anti-depressant does is mask the problem.
• Depression is a natural feeling if your problems seem intractable.
• For years I've tried to overlook this problem.
• Fortunately, it's easy to avoid any potential problems.
• Framing the problem is an important step.
• She believes she may have found a solution to the problem.
• He developed a drinking problem.
• She doesn't really see the problem.
• He doesn't seem to understand my problem.
• She had to undergo surgery to cure the problem with her knee.
• He has been faced with all manner of problems in his new job.
• Her new job had taken her mind off her family problems for a while.
• I didn't imagine there would be a problem about getting tickets.
• I don't anticipate any future problems in that regard.
• I forgot my problems for a moment.
• I'm glad you finally admitted your problem.
• If the problem persists you should see a doctor.
• Inadequate resources pose a problem for all members of staff.
• Most people can see the ethical problem with accepting such an offer.
• No one ever asked why or how the problem originated.
• Our greatest problem is the lack of funds.
• She had serious substance abuse problems with both cocaine and heroin.
• She raised the problem of falling sales at the last meeting.
• Success brings its own problems.
• Systemic security problems have been identified.
• The accident poses a terrible problem for the family.
• The basic problem remains the lack of available housing.
• The plan has been fraught with problems from the start.
• The problem lies in the lack of communication between managers and staff.
• Therein lies the problem.
• The rail strike is a problem for all commuters.
• The role of the sun in climate change is still a big unsolved problem.
• The traffic in illegal drugs is a global problem.
• These symptoms may indicate a serious problem.
• They created a task force to study this problem.
• They sold their car to ease their financial problems.
• This illustrates another potential problem.
• This underscores the biggest problem with electronic voting.
• We need to get to the root of the problem before we can solve it.
• We're faced with a whole host of new problems.
• This is one of the great problems of cosmology: where did the overall structure of the universe come from?
• present (somebody with)
• behaviour/​behavior
• problem about
• problem for
• an approach to a problem
• the crux of the problem
• the heart of the problem

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• mathematical problems
• to find the answer to the problem
• The teacher set us 50 problems to do.
• I have five problems to do for homework.
• trigonometry
• complicated
• find the answer to
• I have no problem with you working at home tomorrow.
• (informal) We are going to do this my way. Do you have a problem with that? (= showing that you are impatient with the person that you are speaking to)
• Do you have a problem with her?
• If they can't afford to go, that's not my problem.
• ‘Can I pay by credit card?’ ‘Yes, no problem.’
• ‘Thanks for the ride.’ ‘No problem.’
• ‘My parents will be furious!’ ‘That’s your problem.’
• What's your problem?—I only asked if you could help me for ten minutes.

Other results

• a chicken-and-egg situation, problem, etc.

Nearby words