mixed number problem solving

Fraction Word Problems - Mixed Numbers

Related Topics: Fraction Word Problems Worksheet More Fractions Worksheets Fraction Games

“Fraction Word Problems” Worksheets: Fraction Word Problems (Add, Subtract) 2-Step Fraction Word Problems (Add, Subtract)

1-Step Mixed Number Word Problems (Add, Subtract) 2-Step Mixed Number Word Problems (Add, Subtract)

Objective: I can solve one-step word problems involving addition and subtraction of mixed numbers.

Follow these steps to solve the mixed numbers word problems.

Step 1. Is it a problem in addition or subtraction?

Step 2. Do you need to find a common denominator?

Step 3. Can you simplify or reduce the answer?

Solve the following word problems. Mark ran 2 1 / 3 km and Shaun ran 3 1 / 5 km. Find the difference in the distance that they ran. Brandon and his son went fishing. Brandon caught 3 3 / 4 kg of fish while his son caught 2 1 / 5 kg of fish. What is the total weight of the fishes that they caught? For the school’s sports day, a group of students prepared 21 1 / 2 litres of lemonade. At the end of the day they had 2 5 / 8 litres left over. How many litres of lemonade were sold? Darren spent 2 1 / 2 hours on his homework on Monday. On Tuesday, he spent 1 3 / 5 hours on his homework. Find the total amount of time, in hours, that Darren spent doing his homework on Monday and Tuesday. Brian has a bamboo pole that was 6 ¾ m long. He cut off 1 1 / 4 m and another 2 1 / 3 m. What is the length of the remaining bamboo pole in m? Lydia bought 2 3 / 4 kg of vegetables, 1 1 / 4 kg of fish and 2 1 / 3 kg of mutton. What is the total mass, in kg, of the items that she bought? Kimberly has 3 1 / 2 bottles of milk in her refrigerator. She used 3 / 5 bottle in the morning and 1 1 / 4 bottle in the afternoon. How many bottles of milk does Kimberly have left over? A tank has 82 3 / 4 litres of water. 24 4 / 5 litres were used and the tank was filled with another 18 3 / 4 litres. What is the final volume of water in the tank?

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Mixed numbers

In previous lessons, it was said that a fraction consisting of a whole part and a fractional part is called a mixed number .

All fractions that have a whole part and a fraction part have one common name: mixed numbers .

Mixed numbers can be added, subtracted, multiplied, and divided, just like proper fractions . In this lesson we will look at each of these operations separately.

Adding whole number to a fraction

What conclusion can be drawn? If you need to add a number to a proper fraction, you can omit the plus sign and write the whole number and fraction together.

If you add half a pizza to two whole pizzas, you get two whole pizzas and half a pizza:

This is the first way. The second way is much easier. You can put an equal sign and write the whole part and the fractional part together. That is, omit the addition sign:

Apply the combinative law of addition . If we add two twos, we get 4:

Now let's roll up the resulting mixed number:

This is the final answer. The detailed solution of this example can be written as follows:

Adding mixed numbers

First, let's write down the mixed numbers in expanded form:

Apply the combinative law of addition . Group the whole and fractional parts separately:

Let's calculate the integers: 2 + 3 = 5. In the main expression, replace the expression in parentheses (2 + 3) with the resulting five:

Now let's calculate the fractional parts. This is the addition of fractions with different denominators. We already know how to add such fractions:

Now let's collapse the resulting mixed number:

Examples like this need to be solved quickly, without stopping for details. If we were in school, we would have to write down the solution to this example as follows:

If you see such a short solution in the future, don't be frightened. You already understand where it came from.

Let's write the mixed numbers in expanded form:

Let's group the integers and fractions separately:

Let's calculate the integers: 5 + 3 = 8. In the main expression, replace the expression in parentheses (5 + 3) with the resulting number 8

Now let's calculate the fractional parts:

Let's add the whole parts. We get 9

We wrap up the finished answer:

The complete solution of this example is as follows:

There is a universal rule for solving such examples. It looks like this:

To add up mixed numbers, you have to:

• reduce the fractional parts of these numbers to a common denominator;
• perform addition of integers and fractions separately.

If adding fractions results in an improper fraction, isolate the whole part of the fraction and add it to the resulting whole.

The use of ready-made rules is acceptable if the essence of the topic is fully understood. A formulaic solution, looking at other similar examples, leads to errors that take extra time to find. Therefore, it is more reasonable to understand the topic first, and then use a ready-made rule.

Let's use a ready-made rule. Let's reduce the fractional parts to a common denominator, then add the whole and fractional parts separately:

Adding whole and mixed numbers

Let's try to represent this solution in the form of a picture. If you add three whole pizzas and a third of a pizza to two whole pizzas, you get five whole pizzas and a third of a pizza:

In this example, as in the previous one, you have to add up the whole parts:

Subtracting a fraction from a whole number

If there is one whole pizza and we subtract half a pizza from it, we have half a pizza:

If there are two whole pizzas and we subtract half from the bottom, that leaves one whole pizza and half:

Let's pretend that the number 3 is three pizzas:

Now imagine what three pizzas would look like if you cut off that third of them

Subtracting a mixed number from a whole number

If you subtract one whole pizza and one half pizza from five whole pizzas, you are left with three whole pizzas and one half pizza:

Examples on subtracting fractions from a number or subtracting mixed fractions from a number can again be done in the mind. This process is easy to imagine.

If you cover two-thirds of the pizza with your hand in the picture (it's shaded), you'll know right away.

Subtracting mixed numbers

If you subtract two whole pizzas and a third of a pizza from three whole pizzas, you are left with one whole pizza and one sixth of a pizza:

We'll come back to the subtraction of mixed numbers. There are many subtleties in subtracting fractions that a beginner is not yet prepared for. For example, it is possible that the minuend may be less than the subtrahend. This can lead us into the world of negative numbers, which we haven't yet studied.

In the meantime, we will study multiplication of mixed numbers. It is not as complicated as addition and subtraction.

Multiplying fractions by whole numbers

Any whole number can be multiplied by a fraction. All you have to do is multiply the number by the numerator of the fraction.

The answer is an improper fraction. Let's separate the whole part of the fraction:

If there are five whole pizzas and we take half of that number, we have two whole pizzas and half a pizza:

Also, you could have shortened the fraction. The result would have been the same. It would look like this:

If there are three whole pizzas and we take two thirds of that amount, we have two whole pizzas:

This example is solved in the same way as the previous ones. The whole and the numerator of the fraction must be multiplied:

Multiplying mixed numbers and fractions

To multiply a mixed number by a fraction, you must convert the mixed number to an improper fraction, then multiply the proper fractions.

Let's say there is one whole pizza and a half pizza:

Multiplying mixed numbers

Let's try to understand this example with the help of a picture. Let's say there is one whole pizza and one half of a pizza:

The multiplier 2 is clear: it means that one whole pizza and one half pizza must be taken twice. Let's take two whole pizzas and two halves:

Convert the mixed numbers into improper fractions and multiply those improper fractions. If the answer is an improper fraction, select the whole part of the fraction:

Dividing a whole number by a fraction

To divide a whole number by a fraction, multiply the whole by the inversed fraction.

Let's say there are three whole pizzas:

Indeed, if we divide each pizza in half, we have six halves:

Let's say there are two whole pizzas:

To answer this question, find the number of pizzas in the two pizzas shown in the following picture:

Two pizzas contain one whole pizza and one half pizza. This can be seen if the second pizza is cut in half:

Dividing a fraction by a whole number

To divide a fraction by a whole number, multiply the fraction by the inverse of the divisor. We did this kind of division in the last lesson . Let's go over it again.

Let there be half a pizza:

Let's divide it equally into two parts. Then each part will be one-fourth of a pizza:

Dividing a whole number by a mixed number

Dividing a mixed number by a whole number

To divide a mixed number by a whole number, you must convert the mixed number into an improper fraction, then multiply that fraction by the number inverse of the divisor.

Divide this amount of pizza equally into two parts. To do this, first divide a whole pizza into two parts:

Then divide equally into two parts and half:

Dividing mixed numbers

To divide mixed numbers, you need to convert them into improper fractions, then do the usual division of fractions. That is, multiply the first fraction by the inversed second fraction.

Let's convert the mixed numbers into improper fractions. We obtain the following expression:

Let's finish this example to the end:

Let's say there are two whole and half pizzas:

Video lesson

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• Comparing Fractions

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Mixed Fractions

(Also called " Mixed Numbers ")

A Mixed Fraction is a whole number and a proper fraction combined. Such as 1 3 4

See how each example is made up of a whole number and a proper fraction together? That is why it is called a "mixed" fraction (or mixed number).

We can give names to every part of a mixed fraction:

Three Types of Fractions

There are three types of fraction:

Mixed Fractions or Improper Fractions

We can use either an improper fraction or a mixed fraction to show the same amount.

For example 1 3 4 = 7 4 , as shown here:

Converting Improper Fractions to Mixed Fractions

To convert an improper fraction to a mixed fraction, follow these steps:

• Divide the numerator by the denominator.
• Write down the whole number answer
• Then write down any remainder above the denominator.

Example: Convert 11 4 to a mixed fraction.

Write down the 2 and then write down the remainder (3) above the denominator (4).

That example can be written like this:

Example: Convert 10 3 to a mixed fraction.

Converting mixed fractions to improper fractions.

To convert a mixed fraction to an improper fraction, follow these steps:

• Multiply the whole number part by the fraction's denominator.
• Add that to the numerator
• Then write the result on top of the denominator.

Example: Convert 3 2 5 to an improper fraction.

Multiply the whole number part by the denominator:

Add that to the numerator:

Then write that result above the denominator:

We can do the numerator in one go:

Example: Convert 2 1 9 to an improper fraction.

Are improper fractions bad .

NO, they aren't bad!

For mathematics they are actually better than mixed fractions. Because mixed fractions can be confusing when we write them in a formula: should the two parts be added or multiplied?

But, for everyday use , people understand mixed fractions better.

Example: It is easier to say "I ate 2 1 4 sausages", than "I ate 9 4 sausages"

We Recommend:

• For Mathematics: Improper Fractions
• For Everyday Use: Mixed Fractions

Mixed numbers - practice problems

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Mixed Numbers & Improper Fractions

This is a collection of improper fraction and mixed number worksheets, including worksheets on adding and subtracting mixed numbers.

Mixed Numbers (Basic Concept)

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Improper Fractions and Mixed Numbers

Ordering and comparing mixed numbers, adding and subtracting mixed numbers.

This page has worksheets for teaching basic fraction skills, equivalent fractions, simplifying fractions, and ordering fractions. There are also links to fraction and mixed number addition, subtraction, multiplication, and division.

Add fractions with same and different denominators; Also add mixed numbers.

There are more mixed number skills on the decimal worksheets page

Sample Worksheet Images

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How to Subtract Mixed Numbers

This comprehensive guide provides step-by-step instructions to solve different types of mixed number subtraction problems.

Author Katie Wickliff

Published October 19, 2023

Published Oct 19, 2023

• Key takeaways
• Mixed numbers consist of a whole number and a fractional part, such as 4 ⅓
• Finding the least common denominator is a key part of subtracting mixed numbers with unlike denominators
• Some mixed number subtraction problems require students to regroup, or “borrow”

Table of contents

What are mixed numbers?

• How to subtract mixed numbers

Practice problems

When your child is learning how to subtract mixed numbers, remembering the steps to the process may seem a little challenging at first. However, with quality instruction and a solid practice routine, your student will soon be able to subtract several types of mixed numbers. This article provides a complete overview of how to subtract mixed numbers with the same and different denominators. 

Before s ubtracting mixed numbers , students need to understand that a mixed number is comprised of a whole number and part of a number, which is also called a fraction. Students should be able to identify each component and recognize both the numerator and the denominator of the fraction, like this:

Subtracting mixed numbers step by step

When learning to subtract mixed numbers , reviewing the process one step at a time can help students recognize each part of the mixed number and determine how to solve for that particular problem.

Subtracting mixed numbers with like denominators

To subtract mixed numbers with like denominators, follow the steps below. 

Let’s use 6 ⅔ – 2 ⅓ as an example. 

First, subtract the whole numbers.

Next, subtract the fractions.

Finally, write the mixed number answer.           

Subtracting mixed numbers with unlike denominators

To subtract mixed numbers with unlike–or unequal–denominators, let’s use the example problem of 5 ¾- 2 ⅛ 

First, we need to look at the fractions and find the least common denominator. 

¾ and ⅛ have a least common denominator of 8. 

What is the least common denominator?

The least common denominator, also known as the lowest common denominator, is the smallest number the denominators can be divided into. 

The denominator in ¾ is 4. 

4 can be divided into 1,2, and 4. 

The denominator in ⅛ is 8. 8 can be divided into 1,2,4,8. 

The smallest number the denominators both have in common is 4. 

4 is the least common denominator. 

Next, we need to rename the fraction using the least common denominator. 

To do this, we multiply both the bottom and top of the fraction.

5 (3×2/4×2) = 5 6/8

Now that the two fractions have equal denominators, we subtract the mixed numbers using the process above. 

5 6/8- 2 ⅛= 

Subtracting mixed numbers with regrouping

Let’s look at the example problem of 7 ⅓- 4 ⅚ 

First, we need to find the least common denominator. 

⅓ and ⅚ have a least common denominator of 6. 

Now we can rewrite the problem as:

Even though our mixed numbers now have the same denominator, we can’t subtract 2/6 from ⅚ because we’d get a negative number . 

Similar to a whole number subtraction problem, we need to borrow one whole from the place to the left and add it to the right — but in fractional form. 

Now, we have 7 8/6 and can easily subtract the like denominators.

7 8/6- 4 ⅚ = 3 3/6 or 3 ½

Answer: 4 4/6

6 8/9-5 ⅔=?

Find the least common multiple of 3 and 9, which is 9.

5 (2×3/3×3)= 5 6/9

6 8/9- 5 6/9= 

Answer: 1 2/9

Answer: 4 6/8

Find the least common multiple of 3 and 6, which is 6.

4 (1×2/3×2)= 4 2/6

4 2/6- 1 ⅙=

Answer: 3 1/6

FAQs about subtracting mixed numbers

To subtract mixed numbers, you must first find the least common denominator of each. Then you can subtract or regroup in order to subtract.

In order to subtract a whole number from a mixed number, you need to first convert the whole number into a fraction. Then, you need to change the mixed number into an improper fraction. Finally, find the common denominator of the two fractions in order to subtract.

Lesson credits

Katie Wickliff

Katie holds a master’s degree in Education from the University of Colorado and a bachelor’s degree in both Journalism and English from The University of Iowa. She has over 15 years of education experience as a K-12 classroom teacher and Orton-Gillingham certified tutor. Most importantly, Katie is the mother of two elementary students, ages 8 and 11. She is passionate about math education and firmly believes that the right tools and support will help every student reach their full potential.

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Mixed Numbers

A mixed number is a combination of a whole number and a proper fraction. Mixed numbers are also known as mixed fractions and they help us to understand a quantity in a simpler way. Let us learn more about mixed numbers, adding mixed numbers, and conversion of mixed numbers in this article.

What are Mixed Numbers?

Mixed numbers consist of a whole number and a proper fraction. For example, \(2\dfrac{1}{4}\) is a mixed number in which 2 is the whole number part and 1/4 is the proper fraction. It should be noted that mixed numbers can be added, subtracted, multiplied, and divided easily once they are converted to an improper fraction.

Converting Improper Fractions to Mixed Numbers

We usually convert improper fractions to mixed fractions because it helps us have a better idea of a quantity. For example, it is easy to understand \(9\dfrac{2}{3}\) liters of milk rather than 29/3 liters of milk. In order to convert improper fractions to mixed numbers, we use the following steps. Let us convert 43/9 to a mixed number.

• Step 1: The first step is to divide the numerator by the denominator and get the remainder and the quotient. In this case, 43 ÷ 9 gives 4 as the quotient and 7 as the remainder.
• Step 2: This quotient (4) becomes the whole number part of the mixed number. The remainder (7) becomes the numerator part while the denominator remains the same.
• Step 3: Therefore, the improper fraction, 43/9 changes to a mixed number and is written as \(4\dfrac{7}{9}\), which means 43/9 = \(4\dfrac{7}{9}\)

Adding Mixed Numbers

Adding mixed numbers becomes easy if the given fractions are converted to an improper fraction. Let us understand this with the help of the following example.

Example: Add \(5\dfrac{1}{3}\) and \(7\dfrac{1}{3}\)

Solution: In order to add the mixed numbers, we use the following steps:

• Step 1: First, let us convert them to improper fractions. So, \(5\dfrac{1}{3}\) = 16/3, and \(7\dfrac{1}{3}\) = 22/3
• Step 2: Now, we will add the fractions using the rules for the addition of fractions.
• Step 3: Since these are like fractions that have the same denominator, we just need to add the numerators. (In the case of unlike fractions , which have different denominators, we convert them to equivalent fractions. We take the LCM of the denominators to get a common denominator and then we add the fractions).
• Step 4: After adding the numerators, we get, (16 + 22)/3. This becomes 38/3. Then, we convert the improper fraction to a mixed fraction. So, 38/3 = \(12\dfrac{2}{3}\)

Converting Mixed Numbers to Decimals

Mixed numbers and decimals have a few things that are common. A decimal number consists of a whole number and a fractional part which is separated by a decimal point. A mixed number also consists of a whole number and a proper fraction but it is not separated by a decimal point. For example, 2.25 is a decimal number in which 2 is the whole number and .25 is the fractional part. The same number can be expressed as a mixed number as \(2\dfrac{1}{4}\), but here the fractional part is expressed in the form of a proper fraction. Let us see how to convert mixed numbers to decimals using two methods.

• Method 1: Change the mixed number to an improper fraction and then divide the numerator by the denominator.
• Method 2: Keep the whole number part of the fraction aside, and convert the fractional part to a decimal. After this, the decimal part is simply added to the whole number part.

Example 1 (using method 1): Convert \(3\dfrac{1}{4}\) to an improper fraction.

Solution: After converting the mixed number to an improper fraction, we get \(3\dfrac{1}{4}\) = 13/4. Now, we divide 13 by 4 which gives us 13 ÷ 4 = 3.25

Example 2 (using method 2): Convert \(3\dfrac{1}{4}\) to an improper fraction.

Solution: Keeping the whole number part (3) aside, we will convert only the fractional part to a decimal by dividing 1 by 4. This gives 1 ÷ 4 = 0.25. Then, we add 0.25 to the whole number part 3 which makes it 3 + 0.25 = 3.25.

Converting Mixed Numbers to Improper Fractions

In order to convert a mixed number into an improper fraction, we multiply the denominator with the whole number then add the resultant product with the numerator.

Example: Convert the mixed number, \(5\dfrac{1}{8}\) to an improper fraction.

Solution: We will multiply the denominator (8) by 5 and the product is 8 × 5 = 40. This product is added to the numerator (1), which makes it 40 + 1 = 41. So, 41 will become the new numerator while 8 will remain as the denominator. Therefore, \(5\dfrac{1}{8}\) is converted to an improper fraction and is expressed as 41/8.

☛Related Topics

Check out the following pages related to mixed numbers.

• Proper fraction
• Improper Fractions

Mixed Numbers Examples

Example 1: Add the given mixed numbers: \(7\dfrac{1}{8}\) + \(5\dfrac{3}{8}\)

Solution: After converting the given numbers to improper fractions, we get \(7\dfrac{1}{8}\) = 57/8; and \(5\dfrac{3}{8}\) = 43/8.

Since these are like fractions, we will just add the numerators. This means, 57/8 + 43/8 = (57 + 43)/8 = 100/8. This can be reduced to 25/2 and then converted to a mixed number which makes it 25/2 = \(12\dfrac{1}{2}\)

Example 2: Convert the mixed number to an improper fraction: \(6\dfrac{1}{7}\)

Solution: In order to convert the given mixed number into an improper fraction we will multiply the denominator with the whole number and add the product with the numerator. Here, 7 × 6 = 42, and after adding this product to the numerator we get 42 + 1 = 43. This becomes the numerator and the denominator remains the same. Hence, \(6\dfrac{1}{7}\) changes to 43/7.

Example 3: There are 5/4 liters of plain juice in the refrigerator. Convert the given quantity into a mixed number.

Solution: To convert the given improper fraction 5/4 to a mixed number, we have to divide 5 by 4. By dividing, we will get 1 as the quotient, and 1 as the remainder. Therefore, the answer is \(1\dfrac{1}{4}\).

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Practice Questions on Mixed Numbers

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FAQS on Mixed Numbers

What are mixed numbers in math.

Mixed numbers are also known as mixed fractions which consist of a whole number and a proper fraction. For example, \(3\dfrac{1}{7}\) and \(8\dfrac{1}{4}\) are a few examples of mixed numbers. In the first example, 3 is the whole number part and 1/7 is the proper fraction. In the second example, 8 is the whole number part and 1/4 is the proper fraction.

How to Add Mixed Numbers?

Adding mixed numbers becomes easy once the mixed numbers are converted to improper fractions. After this step, they can be easily added using the rules of addition of fractions. For example, to add \(3\dfrac{1}{7}\) and \(8\dfrac{1}{7}\), we convert them to improper fractions which means, \(3\dfrac{1}{7}\) = 22/7; and \(8\dfrac{1}{7}\) = 57/7. Since these are like fractions, we just need to add the numerators. This means, (22 + 57)/7 = 79/7 = \(11\dfrac{2}{7}\).

How to Multiply Mixed Numbers?

In order to multiply mixed numbers, we first need to convert them to improper fractions. After this step we multiply them as we multiply regular fractions. In other words, after the conversion, we just need to multiply the numerators first, then the denominators are multiplied. After this, they are reduced to the lowest terms, if needed. The resultant fraction is the product of the given fractions. For example, to multiply \(2\dfrac{1}{3}\) and \(4\dfrac{1}{2}\), we will convert them to improper fractions, which means, 7/3 × 9/2 = 63/6 = 21/2 = \(10\dfrac{1}{2}\)

How to Convert Improper Fractions to Mixed Numbers?

In order to convert improper fractions to mixed numbers, we divide the numerator by the denominator to get the remainder and the quotient. The quotient becomes the whole number part of the mixed number, the remainder becomes the numerator part and the denominator remains the same. For example, to change 56/3 to a mixed number, 56 ÷ 3 gives 18 as the quotient and 2 as the remainder. The quotient (18) becomes the whole number, the remainder (2) becomes the new numerator and the denominator (3) remains the same. Therefore, the improper fraction, 56/3 changes to a mixed number and is written as \(18\dfrac{2}{3}\).

What are Mixed Numbers Examples?

A few examples of mixed numbers are \(18\dfrac{2}{3}\), \(1\dfrac{2}{3}\) and \(4\dfrac{5}{6}\). It should be noted that all these have a whole number and a proper fraction.

How to Divide Fractions with Mixed Numbers?

Mixed numbers are divided easily once they get converted to improper fractions. After this step, they are divided in the same way as the fractions are divided. For example, to divide \(3\dfrac{1}{2}\) ÷ \(1\dfrac{1}{4}\), let us first convert them to improper fractions. this makes them 7/2 ÷ 5/4. This means 7/2 × 4/5 = 28/10 = 14/5 = \(2\dfrac{4}{5}\)

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Add & subtract mixed numbers

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These grade 5 word problems involve adding and subtracting mixed numbers with both like and unlike denominators and sometimes more than two terms .  Some problems include superfluous data, forcing students to read and think about the questions, rather than simply recognizing a pattern to the solutions.

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2.3.2: Subtracting Fractions and Mixed Numbers

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Learning Objectives

• Subtract fractions with like and unlike denominators.
• Subtract mixed numbers without regrouping.
• Subtract mixed numbers with regrouping.
• Solve application problems that require the subtraction of fractions or mixed numbers.

Introduction

Sometimes subtraction, rather than addition, is required to solve problems that involve fractions. Suppose you are making pancakes and need \(\ 4 \frac{1}{2}\) cups of flour but you only have \(\ 2 \frac{3}{4}\) cups. How many additional cups will you have to get to make the pancakes? You can solve this problem by subtracting the mixed numbers.

Subtracting Fractions

The most simple fraction subtraction problems are those that have two proper fractions with a common denominator . That is, each denominator is the same. The process is just as it is for addition of fractions with like denominators , except you subtract! You subtract the second numerator from the first and keep the denominator the same.

Imagine that you have a cake with equal-sized pieces. Some of the cake has already been eaten, so you have a fraction of the cake remaining. You could represent the cake pieces with the picture below.

The cake is cut into 12 equal pieces to start. Two are eaten, so the remaining cake can be represented with the fraction \(\ \frac{10}{12}\). If 3 more pieces of cake are eaten, what fraction of the cake is left? You can represent that problem with the expression \(\ \frac{10}{12}-\frac{3}{12}\).

If you subtract 3 pieces, you can see below that \(\ \frac{7}{12}\) of the cake remains.

You can solve this problem without the picture by subtracting the numerators and keeping the denominator the same:

\(\ \frac{10}{12}-\frac{3}{12}=\frac{7}{12}\)

Subtracting Fractions with Like Denominators

If the denominators (bottoms) of the fractions are the same, subtract the numerators (tops) and keep the denominator the same. Remember to simplify the resulting fraction, if possible.

\(\ \frac{6}{7}-\frac{1}{7}=\frac{5}{7}\)

\(\ \frac{5}{9}-\frac{2}{9}=\frac{1}{3}\)

If the denominators are not the same (they have unlike denominators ), you must first rewrite the fractions with a common denominator. The least common denominator , which is the least common multiple of the denominators, is the most efficient choice, but any common denominator will do. Be sure to check your answer to be sure that it is in simplest form. You can use prime factorization to find the least common multiple (LCM), which will be the least common denominator (LCD). See the example below.

\(\ \frac{1}{5}-\frac{1}{6}=\frac{1}{30}\)

The example below shows using multiples to find the least common multiple, which will be the least common denominator.

\(\ \frac{5}{6}-\frac{1}{4}=\frac{7}{12}\)

\(\ \frac{2}{3}-\frac{1}{6}\) Subtract and simplify the answer.

• \(\ \frac{1}{3}\)
• \(\ \frac{3}{6}\)
• \(\ \frac{5}{6}\)
• \(\ \frac{1}{2}\)
• Incorrect. Find a least common denominator and subtract; then simplify. The correct answer is \(\ \frac{1}{2}\).
• Incorrect. Simplify the fraction. The correct answer is \(\ \frac{1}{2}\).
• Incorrect. Subtract, don’t add, the fractions. The correct answer is \(\ \frac{1}{2}\)
• Correct. \(\ \frac{4}{6}-\frac{1}{6}=\frac{3}{6}=\frac{1}{2}\)

Subtracting Mixed Numbers

Subtracting mixed numbers works much the same way as adding mixed numbers. To subtract mixed numbers, subtract the whole number parts of the mixed numbers and then subtract the fraction parts in the mixed numbers. Finally, combine the whole number answer and the fraction answer to express the answer as a mixed number.

\(\ 6 \frac{4}{5}-3 \frac{1}{5}=3 \frac{3}{5}\)

Sometimes it might be easier to express the mixed number as an improper fraction first and then solve. Consider the example below.

\(\ 8 \frac{1}{3}-4 \frac{2}{3}=3 \frac{2}{3}\)

Since addition is the inverse operation of subtraction, you can check your answer to a subtraction problem with addition. In the example above, if you add \(\ 4 \frac{2}{3}\) to your answer of \(\ 3 \frac{2}{3}\), you should get \(\ 8 \frac{1}{3}\).

\(\ \begin{array}{r} 4 \frac{2}{3}+3 \frac{2}{3} \\ 4+3+\frac{2}{3}+\frac{2}{3} \\ 7+\frac{4}{3} \\ 7+1 \frac{1}{3} \\ 8 \frac{1}{3} \end{array}\)

Sometimes you have to find a common denominator in order to solve a mixed number subtraction problem.

\(\ 7 \frac{1}{2}-2 \frac{1}{3}=5 \frac{1}{6}\)

\(\ 9 \frac{4}{5}-4 \frac{2}{3}\)

Subtract. Simplify the answer and write it as a mixed number.

• \(\ \frac{2}{15}\)
• \(\ 5 \frac{2}{15}\)
• \(\ 4 \frac{7}{15}\)
• Incorrect. Subtract the whole numbers, too. The correct answer is \(\ 5 \frac{2}{15}\).
• Correct. \(\ 9-4=5\); \(\ \frac{4}{5}-\frac{2}{3}=\frac{12}{15}-\frac{10}{15}=\frac{2}{15}\). Combining them gives \(\ 5 \frac{2}{15}\).
• Incorrect. Subtract, don’t add, the fractions. The correct answer is \(\ 5 \frac{2}{15}\).
• Incorrect. Subtract the fractions as well as the whole numbers. The correct answer is \(\ 5 \frac{2}{15}\).

Subtracting Mixed Numbers with Regrouping

Sometimes when subtracting mixed numbers, the fraction part of the second mixed number is larger than the fraction part of the first number. Consider the problem: \(\ 7 \frac{1}{6}-3 \frac{5}{6}\). The standard procedure would be to subtract the fractions, but \(\ \frac{1}{6}-\frac{5}{6}\) would result in a negative number. You don’t want that! You can regroup one of the whole numbers from the first number, writing the first mixed number in a different way:

\(\ \begin{array}{l} 7 \frac{1}{6}=7+\frac{1}{6}=6+1+\frac{1}{6} \\ 6+\frac{6}{6}+\frac{1}{6}=6+\frac{7}{6}=6 \frac{7}{6} \end{array}\)

Now, you can write an equivalent problem to the original:

\(\ 6 \frac{7}{6}-3 \frac{5}{6}\)

Then, you just subtract like you normally subtract mixed numbers:

\(\ 6-3=3\)

\(\ \frac{7}{6}-\frac{5}{6}=\frac{2}{6}=\frac{1}{3}\)

So, the answer is \(\ 3 \frac{1}{3}\).

As with many fraction problems, you may need to find a common denominator. Remember that a key part of adding and subtracting fractions and mixed numbers is making sure to have a common denominator as a first step! In the example below, the original fractions do not have a like denominator. You need to find one before proceeding with the next steps.

\(\ 7 \frac{1}{5}-3 \frac{1}{4}=3 \frac{19}{20}\)

Sometimes a mixed number is subtracted from a whole number. In this case, you can also rewrite the whole number as a mixed number in order to perform the subtraction. You use an equivalent mixed number that has the same denominator as the fraction in the other mixed number.

\(\ 8-4 \frac{2}{5}=3 \frac{3}{5}\)

If the fractional part of the mixed number being subtracted is larger than the fractional part of the mixed number from which it is being subtracted, or if a mixed number is being subtracted from a whole number, follow these steps:

• Subtract 1 from the whole number part of the mixed number being subtracted.
• Add that 1 to the fraction part to make an improper fraction. For example: \(\ 7 \frac{2}{3}=6+\frac{3}{3}+\frac{2}{3}=6 \frac{5}{3}\)
• Then, subtract as with any other mixed numbers.

Alternatively, you can change both numbers to improper fractions and then subtract.

\(\ 15-13 \frac{1}{4}\) Subtract. Simplify the answer and write as a mixed number.

• \(\ 2 \frac{1}{4}\)
• \(\ 28 \frac{1}{4}\)
• \(\ 1 \frac{3}{4}\)
• \(\ 2 \frac{3}{4}\)
• Incorrect. This is the answer to \(\ 15 \frac{1}{4}-13\). The fraction has to be subtracted from the 15. The correct answer is \(\ 1 \frac{3}{4}\).
• Incorrect. Subtract, don’t add, the quantities. The correct answer is \(\ 1 \frac{3}{4}\).
• Correct. \(\ 14 \frac{4}{4}-13 \frac{1}{4}=1 \frac{3}{4}\)
• Incorrect. Subtract 1 from the whole number when rewriting it as a mixed number. The correct answer is \(\ 1 \frac{3}{4}\).

Subtracting Fractions and Mixed Numbers to Solve Problems

Knowing how to subtract fractions and mixed numbers is useful in a variety of situations. When reading problems, look for key words that indicate that the problem can be solved using subtraction.

Sherry loves to quilt, and she frequently buys fabric she likes when she sees it. She had purchased 5 yards of blue print fabric and decided to use \(\ 2 \frac{3}{8}\) yards of it in a quilt. How much of the blue print fabric will she have left over after making the quilt?

Sherry has \(\ 2 \frac{5}{8}\) yards of blue print fabric left over.

Pilar and Farouk are training for a marathon. On a recent Sunday, they both completed a run. Farouk ran \(\ 12 \frac{7}{8}\) miles and Pilar ran \(\ 14 \frac{3}{4}\) miles. How many more miles did Pilar run than Farouk?

Pilar ran \(\ 1 \frac{7}{8}\) miles more than Farouk.

Mike and Jose are painting a room. Jose used \(\ \frac{2}{3}\) of a can of paint and Mike used \(\ \frac{1}{2}\) of a can of paint. How much more paint did Jose use? Write the answer as a fraction of a can.

Jose used \(\ \frac{1}{6}\) of a can more paint than Mike.

Mariah’s sunflower plant grew \(\ 18 \frac{2}{3}\) inches in one week. Her tulip plant grew \(\ 3 \frac{3}{4}\) inches in one week. How many more inches did the sunflower grow in a week than the tulip?

• \(\ 22 \frac{5}{12}\) inches
• \(\ 15 \frac{1}{12}\) inches
• \(\ 15\) inches
• \(\ 14 \frac{11}{12}\) inches
• Incorrect. Subtract, don’t add, the fractions. The correct answer is \(\ 14 \frac{11}{12}\) inches.
• Incorrect. Subtract \(\ \frac{2}{3}-\frac{3}{4}\), not \(\ \frac{3}{4}-\frac{2}{3}\). The correct answer is \(\ 14 \frac{11}{12}\) inches.
• Incorrect. Subtract the fractions as well as the whole numbers in the mixed numbers. The correct answer is \(\ 14 \frac{11}{12}\) inches.
• Correct. \(\ 17 \frac{20}{12}-3 \frac{9}{12}=14 \frac{11}{12}\)

Subtracting fractions and mixed numbers combines some of the same skills as adding whole numbers and adding fractions and mixed numbers. When subtracting fractions and mixed numbers, first find a common denominator if the denominators are not alike, rewrite each fraction using the common denominator, and then subtract the numerators. When subtracting mixed numbers, if the fraction in the second mixed number is larger than the fraction in the first mixed number, rewrite the first mixed number by regrouping one whole as a fraction. Alternatively, rewrite all fractions as improper fractions and then subtract. This process is also used when subtracting a mixed number from a whole number.

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Adding Mixed Numbers Word Problems Worksheet

This downloadable worksheet is designed to practice word problems on adding mixed numbers..

Know more about Adding Mixed Numbers Word Problems Worksheet

Help your child become an expert in fractions with this worksheet. Students will strengthen their problem-solving ability by working with word problems on addition of mixed numbers in this worksheet. They will on a set of add to scenarios and find the unknown quantity. This worksheet will help your students learn addition of fractions in an efficient manner.

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Course: 4th grade   >   Unit 8

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improper fraction/mixed number word problems

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

Last updated

20 January 2015

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terible word porblems becuse i dont like it

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I was unfamiliar with the low, moderate, and high achiever acronym, but Google works.

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This is just what I was looking for, word problems for application. Thank you.

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