# How to Subtract Fractions from Whole Numbers

Laura Foist, Julie Zundel, Robert Ferdinand
• Author
Laura Foist

Laura has a Masters of Science in Food Science and Human Nutrition and has taught college Science.

• Instructor
Julie Zundel

Julie has taught high school Zoology, Biology, Physical Science and Chem Tech. She has a Bachelor of Science in Biology and a Master of Education.

• Expert Contributor
Robert Ferdinand

Robert Ferdinand has taught university-level mathematics, statistics and computer science from freshmen to senior level. Robert has a PhD in Applied Mathematics.

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

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## Whole Numbers, Fractions, and Mixed Numbers

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}

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## How to Subtract Fractions with Whole Numbers

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.

### Example 1: Subtracting Fractions with Whole Numbers

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}

### Example 2: Adding Fractions with Whole Numbers

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}

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## Subtracting Fractions from Whole Numbers: Additional Problems

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.

### Solutions

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.

• 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.

• 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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