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: acbc=abc{\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 2515\frac{{2}}{{5}}-\frac{{1}}{{5}}.

2515=215=15\frac{{2}}{{5}}-\frac{{1}}{{5}}=\frac{{{2}-{1}}}{{5}}=\frac{{1}}{{5}}.

Try to reduce fraction: 15\frac{{1}}{{5}} is irreducible.

Answer: 15\frac{{1}}{{5}}.

Next example.

Example 2. Find 3757\frac{{3}}{{7}}-\frac{{5}}{{7}}.

3757=357=27\frac{{3}}{{7}}-\frac{{5}}{{7}}=\frac{{{3}-{5}}}{{7}}=-\frac{{2}}{{7}}.

Try to reduce fraction: 27-\frac{{2}}{{7}} is irreducible.

Answer: 27-\frac{{2}}{{7}}.

Next example.

Example 3. Find 322522\frac{{3}}{{22}}-\frac{{5}}{{22}}.

322522=3522=222\frac{{3}}{{22}}-\frac{{5}}{{22}}=\frac{{{3}-{5}}}{{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 47107-\frac{{4}}{{7}}-\frac{{10}}{{7}}.

47107=4107=147-\frac{{4}}{{7}}-\frac{{10}}{{7}}=\frac{{-{4}-{10}}}{{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}}-{\left(-\frac{{1}}{{15}}\right)}.

1515(115)=1515+115=15+115=1615\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: 1615\frac{{16}}{{15}} is irreducible.

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

Now, it is time to do some exercises.

Exercise 1. Find 6757\frac{{6}}{{7}}-\frac{{5}}{{7}}.

Answer: 17\frac{{1}}{{7}}.

Next exercise.

Exercise 2. Find 8959\frac{{8}}{{9}}-\frac{{5}}{{9}}.

Answer: 13\frac{{1}}{{3}}.

Next exercise.

Exercise 3. Find 58+38-\frac{{5}}{{8}}+\frac{{3}}{{8}}.

Answer: 14-\frac{{1}}{{4}}.

Next exercise.

Exercise 4. Find 1110(1410)\frac{{11}}{{10}}-{\left(-\frac{{14}}{{10}}\right)}.

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

Next exercise.

Exercise 5. Find 4232-\frac{{4}}{{2}}-\frac{{3}}{{2}}.

Answer: 72-\frac{{7}}{{2}}.