Adding Fractions with Like Denominators

Related calculator: Fractions Calculator

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