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35 Math Questions For 5th Graders: Answers With Worked Examples

Anantha Anilkumar

In 5th grade math, the toughest questions are often the reasoning questions. In this article, we’ve put together a collection of math questions for 5th graders, organized by the different kinds of reasoning questions that students may encounter on standardized tests and beyond.

Why Focus On Math Reasoning Questions?

Most fifth graders find reasoning questions to be the most difficult. Unsurprisingly, we teach thousands of students in the weeks leading up to standardized tests. Teaching them math reasoning skills at the elementary level is a big part of what we do here at Third Space Learning.

We even recently made the decision to restructure our elementary lessons to introduce math reasoning questions earlier in their learning journey as the difficulty level was just too high at the end of the lesson. We  definitely feel fifth grade teachers’ pain!

Whatever level your students are currently achieving in math, math reasoning questions will appear from elementary to high school, so it is an essential skill for the future.

If you find you have children in your class with a lot more catching up to do than others, then we may be able to support them with some personalized one-on-one tutoring if you get in touch.

Reasoning Questions for 5th Grade

Help your 5th grade students to feel confident with different types of reasoning questions.

35 Math Questions For 5th Graders

There are 7 types of math reasoning questions that fifth graders are likely to encounter:

For each of these types we’ll examine an example problem, looking at the question, the correct answer, and how to go about answering this problem.

We’ll also look at further examples of each type of math reasoning question and answer, again with worked examples and an explanation of how to answer each.

Our aim is to provide you with a sample of the types of math reasoning questions and how to teach the reasoning and problem solving skills they’ll need to solve them.

For more word problems like this, check out our collection of 2-step and multi-step word problems . For advice on how to teach children to solve problems like this, check out these math problem solving strategies.

Math Question Type 1: Single step word problems

The simplest type of reasoning question students are likely to encounter, single step problems are exactly that: students are asked to interpret a written question and carry out a single mathematical step to solve it.

Take a look at the question below:

Reasoning Question 1

Answer: $0.65

A relatively easy question to interpret–the first step will be to rewrite the amounts given so that they can properly line up the place values in order to solve. From here the simple mathematical step is subtraction i.e. $2.00 – $1.35 = 0.65.

The most crucial skill for grade schoolers in this question is a solid understanding of money as relating to place value. If this understanding is present, the mathematical step itself is quite easy.

Below are several more examples:

Reasoning Question 2

Answer : 7 hours 24 minutes

Students need to understand that one hour is equal to 60 minutes. From here the single mathematical step is division: 444/60, to find a whole number answer with a remainder.

Reasoning Question 3

Answer : 48 cm 3

Students must multiply length by width by height, using the amounts provided by the question.

Reasoning Question 4

Answer : 1,488 cubic cm

A simple enough calculation (multiplying) if students are aware that the volume of a rectangular prism can be found by multiplying the area of the base by the height.

Reasoning Question 5

Answer : 7,590

A single, relatively simple rounding problem – students should recognize that ’94’ is the place they should focus on for this problem.

Math Question Type 2: Multiple step worded problems

A more complex version of the single step word problem, multi-step problems require students to interpret a written problem, but solving it then requires the use of two or three math skills.

For example, consider this question below:

Answer: $1.85

This question encompasses three different math skills: multiplying (and dividing) decimals, addition and subtraction. Students can choose to work out the multiplication or division first, but must complete both before moving on.

Once these values have been worked out the next steps are relatively simple – adding the two values together, and subtracting the total from $5.

Multi-step problems are particularly valuable to include in practice tests because they require children to apply their knowledge of math language and their reasoning skills several times across the course of a single question, usually in slightly different contexts.

More examples:

Answer : $5,520

There are two steps to this problem, but both are multiplication. The first is to work out how much money is made per day – 92 x $15. This product is then multiplied by 4 – the number of days – to get to the answer.

Answer : 1360 miles

Another two step problem. The first step is to work out 4 of 3,400 miles. Then divide this by 10 to solve for 4/10 of 3,400.

Answer : $153

There are four steps involved in solving this problem: multiplication (doubling $51), division (dividing $51 in half), multiplication again (doubling half of $51–which some students may recognize those last two steps were unnecessary as that brings us back to $51), and addition (putting the two costs together).

Given the number of steps involved it can be easy for students to make arithmetic mistakes.

Answer : 11.45 lbs

A two-step problem again: multiplying 3.45 lbs by 4, then subtracting 2.35 lbs from the total. 

Math Question Type 3: Problems involving measurements

As their name suggests, these questions ask students to solve a problem that includes one or more units of measurement.

Answer: 40 washes

This is a two step problem; students must first be able to read and convert kilograms to grams (and therefore know the relationship and conversions between the two units- 1,000 grams to 1 kilogram), multiply 2.6 by 1,000 which equals 2,600, then divide 2,600 by 65. The quotient is the number of washes possible.

Further examples:

Answer : 50g

A relatively simple division problem, relying on students having knowledge that 200g is one fifth of a kilogram.

Answer : 5.12 miles

Another three step problem, and this requires students to subtract and divide decimals – subtracting 12.63 miles from the total amount, taking the difference, 13.91, and subtracting 3.67 miles, and then dividing that difference, 10.24, in half to obtain the distance the other two friends ran.

Answer : 84 inches/7 foot

To find 8 feet in inches, students must multiply 8 by 12. This gives the answer 96 inches. Students must then divide 96 by 40 to find the height of one box: 2.4 inches. Multiply 2.4 by 5 and minus this from the original 96 inch tower. 

Interesting to note that the units for the answer may or may not be specified – an answer given in inches or feet will be accepted, however sometimes the unit will be specified in the answer box. This is why we encourage students to keep an eye on whether units are provided in the answer box.

Answer : 0.05 lbs

As with the running question there are three steps involved to solve this problem: subtracting the heaviest car from the total amount (3.85 – 1), figuring out the weight of the remaining three cars (2.85/3) and subtracting 0.95 from 1 to get the remaining amount of 0.05 lbs.

Question Type 4: Problems involving drawing

Problems involving drawing require students to construct an accurate drawing by following a set of instructions, or through reflection, translation, or scaling.  

Answer: Any pair of lines that make a square of 4 units, a rectangle of 6 units, and a square of 25 units.

This question is considerably more complex than it appears, and incorporates aspects of multiplication as well as spatial awareness. One potential solution is to work out the area of the card (35), then work out the possible square numbers that will fit in (understanding that square numbers produce a square when drawn out as on a grid), and which then leave a single rectangle behind.

A lot of work for a single point!

Some further examples:

Answer : Any quadrilateral made by joining the dots that has 3 acute angles e.g. an arrowhead shape.

Answer : An accurately drawn angle.

This question demands students to have an understanding of and ability to accurately use a protractor. Often, a mark scheme allows some room for error – “between 34 and 36 degrees” is acceptable.

As with the question above, a small amount of room for error is given as it acceptable to be between 139 and 141 degrees.

Answer : Points drawn at (2,1), (5,1) and (2,4).

Math Question Type 5: Explanation questions

These problems ask children to explain a mathematical statement or error.

As an example:

Answer: If the distance from P to R is 800 yards and the distance from P to Q is (Q -> R x 4), it must be 4/5 of 800 = 640 yards. Therefore Olivia is wrong.

More than most problems, this type requires students to actively demonstrate their reasoning skills as well as their mathematical ones. Here students must articulate either in words or (where possible) numerically that they understand that Q to R is 1/5 of the total, that therefore P to Q is 4/5 of the total distance, and then calculate what this is via division and multiplication.

Further examples below:

Answer : No, 2/100 is the same as 2 divided by 100, which equals 0.02.

Answer : No; multiplication and division have the same priority in the order of operations, so in a problem like 40 x 6 ÷2, you would carry out the multiplication first as it occurs first.

Answer : No

Any explanation that provides a counter-example is acceptable e.g. “Not if the number is 1”, “Not for 0,” “Not if the number is less than 1” etc.

Answer : Any answer that refers to the fact that there is a 5 in the hundredths place, AND a 9 in the thousandths place, so that the number has to be rounded up as far as the ten-thousands place.

Math Question Type 6: Sequence questions

Another relatively simple kind of reasoning question, sequence problems involve students completing mathematical sequences.

Consider this example:

Answer: 35 , 42, 49, 56 , 63, 70

The question’s instructions point clearly to the solution: figure out what the increase between numbers is, then apply this via addition or subtraction to find the missing numbers.

Higher achieving students might quickly pick up that this is in fact the 7 times table and rely on their knowledge of multiplication facts to obtain the answer – this should be encouraged so long as they then check their answer in the normal method to ensure they haven’t made a mistake.

Answer(s) : 8/8 or 1 and 2 1/8 (OR 17/8)

Both answers must be correct to receive the point. Students must recognize that 3/4 is the same as 6/8, so the sequence is increasing in 3/8 each time. The first number is 3/8 less than 1 3/8 and the final number is 3/8 greater than 1 3/4. They then must be able to add and subtract fractions to obtain the answers.

Answer(s) : 4.2 and 7

Answer(s) : 128, 135 and 156.

Answer(s) : 0 and 24

This number line question can be a little tricky; students need to figure out that the marks on the line represent increments of 3, and count backwards and forwards in 3’s to obtain the missing numbers.

Math Question Type 7: Ordering questions

A slightly more complex variation of the sequence question, ordering problems require students to put a set of numbers, fractions or measures in the correct order.

A good example is this fifth grade math question below:

Answer: 3/5, 3/4, 6/5

This question throws a wrench in things by including an improper fraction, but this is hardly unusual. These sorts of questions are just the place to find other ‘curveballs’ such as equivalent fractions, mixed numbers, decimal numbers, and fractions all mixed into one problem.

A good knowledge of the fundamentals of fractions is essential here: students must understand what a larger denominator means, and the significance of a fraction with a numerator greater than its denominator.

Answer : D,C,A,B

Encourage students to convert all the fractions to one denominator value to make ordering easier.

Answer : (descending down the ‘Place’ column) 3rd, 5th, 2nd, 4th

Students could use many strategies to solve this problem. The most time consuming would be to rewrite all the fractions with a common denominator. More efficient strategies would include reasoning about the size of the fractions in comparison to ½ or 1. For instance, a student may notice that ⅜ is the only fraction less than ½, putting Ben in 5th place. 4/8 is exactly ½ whereas the others are greater than ½, putting Michael in 4th place. Then the student may recognize that 10/12 is closer to 1 than ¾, completing the rest of the table.

Answer : C, B, D, A

Answer : D, A, C, B

7 Top Tips For Answering 5th Grade Math Reasoning Questions

Now that we’ve covered how to answer some specific types of reasoning questions, here are some more generic tips for success in standardized tests. They may not all be applicable to every single question, but will apply to at least two, usually more.

• Get students in the habit of identifying what information they’re given in a question, and what they need to know to solve the problem. This helps them start to form the steps needed to find the solution.
• Ask students to ‘spot the math’ in a question – which operations or skills do they actually need to use to solve the problem? This is useful even for arithmetic questions – it’s no surprise how often children can misread a question.
• Check the units! Especially in questions involving multiple measures, it can be easy to give the answer in the wrong one. The answer box might give a specific unit of measurement, so students should work to give their answer in that unit.
• In a similar vein, remind students to convert different units of measurement in a question into the same unit to make calculations easier e.g. lbs to oz.
• Encourage numerical answers where possible. Even in explanation questions demonstrating the mathematical equation is a better explanation than trying to write it out.
• The bar model can be a useful way of visualizing many different types of questions, and might make it easier to spot the ‘steps’ needed for the solution.
• Check your work! Even if the work is ultimately irrelevant to the question, you can lose points if it is wrong.

Do you have students who need extra support in math? Give your students more opportunities to consolidate learning and practice skills through personalized math tutoring with their own dedicated online math tutor. Each student receives differentiated instruction designed to close their individual learning gaps, and scaffolded learning ensures every student learns at the right pace. Lessons are aligned with your state’s standards and assessments, plus you’ll receive regular reports every step of the way. Personalized one-on-one math tutoring programs are available for: – 2nd grade tutoring – 3rd grade tutoring – 4th grade tutoring – 5th grade tutoring – 6th grade tutoring – 7th grade tutoring – 8th grade tutoring Why not learn more about how it works ?

The content in this article was originally written by Anantha Anilkumar at Third Space Learning and has since been revised and adapted for US schools by elementary math teacher Katie Keeton.

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35 math problems for 5th graders

Here are 35 fifth-grade math problems that will help your child stay on track!

Author Amber Watkins

Published September 13, 2023

• Key takeaways
• 5th-grade math word problems help students apply mathematical concepts to real-world scenarios.
• In fifth-grade math, it’s important to master fractions, decimals, and order of operations.
• Hard problems for 5th graders can be simplified by drawing a picture or using a method that makes them easier to solve.

Table of contents

• Word problems

Numbers & place value

• Multiplication

If this math page has 5 sections of math problems for 5th graders with an average of 7 questions in each section, can you guess how many problems there will be in all? That’s right, there will be a total of 35 math problems for 5th graders for us to practice. Without realizing it, you just solved one of our first 5th-grade math word problems . Excellent work! Together we will review fifth-grade math problems with decimals, fractions, order of operations, and rounding. We will even consider hard math problems for 5th graders, like multiplying using square models and number lines. Don’t worry about getting the answers right the first time, each section includes math problems for 5th graders with answers if you need a sneak peek. So grab a pad and pencil and let’s begin.

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Select a year group

• Kindergarten

Measurement and data

Sample questions, word problems for 5th graders.

Let’s begin by covering math word problems for 5th graders.

Mia’s water bottle can hold 24 ounces of water. She drinks two full water bottles each day. How many total cups of water does Mia drink each day? [Conversions]

The playground is made up of four rectangular lots that are each 10 ft by 7 ft. What is the total area of the playground? [Finding area]

 Josh lives 2.5 miles away from the park. Josh rides his bike to the park and back home four days a week. How many miles does Josh ride his bike each week? [Calculations]

Place value

In this section, we will cover math problems for 5th graders that use place values, word form to standard form, standard form to word form, and expanded form.

Which digit in the number 245 is in the hundreds place?

Which digit in the number 4,602 is in the tens place?

Which digit in the number 752 is in the ones place?

Word form to standard form

Standard form to expanded form.

4,000 + 300 + 2 = 4,302

600 + 50 + 4 = 654

20,000 + 2,000 + 300 + 60 + 5 = 22,365

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In this section, we will cover fifth-grade math problems that include comparing decimals and rounding decimals to the nearest tenth, hundredth, and thousandths place. Let’s get started.

8.9 and 8.900 are the same.

Remember if the number to the right is 5 or larger, you can borrow and become one digit larger. If the number to the right is between 0 and 4, you can’t borrow and the number remains the same.

In this section, we will review math problems for fifth graders that cover the topics of adding and subtracting two and three-digit numbers using transformation, division using area models, and the order of operations .

Adding and subtracting whole numbers by transformation

A large portion of fifth-grade math problems can be made easier to solve by transformation or changing numbers to make the problem simpler. Let’s practice adding and subtracting two and three-digit numbers by transformation.

How to add numbers using transformation?

When adding or subtracting numbers, look for ways to round to make the problem simpler. Don’t forget what you do to one number, you have to do the opposite to the other. This makes sure the problem stays balanced. Let’s see how this is done. What is 48 + 52? 48 + 2 = 50

52 – 2 = 50 

50 + 50 = 100.

It may be difficult to add 48 + 52 in your head, so we round 48 to 50 by adding 2. Since we added 2 to the first number, we have to make sure to subtract 2 from the second number. So now the problem is 50 plus 50, which is much easier to calculate! 

32 – 2 = 30 68 + 2 = 70 30 + 70 = 100 The answer is 100.

208 – 8 = 200 432 + 8 = 440 200 + 440 = 640 The answer is 640.

321- 1 = 320 199 + 1 = 200 320 – 200 = 120 120 + 2 = 122 The answer is 122

Division using area models

Don’t know what an area model is? See our area model guide to help with these problems.

Using an area model find the quotient of 365 ፥ 5 =

Using an area model find the quotient of 504 ፥ 6 =

Using the area model below, find the quotient of 872 ፥ 2 =

Order of operations

Many people remember the Order of Operations with the acronym PEMDAS- “Please Excuse My Dear Aunt Sally”, with each letter representing an operation: Parentheses, Exponents, Multiply or Divide, Add or Subtract. Solve the following equations using the order of operations.

Hard multiplication math problems

Some of the hardest math problems for fifth graders involve multiplying: multiplying using square models, multiplying fractions and whole numbers using expanded form, and multiplying fractions using number lines. Let’s practice a few of each!

Multiplying using square models

Multiplying using square models is a method to help students “see” multiplication problems in a simpler way.

Multiply 42 x 35 using the square model below.

Multiply 55 x 76 using the square model below.

Multiply 98 x 42 using the square model below.

Multiplying fractions and whole numbers using expanded form

Multiply ½ x 5 using expanded form.

Multiply ⅔ x 6 using expanded form.

Multiply ⅙ x 7 using expanded form.

Multiplying fractions using a number line

Multiply ½ x 4/6 by using a number line.

For more math practice for 5th graders , our app for math help provides 5th-grade math help in a way that makes math fun, rewards effort over being correct, and scaffolds learning. Plus, you’ll get access to a dashboard that displays your child’s participation and progression on math topics they struggle with. Check it out today!

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Word problem answer sheet

Mia drinks 6 cups of water each day. Explanation: There are 8 ounces in each cup. So 24 divided by 8 is equal to 3 cups each day.

280 square feet. Explanation: The area of one lot is 10 x 7 = 70 square feet. Take that area and times it by four, so 70 x 4 = 280 square feet.

Josh rides 20 miles on his bike each week. Explanation: Each day Josh rides 5 total miles: 2.5 miles to the park and 2.5 miles back home. If we multiply that number by 4 days a week, it equals 20 miles in all.

Writing numbers answer sheet

2 is in the hundreds place.

0 is in the tens place.

2 is in the ones place.

Division using area models answer sheet

Multiplying using square models answer sheet

Multiplying fractions and whole numbers using expanded form answer sheet

Multiplying fractions using a number line answer sheet

Explanation – First divide the number line into 6 equal parts and draw up a line up to 4/6. Then find the ½ way mark of that line you drew up to 4/6. You will now see the line is divided into three parts. So the answer would be ⅓. 

Lesson credits

Amber Watkins

Amber is an education specialist with a degree in Early Childhood Education. She has over 12 years of experience teaching and tutoring elementary through college level math. "Knowing that my work in math education makes such an impact leaves me with an indescribable feeling of pride and joy!"

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5th Grade Math Word Problems Real-Life Problems

Welcome to our 5th Grade Math Word Problems page. Here you will find our range of Fifth Grade Math Problem Worksheets which will help your child apply and practice their Math skills to solve a range of 'real life' problems.

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5th Grade Math Word Problems

Here you will find a range of problem solving worksheets.

The sheets involve using a range of math skills and knowledge to solve problems.

Each problem sheet is available in both standard and metric units (where appropriate), and come complete with an answer sheet.

The sheets in this section have all come from 'real life' data such as mountains, rivers or space. Children will be able to apply their math to solve and answer 'real' problems.

Using these sheets will help your child to:

• apply their addition, subtraction, multiplication and division skills;
• apply their knowledge of rounding and place value;
• solve a range of 'real life' problems.

5th Grade Word Problems

The 7 longest rivers.

The 7 longest rivers involves adding and subtracting numbers in the thousands, and also place value and ordering numbers to 10,000.

• 7 Longest Rivers metric units
• PDF version
• 7 Longest Rivers standard units

On the Mountains

On the mountains involves addition and subtraction of numbers to 5 digits, and also rounding and ordering numbers to 10,000 (metric) or 100,000 (standard).

• On the Mountains metric units
• On the Mountains standard units

Temperatures around the world

This problem worksheet involves ordering positive and negative numbers, as well as working out differences between positive and negative numbers. The mean and median temperatures also need to be calculated.

• Temperatures Around the World 3 (Celsius)
• Temperatures Around the World 3 (Fahrenheit)

The Solar System

The Solar System worksheets involves doubling numbers and rounding to the nearest 1000. Addition and subtraction of large numbers to 5 digits, ordering large numbers and approximation are also tackled.

• The Solar System (Metric units)
• The Solar System (Standard units)

US National Parks

This 5th grade math word problem sheet involves addition and subtraction of large numbers to 5 digits, place value and ordering. Approximation and multiplication are also used.

• US National Parks (metric units)
• US National Parks (standard units)

Salamanders of the Caribbean Problems

This problem sheet involves rounding and ordering BIG numbers up to 12 million to the nearest 1000, as well as addition and subtraction of the numbers.

• Salamanders of the Caribbean problems

Nearest Stars

This problem sheet involves rounding decimals to the nearest whole number, as well as ordering decimals to 2 decimal places. Adding and subtracting decimals, and doubling decimals are also used.

• Nearest stars

Whales Problems

This worksheet involves ordering decimals to 1 or 2dp, as well as ordering large numbers. Addition and subtraction of large numbers and decimals is also used, as well as approximation and multiplication.

• Whale problems metric units
• Whale problems standard units

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

Ratio Problems

Here you will find a selection of ratio problem sheets which will help your child practice and apply their ratio knowledge and skills to solve a range of problems.

Looking for some easier word problems?

If you are looking for some easier math problems, why not try our 4th grade math problem page.

The problems on this page are at an easier level than those here.

The numbers are simpler and the problems themselves are less complex.

• 4th Grade Math Word Problems

More 5th Grade Math Problems

Here you will some more of our 5th grade math word problems.

Each sheet is availabel in both standard and metric units (where applicable).

Each sheet comes complete with a separate answer sheet.

All the problems are based around 'real life' such as the planets, heights of mountains, or length of rivers.

Using these sheet will help your child to:

• solve a range of problems including "real life" problems and ratio problems.

All the worksheets help to support Elementary math benchmarks.

These sheets involve solving one or two more challenging longer problems.

• 5th Grade Math Problems

These sheets involve solving a range of ratio problems.

• Multiplication Word Problems 5th Grade
• 5th Grade Measurement Worksheets

Here is our selection of measurement worksheets for 5th graders.

These sheets involve reading scales in both the standard and metric systems.

The scales include finding the length, weight or liquid capacity.

Using these sheets will help your child understand how to:

• learn how to read a standard scale going up in different fractions: halves, quarters, eighths and sixteenths;
• learn how to read a metric scale going up in 0.1s, 5s, 10s, 25s, 50s & 100s;
• learn how to estimate a measurement of length, weight or liquid.

Using these sheets will help children to consolidate their fractions and place value learning.

Fifth Grade Math Games

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5th Grade Math Word Problems

Looking for engaging word problems for upcoming lessons or homeschool math activities? Pass our collection of free 5th grade math word problems with answers and solutions. Train and improve your math skills with LogicLike!

Math Problems for Grade 5

During the summer holidays, Ginny earns extra money mowing lawns. He mows 8 lawns an hour and has 32 lawns to mow. How long will it take him?

Our class made 360 ​​cookies for the school fair. Each family prepared 40 cookies. How many families have made cookies?

Mom bought her daughter Molly 4 gifts of $24 each and Sun Max 6 gifts of $18 each. How much money did she spend in total?

4*24+6*18=204.

5th grade students going on an excursion. This means that 125 students must board the buses, and each bus can accommodate 48 students. How many buses will the school need?

Your mom bought you a one-year tennis pass for $300. She’s making 12 payments of how much money to pay for the pass?

The mean average of the following 5 math marks will become Sandra’s report card mark: 96, 69, 83, 73 and 85. What will her report card mark be?

In July Potter earns extra money mowing lawns. He mows 8 lawns an hour and has 28 lawns to mow. How long will it take him?

Maggie wants to ride the Ferris wheel, the roller coaster, and the log ride. The Ferris wheel costs 6 tickets, the roller coaster costs 5 tickets and the log ride costs 8 tickets. Maggie has 13 tickets. How many more tickets should Maggie buy?

Mount Kilimanjaro is 19,340 feet high. Mount Everest is 29, 028 feet high. How much smaller is Mount Kilimanjaro?

Betty had 29 dolls. Then she bought 23 dolls from the toy store and got 25 dolls for her birthday. Betty gave 12 of the dolls to her sister and 17 to her friend Lily. How many dolls does Betty have left?

solve 10-20 problems and riddles a day. Can you do more?

Understand fractions as division

* Write the answer as a proper fraction or a mixed number.

Mr. Green ordered a giant sausage for the party. It was 6 feet long! When the sausage arrived, it was cut into 16 equal pieces. How long is each piece?

Mrs. Brown decided to make a healthy snack for the 20 students in his class. She gave each student a dish of yogurt, and divided 6 cups of berries equally among the dishes. How many cups of berries did each student get in their yogurt?

5th-grade students take an excursion to the Nature Museum. They will be in the museum for 3 hours and they want to spread their time evenly among the 10 exhibits. How much time should they spend at each exhibition?

On the birthday, Luca wants to bring in homemade breakfast biscuits for his classmates. He makes a batch of 25 biscuits using 8 cups of flour. How much flour is in each biscuit?

Variable equations

Michelle had a list of 28 books she wanted to read. Then she read 4 and crossed them off the list. The letter X stands for the number of books Michelle has left on her list. Which equation can you use to find X?

28+4=X or 28-4=X.

At Henry's birthday party, the kids get into 2 groups for a treasure hunt. Each group has 6 kids. The letter Y stands for the total number of kids. Which equation can you use to find Y?

Add 3 or more fractions

Granny made a fruit salad with 2/3 of a pound of melon, 2/3 of a pound of bananas, and 2/3 of a pound of pineapple. How many pounds of fruit did Granny use in total?

A waitress put leftover tarts into the fridge on Thursday night. She noticed that the restaurant had 2/3 of a tart filled with cherries, 1/3 of a tart filled with blueberries, and 2/3 of a tart filled with peaches. How many leftover tarts did the restaurant have in all?

During his visit to the garden, Arnold collected 4/7 a bag of apples, 2/7 a bag of peas and 1/7 a bag of plums. How many bags of fruit Arnold collected?

Fractions of a Number

Of the 10 cups on the shelf, one-fifth are white. How many white cups are on the shelf?

Four-fifths of the 20 bowls in the cupboard are yellow. How many yellow bowls are in the cupboard?

16 yellow bowls.

There are 10 people waiting for the train. Two-fifths of them have an umbrella. How many people waiting for the train have an umbrella?

Of the 16 cookies in the cookie jar, two-quarters are peanut butter cookies. How many peanut butter cookies are in the cookie jar?

8 peanut butter cookies.

Of the 20 people in line for ice cream, seven-tenths want vanilla. How many people want vanilla ice cream?

Pour 2 2/4 cups of walnuts and 3 3/8 cups of pecans into the squirrel feeder. How many glasses of nuts did the squirrel fill?

When painting my kitchen, I used 3 1/2 liters of wight paint and 2 1/4 liters of green paint. How much paint did I use in all?

Kathleen used 6 1/3 liters to water her orchids and 2 6/9 liters to water her potted cacti. How many liters of water did Kathleen use for the flowers?

Molly is making strawberry milkshake. She added a 1/4 cup of strawberry syrup to 2/3 cup of milk. How much strawberry milkshake did Molly make?

A jug of water is ½ full. If 3 children equally share the water, what fraction of the full jug does each child get?

Each child would get 1/6 of the 1/2 left of water.

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• Reduce Fractions Calculator. Rewrite Fractions in reduced form.

Grade 5 Word Problem Worksheets

Free printable fifth grade math worksheets to help your students improve their ability to solve word problems! Applying mathematical concepts to solve word problems can be challenging. These free worksheets are great repetition for your students! Scroll down to access all of the free grade 5 word problem worksheets. For more word problem resources, click on the image to the right to check out the word problem task cards. They cover a range of different math concepts for students in grades 4 & 5. 

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Solving Word Problems in Grade 5 Math

• by Diana Insegment
• 05/31/2023 05/31/2023
• Published: 05.31.2023

We all know that math is a unique subject when it comes to the expressions used. Unlike most subjects in which students use words, letters, and language, math forces students to become comfortable using numbers, too. 

By the time students make it to 5th grade , no longer can they expect their math class to include numbers alone. In middle school, word problems are one of the most common math problems that students will encounter. 

Solving word problems can be tricky for students – especially in math class because they are so used to using numbers. The words can throw certain students off, confusing them and leading to errors .

Let’s take a closer look at the various ways we can solve word problems and hopefully, they will trip fewer people up in the future.

Solving word problems through operations

Word problems are a key part of a complete math education. They help students develop vital problem-solving skills, and properly apply mathematical concepts to real-life scenarios.

In grade 5, students are expected to understand many different word problems. One way they can be solved is by performing appropriate operations, such as addition, subtraction, multiplication, and division .

Remove the values and focus on operations

To solve word problems through operations, the first step is to remove the specific numerical values that are mentioned in the problem. While this may seem counterintuitive, this lets students understand the question conceptually properly and identify the operations they will have to apply to solve the problem.

Let’s look at an example. 

“John has 12 apples, and he gives 5 apples to his friend. How many apples does John have left?” To solve this, we can remove the specific values and focus purely on the operation we need to perform: subtraction. Since John starts with a certain number of apples and we see that he is giving some away, we know that subtraction is the appropriate operation.

This approach helps students better understand important mathematical concepts and greatly improves their problem-solving capabilities.

Mixed Word Problems

After seeing our first problem, we can see that solving word problems can be straightforward. Things can get a little bit more complicated, however, when we encounter mixed word problems.

Mixed word problems are problems that involve multiple operations. This means that students will need to use a combination of the operations mentioned above: addition, subtraction, multiplication, and division.

Let’s try one of these more advanced examples.

Consider the following mixed-word problem:

“Joey went to the store and bought 8 packs of pens. Each pack contains 6 pens. He gave 4 pens to his friend and divided the rest equally among his siblings. If Joey has 4 siblings, how many pens does each sibling get?”

Clearly, we need to perform multiple operations to solve this problem. First, we need to multiply the number of packs (8) by the number of pens per pack (6) to find the total number of pens that Joey bought (48). Next, we need to take the number of pens he gave to his friend (4) away from the total number of pens. Finally, we need to divide this number (44) by the number of siblings Joey has (4), to find out how many pens each sibling will get. So, we divide 44 by 4 and our answer is 11.

As you can see, mixed word problems are more difficult, because students need to analyze these questions more carefully, and since they require multiple operations, there is more room for error. With plenty of practice, mixed word problems help students accelerate toward possessing high-level problem-solving skills.

Solving word problems with tables

Another way that grade 5 students can solve word problems is with tables . Tables provide a visual, structured format for organizing and analyzing information. This structure makes it easy for students to identify patterns and relationships, and, ultimately, solve the problems.

Completing the Table

Completing a table is a method that students can use to solve word problems quickly and effectively. Students must create a table with labeled rows and columns, into which they can input information and track the variable in the particular problem.

For example, let’s consider this problem:

“A bakery sold 15 loaves of bread on Monday, 20 loaves on Tuesday, and 16 loaves on Wednesday. If they sell the same number of loaves each day, how many loaves did they sell on Thursday?”

To solve this, students would construct a table and create columns for the days of the week, filling the number of loaves sold in the rows across. With the values for Monday, Tuesday, and Wednesday already given, students would then use the pattern that they’ve observed in the table to identify the number of loaves sold on Thursday.

Completing the table is a great way for young students to learn quickly. The visual aspect is very effective in helping students see the problems clearly, which will help them find their answers faster and, most importantly, accurately. 

At Online Math Center

At Online Math Center, we have the tools, expertise, and experience to help your kids thrive in their math lessons. With individual courses , SAT prep courses , and tutoring lessons for students of all ages in middle and high school, OMC is the best place to give your kids the advantage in math class.

Contact OMC today for more information and to enroll your child in our grade 5 math course .

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• 5th Grade Math

Grade 5 money math worksheets: Word problems with solutions

Hi there! Are you ready to ace your 5 th grader's money skills? Worry less! This article provides fun and engaging Grade 5 money math worksheets and exciting word problems with solutions . Also, in this article, you will find the simplest ways to explain:

How to master money word problems in 5 easy steps!

• Fun and engaging 5th-grade worksheets to practice money skills

Adding and subtracting money word problems

• Multiplying and dividing money word problems

How to calculate sales tax and discounts

• Tips and tricks to solve any money word problem
• Real-life examples of money word problems and how to solve them
• Bonus: additional grade 5 money math worksheets to boost 5 th graders' confidence and knowledge

Conclusion: applying money math skills to real-life situations

Grade 5 money math worksheets: the ultimate guide to saving and spending.

Help your 5 th graders find an ultimate guide to saving and spending with the help of these fantastic Grade 5 money math worksheets from selected Mathskills4kids.com .

These engaging 5th-grade money worksheets from Mathskills4kids consist of simple exercises for practicing money skills, such as adding and subtracting money, multiplying and dividing money, calculating sales tax and discounts, and more.

In this article, we'll also show 5th graders how to solve money word problems in 5 easy steps. Plus, we'll share some tips and tricks to solve any money word problem and real-life examples of money word problems.

And as a bonus, we'll give you access to some additional grade 5 money math worksheets that will take your 5th grader's money math skills to the next level!

Ready to get started? Let's dive in!

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Download free worksheets, 5th grade math topics.

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Multiplication

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• Divide decimals
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Start practice on Fifth Grade here

Money word problems can be tricky but don't have to be. Here are 5 easy steps that will help 5 th graders to master money word problems solving skills in no time:

• Read the problem carefully and identify what is given and what is asked. Look for keywords that indicate the operation needed, such as "total," "change," "spent," "earned," "saved," etc.
• Write down the given information using the same units of money (dollars or cents). If necessary, convert between units using the rule that 100 cents = 1 dollar.
• Choose the appropriate operation (addition, subtraction, multiplication, or division) and set up an equation using variables or symbols to represent the unknown quantities.
• Solve the equation using the order of operations (PEMDAS) and check your answer by plugging it back into the equation.
• Write your answer in a complete sentence using the correct units of money and label it clearly.

That's it! Following these 5 steps, your 5th grader can confidently and accurately solve any money word problem.

Fun and engaging Grade 5 money math worksheets to practice money skills

Now that you know how to solve money word problems, it's time to practice! We've selected some fun and engaging grade 5 money math worksheets from Mathskills4kids.com that cover various money skills, such as:

• Adding and subtracting money word problems : These worksheets will help your 5th grader practice adding and subtracting money amounts with decimals and finding the change from a given amount.
• Multiplying and dividing money word problems : These worksheets will help your 5th grader practice multiplying and dividing money amounts by whole numbers or decimals and finding the unit price or rate of a given item or service.
• How to calculate sales tax and discounts : These worksheets will help your 5th grader practice calculating sales tax and discounts on purchases and finding the final price or cost of an item or service after applying the tax or discount.
• Real-life examples of money word problems and how to solve them : These worksheets will present your 5th grader with some realistic scenarios of money word problems that they may encounter in their daily lives, such as shopping, budgeting, saving, investing, etc.

Let's start with adding and subtracting money word problems . These are problems where you will find the total amount of money or the change after buying something. For example, how much money do you spend buying a book for $12.50 and a pencil for $0.75? Or, if you have $20 and buy a sandwich for $4.25, how much money do you have left?

To solve these problems, you must line up the decimal points and add or subtract the numbers as usual. Remember to put the dollar sign and the decimal point in your answer!

Multiplying and dividing money word problems worksheet

Next, we have multiplying and dividing money word problems . These are problems where you will find the product or the quotient of money and a number. For example, if you earn $8 per hour and work 5 hours, how much money do you earn? Or, if you have $50 and want to split it equally among 4 friends, how much money does each friend get?

To solve these problems, you will multiply or divide the numbers as usual, but be careful with the decimal point. Move it two places to the left when multiplying and two places to the right when dividing. Also, remember to put the dollar sign and the decimal point in your answer!

Another important topic is how to calculate sales tax and discounts . Sales tax is a percentage of the price you must pay extra when buying something. For example, how much do you have to pay if you buy a shirt for $15 and the sales tax is 10%?

To find the sales tax amount, multiply the price by the sales tax rate as a decimal (10% = 0.1). Then, add the sales tax amount to the original price to get the total price. In this case, the sales tax amount is $15 x 0.1 = $1.5, and the total price is $15 + $1.5 = $16.5.

Discounts are a percentage of the price you save when buying something on sale. For example, how much do you pay if you buy a pair of shoes for $40 and the discount is 25%?

To find the discount amount, multiply the original price by the discount rate as a decimal (25% = 0.25). Then, subtract the discount amount from the original price to get the sale price. In this case, the discount amount is $40 x 0.25 = $10, and the sale price is $40 - $10 = $30.

10 real-life examples of 5 th Grade money word problems with solutions

Finally, let's look at some real-life examples of 5th Grade money word problems with solutions . These are problems that involve more than one step or operation, requiring careful reading and thinking. For example;

If you go to a movie theater with your friend and buy two tickets for $8 each, a large popcorn for $6, and two drinks for $3 each, how much money do you spend? To solve this problem, add all the costs: 2 x $8 + $6 + 2 x $3 = $28.

Or, if you have a coupon that gives you 20% off on any item at a store, and you buy a jacket that costs $45 before tax, and the sales tax is 8%, how much do you pay? To solve this problem, first find the sale price after applying the coupon: $45 - ($45 x 0.2) = $36. Then, find the sales tax amount: $36 x 0.08 = $2.88. Finally, add the sale price and the sales tax amount: $36 + $2.88 = $38.88.

Real-life situations-money math problems with solutions

Solution: To solve this problem, find out how much more money Anna needs to buy the bike and then divide that by her weekly income. We can use subtraction and division to do this.

$250 - $120 = $130

$130 / $10 = 13

Anna needs 13 more weeks to save enough money for the bike.

Solution: To solve this problem, we need to find out how much money Ben earns and how much he spends for each cup of lemonade, then subtract the cost from the revenue. We can use multiplication and subtraction to do this.

$0.50 x 1 = $0.50 (revenue)

$0.20 x 1 = $0.20 (cost)

$0.50 - $0.20 = $0.30 (profit)

Ben makes 30 cents of profit for each cup of lemonade he sells.

Solution : To solve this problem, we need to find out how much money Charlie's parents will pay and how much Charlie has to pay, and then subtract what he already has from what he needs. We can use division and subtraction to do this.

$60 / 2 = $30 (Charlie's parents' share)

$60 / 2 = $30 (Charlie's share)

$30 - $15 = $15

Charlie needs $15 more to buy the video game.

Solution : To solve this problem, we need to find out how much money Dani will save with the coupon and how much she will pay after applying the discount. We can use multiplication and subtraction to do this.

$12 x 0.20 = $2.40 (discount amount)

$12 - $2.40 = $9.60 (final price)

Dani will pay $9.60 for the book after using the coupon.

To solve this problem, we need to find out how much Ella has in total and how much she will spend on the necklace, then subtract the price from the amount. We can use addition and subtraction to do this.

$10 + $5 + $1 = $16 (total amount)

$18 - $16 = $2 (change amount)

Ella will get back $2 in change if she pays with these bills.

To solve this problem, we will determine how much each type of coin is worth and add up the total. We can use multiplication and addition to do this.

$0.25 x 12 = $3 (quarters)

$0.10 x 15 = $1.50 (dimes)

$0.05 x 18 = $0.90 (nickels)

$0.01 x 20 = $0.20 (pennies)

$3 + $1.50 + $0.90 + $0.20 = $5.60 (total amount)

Frank has $5.60 in his jar of coins.

To solve this problem, we need to find out how many slices each person gets and how much each slice costs, then multiply the cost by the number of slices. We can use division and multiplication to do this.

8 / 3 = 2.67 (slices per person)

$12 / 8 = $1.50 (cost per slice)

$1.50 x 2.67 = $4.01 (cost per person)

Each person should pay $4.01 if they share the pizza equally.

To solve this problem, we need to determine how much money Jack makes per day, week, and month and then add the amounts. We can use multiplication and addition to do this.

$0.25 x 40 = $10 (daily income)

$10 x 7 = $70 (weekly income)

$70 + $5 = $75 (weekly income with bonus)

$75 x 4 = $300 (monthly income)

Jack makes $300 a month.

Solution : To solve this problem, we need to find out how much money Kelly will save with the coupon, how much she will pay before tax, and how much tax she will pay, and then add up the amounts. We can use multiplication and addition to do this.

$40 x 0.15 = $6 (discount amount)

$40 - $6 = $34 (price before tax)

$34 x 0.08 = $2.72 (tax amount)

$34 + $2.72 = $36.72 (final price)

Kelly will pay $36.72 for the jeans after using the coupon and paying the tax.

Solution : To solve this problem, we need to find out how much money Leo will spend on each item and how many items he can buy with his budget, then compare the amounts. We can use multiplication and division to do this.

$12 x 1 = $12 (one pizza)

$15 x 1 = $15 (one cake)

$6 x 1 = $6 (one gallon of ice cream)

$2 x 1 = $2 (one liter of soda)

$100 / $12 = 8.33 (maximum number of pizzas)

$100 / $15 = 6.67 (maximum number of cakes)

$100 / $6 = 16.67 (maximum number of ice creams)

$100 / $2 = 50 (maximum number of sodas)

One possible solution is to buy 8 pizzas, 1 cake, 2 gallons of ice cream, and 10 liters of soda.

$12 x 8 = $96 (cost of pizzas)

$15 x 1 = $15 (cost of cake)

$6 x 2 = $12 (cost of ice cream)

$2 x 10 = $20 (cost of soda)

$96 + $15 + $12 + $20 = $143 (total cost)

However, this solution exceeds Leo's budget by $43, so he needs to reduce some items or find cheaper alternatives.

Another possible solution is to buy 6 pizzas, 1 cake, 1 gallon of ice cream, and 12 liters of soda.

$12 x 6 = $72 (cost of pizzas)

$6 x 1 = $6 (cost of ice cream)

$2 x 12 = $24 (cost of soda)

$72 + $15 + $6 + $24 = $117 (total cost)

This solution is within Leo's budget by $17, so he can either save the money or buy more items if he wants.

There may also be other possible solutions, as long as they are within Leo's budget.

These money math questions are fun, engaging, and challenging. They will help you develop 5 th graders’ math, critical thinking, and financial literacy skills.

Bonus: Additional money math resources to boost 5th graders' confidence and knowledge

If you want to give your 5th grader some extra practice and challenge in money math skills, we can advise you with some excellent websites, games, videos, and worksheets that you can use to supplement your money math lessons.

These resources cover decimals, fractions, percentages, interest, taxes, budgeting, etc. Check them out and see how they can boost your 5th graders' confidence and knowledge in money math!

• Math Playground : This website has tons of interactive games and activities that teach and practice money math skills. You can find games for different grade levels and topics, such as Decimal Place Value Pirates, Fraction Matcher, Percent Shopping, and Money Word Problems. Your students will love playing these games and learning at the same time! Visit https://www.mathplayground.com/ASB_Dolphin_Dash.html to explore the games.
• co Academy : This website is a great resource for learning and reviewing money math concepts. You can watch videos to teach your 5th-grade students how to do addition and subtraction with various money amounts. You can also teach them to solve word problems and calculate the merchandise's unit price. Visit https://study.com/academy/topic/5th-grade-math-money.html and teach money math in an exciting way.
• Math is Fun : This website has a lot of helpful information and examples that help you understand money math topics. You can read about the basics of money, such as coins, bills, currency, exchange rates, and rounding. You can also learn about more advanced topics, such as decimals, fractions, percentages, interest, taxes, budgeting, and saving. Visit https://www.mathsisfun.com/money/index.html to browse the topics.
• BrainPOP : This website has engaging videos and quizzes that teach you about money math topics. You can watch videos that feature Tim and Moby, two funny characters who explain the topics in a fun and easy way. You can also take quizzes that test your knowledge and give you feedback. Visit https://www.brainpop.com/games/moneymagic/ to watch the video on money.

Thank you for sharing the links of MathSkills4Kids.com with your loved ones. Your choice is greatly appreciated.

Money math skills are essential for 5th graders to learn and master, as they will help them become financially literate and responsible in the future. By practicing money word problems and other money math skills using Mathskills4kids’ worksheets, your 5th grader will be able to apply their knowledge and skills to real-life situations, such as:

• Planning and managing their finances, such as saving, spending, budgeting, investing, etc.
• Making intelligent and informed shopping decisions, such as comparing prices, finding the best deals, calculating taxes and discounts, etc.
• Understanding and using different forms of money, such as cash, checks, debit cards, credit cards, etc.
• Developing a positive attitude towards money and its value, such as appreciating what they have, being generous and charitable, avoiding debt and fraud, etc.

We hope you enjoyed this article and found it helpful. We encourage you to use our worksheets to help your 5th grader master money word problems and other money math skills.

We invite you to visit mathskills4kids.com for more enriching math worksheets in all Grades. Thank you for reading, and happy teaching!

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