# Subtracting Fractions with Whole Numbers

## Related calculator: Fractions Calculator

Subtracting fractions with whole numbers doesn't differ much from adding fractions with whole numbers (just remember how to subtract integers correctly).

Indeed, suppose we want to subtract whole number ${m}$ from fraction $\frac{{n}}{{q}}$.

It is known that whole number ${m}$ can be represented as fraction $\frac{{m}}{{1}}$.

Now, ${m}-\frac{{n}}{{q}}=\frac{{m}}{{1}}-\frac{{n}}{{q}}=\frac{{{m}{q}}}{{q}}-\frac{{n}}{{q}}=\frac{{{m}{q}-{n}}}{{q}}$.

Formula for subtracting fractions with whole numbers: ${\color{green}{{{m}-\frac{{n}}{{q}}=\frac{{{m}{q}-{n}}}{{q}}}}}$.

Example 1. Find ${3}-\frac{{6}}{{7}}$.

Let's solve it step-by-step:

${3}+\frac{{6}}{{7}}=\frac{{3}}{{1}}-\frac{{6}}{{7}}=\frac{{{3}\cdot{\color{red}{{{7}}}}}}{{{1}\cdot{\color{red}{{{7}}}}}}-\frac{{6}}{{7}}=\frac{{21}}{{7}}-\frac{{6}}{{7}}=\frac{{15}}{{7}}$.

If you need mixed number, convert $\frac{{15}}{{7}}$ into midex number: $\frac{{15}}{{7}}={2}\frac{{1}}{{7}}$.

Answer: $\frac{{15}}{{7}}={2}\frac{{1}}{{7}}$.

Next example.

Example 2. Find $-{9}-\frac{{13}}{{8}}$.

Let's use direct formula:

$-{9}-\frac{{13}}{{8}}=\frac{{-{9}\cdot{8}-{13}}}{{8}}=\frac{{-{72}-{13}}}{{8}}=-\frac{{85}}{{8}}$.

Convert to mixed number if needed: $-\frac{{85}}{{8}}=-{10}\frac{{5}}{{8}}$

Answer: $-\frac{{85}}{{8}}=-{10}\frac{{5}}{{8}}$.

Next example.

Example 3. Find $-\frac{{9}}{{4}}-{3}$.

$-\frac{{9}}{{4}}-{3}=-\frac{{9}}{{4}}-\frac{{{3}\cdot{\color{red}{{{4}}}}}}{{{1}\cdot{\color{red}{{{4}}}}}}=-\frac{{9}}{{4}}-\frac{{12}}{{4}}=\frac{{-{9}-{12}}}{{4}}=-\frac{{21}}{{4}}$.

Convert to mixed fraction if needed: $-\frac{{21}}{{4}}=-{5}\frac{{1}}{{4}}$.

Answer: $-\frac{{21}}{{4}}=-{5}\frac{{1}}{{4}}$.

Now, it is time to practice.

Exercise 1. Find ${2}-\frac{{6}}{{7}}$.

Answer: $\frac{{8}}{{7}}={1}\frac{{1}}{{7}}$.

Next exercise.

Exercise 2. Find $\frac{{29}}{{5}}-{9}$.

Answer: $-\frac{{16}}{{5}}=-{3}\frac{{1}}{{5}}$.

Next exercise.

Exercise 3. Find ${5}-{\left(-\frac{{97}}{{8}}\right)}$.

Answer: $\frac{{135}}{{8}}={16}\frac{{7}}{{8}}$.