Adding Fractions with Like Denominators

To add fractions with like denominators we just add numerators (just like we add 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 sum.

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

$\frac{{1}}{{5}}+\frac{{2}}{{5}}=\frac{{{1}+{2}}}{{5}}=\frac{{3}}{{5}}$ .

Try to reduce fraction: $\frac{{3}}{{5}}$ is irreducible.

Answer: $\frac{{3}}{{5}}$ .

Next example.

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

$\frac{{3}}{{7}}+\frac{{5}}{{7}}=\frac{{{3}+{5}}}{{7}}=\frac{{8}}{{7}}$ .

Try to reduce fraction: $\frac{{8}}{{7}}$ is irreducible.

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

Next example.

Example 3. Find $\frac{{3}}{{22}}+{\left(-\frac{{5}}{{22}}\right)}$ .

$\frac{{3}}{{22}}+\frac{{5}}{{22}}=\frac{{{3}+{\left(-{5}\right)}}}{{22}}=-\frac{{2}}{{22}}$ .

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

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

Next example.

Example 4. Find $-\frac{{4}}{{7}}+\frac{{18}}{{7}}$ .

$-\frac{{4}}{{7}}+\frac{{18}}{{7}}=\frac{{-{4}+{18}}}{{7}}=\frac{{14}}{{7}}$ .

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

Answer: 2.

Next example.

Example 5. Find $\frac{{15}}{{15}}+\frac{{1}}{{15}}$ .

$\frac{{15}}{{15}}+\frac{{1}}{{15}}=\frac{{{15}+{1}}}{{15}}=\frac{{16}}{{15}}$ .

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: $\frac{{11}}{{7}}$ .

Next exercise.

Exercise 2. Find $\frac{{10}}{{9}}+\frac{{5}}{{9}}$ .

Answer: $\frac{{5}}{{3}}$ .

Next exercise.

Exercise 3. Find $\frac{{15}}{{8}}+{\left(-\frac{{7}}{{8}}\right)}$ .

Answer: 1.

Next exercise.

Exercise 4. Find $\frac{{11}}{{10}}+\frac{{14}}{{10}}$ .

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

Next exercise.

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

Answer: $-\frac{{1}}{{2}}$ .