Subtracting Fractions with Like Denominators

To subtract fractions with like denominators we just subtract numerators (just like we subtract integers) and denominator leave the same: ${\color{red}{{\frac{{a}}{{c}}-\frac{{b}}{{c}}=\frac{{{a}-{b}}}{{c}}}}}$ .

It is possible that you need to reduce fraction after finding difference.

Example 1. Find $\frac{{2}}{{5}}-\frac{{1}}{{5}}$ .

$\frac{{2}}{{5}}-\frac{{1}}{{5}}=\frac{{{2}-{1}}}{{5}}=\frac{{1}}{{5}}$ .

Try to reduce fraction: $\frac{{1}}{{5}}$ is irreducible.

Answer: $\frac{{1}}{{5}}$ .

Next example.

Example 2. Find $\frac{{3}}{{7}}-\frac{{5}}{{7}}$ .

$\frac{{3}}{{7}}-\frac{{5}}{{7}}=\frac{{{3}-{5}}}{{7}}=-\frac{{2}}{{7}}$ .

Try to reduce fraction: $-\frac{{2}}{{7}}$ is irreducible.

Answer: $-\frac{{2}}{{7}}$ .

Next example.

Example 3. Find $\frac{{3}}{{22}}-\frac{{5}}{{22}}$ .

$\frac{{3}}{{22}}-\frac{{5}}{{22}}=\frac{{{3}-{5}}}{{22}}=-\frac{{2}}{{22}}$ .

Try to reduce fraction: $-\frac{{2}}{{22}}=-\frac{{1}}{{11}}$ .

Answer: $-\frac{{1}}{{11}}$ .

Next example.

Example 4. Find $-\frac{{4}}{{7}}-\frac{{10}}{{7}}$ .

$-\frac{{4}}{{7}}-\frac{{10}}{{7}}=\frac{{-{4}-{10}}}{{7}}=-\frac{{14}}{{7}}$ .

Try to reduce fraction: $-\frac{{14}}{{7}}=-{2}$ .

Answer: -2.

Next example.

Example 5. Find $\frac{{15}}{{15}}-{\left(-\frac{{1}}{{15}}\right)}$ .

$\frac{{15}}{{15}}-{\left(-\frac{{1}}{{15}}\right)}=\frac{{15}}{{15}}+\frac{{1}}{{15}}=\frac{{{15}+{1}}}{{15}}=\frac{{16}}{{15}}$ .

Try to reduce fraction: $\frac{{16}}{{15}}$ is irreducible.

Answer: $\frac{{16}}{{15}}$ .

Now, it is time to do some exercises.

Exercise 1. Find $\frac{{6}}{{7}}-\frac{{5}}{{7}}$ .

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

Next exercise.

Exercise 2. Find $\frac{{8}}{{9}}-\frac{{5}}{{9}}$ .

Answer: $\frac{{1}}{{3}}$ .

Next exercise.

Exercise 3. Find $-\frac{{5}}{{8}}+\frac{{3}}{{8}}$ .

Answer: $-\frac{{1}}{{4}}$ .

Next exercise.

Exercise 4. Find $\frac{{11}}{{10}}-{\left(-\frac{{14}}{{10}}\right)}$ .

Answer: $\frac{{5}}{{2}}$ .

Next exercise.

Exercise 5. Find $-\frac{{4}}{{2}}-\frac{{3}}{{2}}$ .

Answer: $-\frac{{7}}{{2}}$ .