Adding and Subtracting Fractions

Grade 7 Math Worksheets

What are the rules to adding and subtracting fractions?

$adding and subtracting fractions$

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How do you add and subtract fractions with like denominators?

Like fractions are those whose denominators are the same. Like, $\frac{3}{14}$ and $\frac{5}{14}$ have the same denominators.

For adding like fractions, simply add the numerators.

$\frac{3}{14}$ + $\frac{5}{14}$ = $\frac{3+5}{14}$ = $\frac{8}{14}$

Reduce the fraction or simplify the answer
$\frac{8}{14}$ = $\frac{8/2}{14/2}$ = $\frac{4}{7}$

Example : $\frac{8}{7}$ – (- $\frac{8}{7}$ )

$\frac{8}{7}$ – (- $\frac{8}{7}$ )= $\frac{8-(-8))}{7}$ = $\frac{8+8}{7}$ = $\frac{16}{7}$

Example: In Sharon’s wardrobe, $\frac{2}{5}$ th of the woollen clothes are grey and $\frac{1}{5}$ th of the woollen clothes are pink. What fraction of woollen clothes are either grey or pink?

Solution: Fraction of clothes that are either grey or pink = $\frac{2}{5}$ + $\frac{1}{5}$ =

$\frac{2+1}{5}$ = $\frac{3}{5}$ (Answer)

How do you add and subtract fractions with different denominators?

In unlike fractions, denominators of fractions are not the same. Like, $\frac{3}{8}and$ $\frac{7}{9}$ and have different denominators.

So, if two fractions $\frac{p}{q}and$ $\frac{r}{s}$ have different denominators, we can follow these steps to subtract them:

$\frac{p}{q}$ – $\frac{r}{s}$ = $\frac{p*s-r*q}{q*s}$

Example: $\frac{3}{5}$ + $\frac{5}{4}$

$\frac{3}{5}$ + $\frac{5}{4}$ = $\frac{3*4+5*5}{5*4}$ = $\frac{12 + 25}{20}$ = $\frac{37}{20}$

Example: 6 $\frac{2}{3}-$ 1 $\frac{3}{4}$

6 $\frac{2}{3}-1$ $\frac{3}{4}$ = $\frac{20}{3}-$ $\frac{7}{4}$ = $\frac{20\times4-7\times3}{3\times4}$ = $\frac{80-21}{12}$ = $\frac{59}{12}$ = $4\frac{11}{12}$

Check Point

$\frac{5}{4}-$ $\frac{6}{7}$
4 $\frac{1}{5}-$ 2 $\frac{1}{4}$
Pamela walked $\frac{7}{9}$ of a mile. Then she jogged for $\frac{5}{7}$ of a mile. How much distance did she covered altogether?
2 $\frac{2}{7}+$ $\frac{2}{3}$
Linda used 1 $\frac{3}{8}$ cups of flour to make chocolate cake and $\frac{3}{4}$ cup flour to make cookies. How much cups of flour did she use in all?

Answer key

$\frac{11}{28}$
1 $\frac{19}{20}$
$\frac{94}{63}$ or 1 $\frac{31}{63}$ mile
2 $\frac{20}{21}$
$\frac{17}{8}$ or 2 $\frac{1}{8}$ cups

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