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: ac+bc=a+bc{\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 15+25\frac{{1}}{{5}}+\frac{{2}}{{5}}.

15+25=1+25=35\frac{{1}}{{5}}+\frac{{2}}{{5}}=\frac{{{1}+{2}}}{{5}}=\frac{{3}}{{5}}.

Try to reduce fraction: 35\frac{{3}}{{5}} is irreducible.

Answer: 35\frac{{3}}{{5}}.

Next example.

Example 2. Find 37+57\frac{{3}}{{7}}+\frac{{5}}{{7}}.

37+57=3+57=87\frac{{3}}{{7}}+\frac{{5}}{{7}}=\frac{{{3}+{5}}}{{7}}=\frac{{8}}{{7}}.

Try to reduce fraction: 87\frac{{8}}{{7}} is irreducible.

Answer: 87\frac{{8}}{{7}}.

Next example.

Example 3. Find 322+(522)\frac{{3}}{{22}}+{\left(-\frac{{5}}{{22}}\right)}.

322+522=3+(5)22=222\frac{{3}}{{22}}+\frac{{5}}{{22}}=\frac{{{3}+{\left(-{5}\right)}}}{{22}}=-\frac{{2}}{{22}}.

Try to reduce fraction: 222=111-\frac{{2}}{{22}}=-\frac{{1}}{{11}}.

Answer: 111-\frac{{1}}{{11}}.

Next example.

Example 4. Find 47+187-\frac{{4}}{{7}}+\frac{{18}}{{7}}.

47+187=4+187=147-\frac{{4}}{{7}}+\frac{{18}}{{7}}=\frac{{-{4}+{18}}}{{7}}=\frac{{14}}{{7}}.

Try to reduce fraction: 147=2\frac{{14}}{{7}}={2}.

Answer: 2.

Next example.

Example 5. Find 1515+115\frac{{15}}{{15}}+\frac{{1}}{{15}}.

1515+115=15+115=1615\frac{{15}}{{15}}+\frac{{1}}{{15}}=\frac{{{15}+{1}}}{{15}}=\frac{{16}}{{15}}.

Try to reduce fraction: 1615\frac{{16}}{{15}} is irreducible.

Answer: 1615\frac{{16}}{{15}}.

Now, it is time to do some exercises.

Exercise 1. Find 67+57\frac{{6}}{{7}}+\frac{{5}}{{7}}.

Answer: 117\frac{{11}}{{7}}.

Next exercise.

Exercise 2. Find 109+59\frac{{10}}{{9}}+\frac{{5}}{{9}}.

Answer: 53\frac{{5}}{{3}}.

Next exercise.

Exercise 3. Find 158+(78)\frac{{15}}{{8}}+{\left(-\frac{{7}}{{8}}\right)}.

Answer: 1.

Next exercise.

Exercise 4. Find 1110+1410\frac{{11}}{{10}}+\frac{{14}}{{10}}.

Answer: 52\frac{{5}}{{2}}.

Next exercise.

Exercise 5. Find 42+32-\frac{{4}}{{2}}+\frac{{3}}{{2}}.

Answer: 12-\frac{{1}}{{2}}.