## Table of Contents

- Whole Numbers, Fractions, and Mixed Numbers
- How to Subtract Fractions with Whole Numbers
- How to Subtract Mixed Fractions with Whole Numbers
- Lesson Summary

Learn how to subtract fractions with whole numbers and how to subtract mixed fractions with whole numbers. Compare that to adding fractions with whole numbers.
Updated: 08/24/2021

- Whole Numbers, Fractions, and Mixed Numbers
- How to Subtract Fractions with Whole Numbers
- How to Subtract Mixed Fractions with Whole Numbers
- Lesson Summary

A **whole number** is an integer with no fractions such as 0, 1, 2, 3, etc. A **fraction** is a number that shows how many parts of a whole number it is by having a **numerator** (the top number) and a **denominator** (the bottom number). For example:

- {eq}\frac{2}{7} {/eq}

Fractions include numbers higher than 1:

- {eq}\frac{9}{2} {/eq}

A whole number can be shown as a fraction, and simplified down as a whole number. For example:

- {eq}\frac{10}{5}=2 {/eq}

If a fraction that is higher than 1 cannot be simplified down to a whole number, it can also be shown as a mixed number. A **mixed number** is a combination of a whole number with a fraction:

- {eq}\frac{11}{3}=3\frac{2}{3} {/eq}

Whole numbers, fractions, and mixed numbers can all be added and subtracted from each other:

- {eq}6-\frac{4}{5}=5\frac{1}{5} {/eq}

- {eq}25+\frac{7}{3}=25\frac{7}{3}=27\frac{1}{3} {/eq}

- {eq}14-11\frac{2}{9}=3\frac{2}{9} {/eq}

- {eq}158+54\frac{25}{64}=212\frac{25}{64} {/eq}

Let's look further at how to do this.

When subtracting fractions from whole numbers, it is easiest to first convert the whole number into a fraction, where the denominator is the same as in the fraction. Then the two fractions can be added together by adding the numerators together and keeping the denominators the same. Finally, convert the fraction into a mixed number.

When adding fractions and whole numbers, the same process can be done. Simply combine the fraction and whole number into a mixed number. If the fraction is over 1, convert it into a mixed number. Add the two whole number integers together, and combine the fraction with it to make the final mixed number.

Look at the following computation:

{eq}12-\frac{2}{8} {/eq}

Step 1: convert the whole number into a fraction with the same denominator as the fraction. The denominator in this fraction is 8. So, 12 needs to be converted into a fraction with a denominator of 8. In order to do this multiply the whole number by the desired denominator:

- {eq}12\times 8=96 {/eq}

This number is the numerator, making the fraction: {eq}\frac{96}{8} {/eq}

Step 2: Subtract the two fractions

The new equation looks like: {eq}\frac{96}{8}-\frac{2}{8} {/eq}

When adding and subtracting fractions with the same denominator, the denominator stays the same, and the numerators are subtracted:

- Subtract the numerators: {eq}96-2=94 {/eq}

- The total: {eq}\frac{94}{8} {/eq}

Step 3: Make the fraction into a mixed number. In order to do this, divide the numerator by the denominator:

{eq}94\div8=11.75 {/eq}

The whole number is 11 (the number before the decimal place). To find how much is left in the fraction, multiply the whole number by the denominator, then subtract from the original numerator:

- {eq}11\times 8 = 88 {/eq}

- {eq}94-88=6 {/eq}

- Final mixed number: {eq}11\frac{6}{8} {/eq}

When adding fractions and whole numbers, the process differs if the fraction being added is over 1 or under 1. If the fraction is over 1, convert it into a mixed fraction and see the section on adding mixed fractions and whole numbers. If the fraction is under 1, the whole number and fraction can be combined to form a mixed fraction:

- {eq}5+\frac{3}{4}=5\frac{3}{4} {/eq}

- {eq}26+\frac{31}{32}=26\frac{31}{32} {/eq}

- {eq}154+\frac{2}{3}=154\frac{2}{3} {/eq}

To subtract mixed fractions and whole numbers, all the numbers need to be changed into a fraction with the same denominators, and then the numerators can be subtracted and converted back into a mixed fraction. This same method can also be used to add mixed fractions and whole numbers. Another way to add mixed fractions and whole numbers is by adding the whole number with the number in front of the fraction on the mixed fraction, and then the fraction is combined with the sum to form a new mixed fraction.

Let's start with the subtraction problem: {eq}29-5\frac{2}{13} {/eq}

First, since the fraction in the mixed number has a denominator of 13, all the fractions need to have a denominator of 13. Let's first change the mixed number into a fraction, with the denominator of 13.

- Multiply the number in front of the fraction by the desired denominator: {eq}13\times5=65 {/eq}

- Add the numerator to the product: {eq}65+2=67 {/eq}

- Write the new fraction: {eq}\frac{67}{13} {/eq}

Next, change the whole number into a fraction with a denominator of 13:

- Multiply the whole number by the desired denominator: {eq}29\times13=377 {/eq}

- Make the fraction: {eq}\frac{377}{13} {/eq}

Next, set up the new problem with the fractions:

- {eq}\frac{377}{13}-\frac{67}{13} {/eq}

Subtract the numerators, keeping the denominators the same:

- {eq}\frac{377-67}{13}=\frac{310}{13} {/eq}

Make into a mixed fraction:

- Divide numerator by denominator:{eq}310\div 13=23.846 {/eq}

- Multiply resulting whole number by denominator: {eq}23\times13=299 {/eq}

- Subtract product from original numerator: {eq}310-299=11 {/eq}, this is the new numerator

- Make new mixed fraction: {eq}23\frac{11}{13} {/eq}

Adding mixed fractions and whole numbers can be done in the same way as with subtraction. Or the whole numbers can be added together with the fraction attached to create a new mixed fraction:

- {eq}6\frac{15}{28}+12=18\frac{15}{28} {/eq}

- {eq}24\frac{3}{5}+4=28\frac{3}{5} {/eq}

- {eq}2\frac{1}{2}+5=y\frac{1}{2} {/eq}

**Fractions** and **whole numbers** can be added together and subtracted from each other by:

- Making all numbers a fraction with the same
**denominator**- Multiplying whole number by desired denominator; this is the
**numerator**for that fraction - Typically choosing the denominator that is already in the fraction

- Multiplying whole number by desired denominator; this is the
- Adding or subtracting the numerators, keeping the denominator the same
- When adding and subtracting fractions with the same denominator, the denominator stays the same and the numerators are added or subtracted

- Simplifying into a new mixed fraction

When subtracting whole numbers and mixed fractions, first change the mixed fraction into a fraction, and then follow the same steps as above. Addition of fractions can occur in the same method as with subtraction, but it can also be simplified by just combining the whole number and the fraction into a mixed fraction.

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Additional Activities

**1.** Subtract the fraction 7/8 from the whole number 7.

**2.** Subtract the mixed fraction 1 and 5/6 from the whole number 9.

**3.** Subtract 10 minus the fraction 10/11.

**4.** From the whole number 13, subtract the mixed fraction 4 and 5/7.

**1.** Convert the whole number 7 to a fraction (7/1) with denominator 8 to match the fraction being subtracted as follows:

(7 x 8)/(1 x 8) = 56/8.

Now perform your subtraction:

- 7 - 7/8
- 56/8 - 7/8
- (56 - 7)/8
- 49/8 = 6 and 1/8

Note: Here we only subtract the numerators since we have a common denominator (8) and leave the denominator alone.

**2.** Convert the mixed fraction to an improper fraction as follows: 1 and 5/6 = 11/6.

Convert the whole number 9 to a fraction (9/1) with denominator 6 to match the fraction being subtracted as follows:

(9 x 6)/(1 x 6) = 54/6.

Perform the subtraction as follows:

- 9 - (1 and 5/6)
- 54/6 - 11/6
- (54 - 11)/6
- 43/6 = 7 and 1/6

Note: Here we only subtract the numerators since we have a common denominator and leave the denominator alone.

**3.** Convert the whole number 10 to a fraction (10/1) with denominator 11 to match the fraction being subtracted as follows:

(10 x 11)/(1 x 11) = 110/11.

Now perform your subtraction:

- 10 - 10/11
- 110/11 - 10/11
- (110 - 10)/11
- 100/11 = 9 and 1/11

Note: Here we only subtract the numerators since we have a common denominator (11) and leave the denominator alone.

**4.** Convert the mixed fraction to an improper fraction as follows: 4 and 5/7 = 33/7.

Convert the whole number 13 to a fraction (13/1) with denominator 7 to match the fraction being subtracted as follows:

(13 x 7)/(1 x 7) = 91/7.

Perform the subtraction as follows:

- 13 - (4 and 5/7)
- 91/7 - 33/7
- (91 - 33)/7
- 58/7 = 8 and 2/7

Note: Here we only subtract the numerators since we have a common denominator 7 and leave the denominator alone.

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