Subtracting Fractions with Like Denominators
Related calculator: Fractions Calculator
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: $$$-\frac{{7}}{{2}}$$$.