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Adding and Subtracting Fractions

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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.


  • 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?

adding and subtracting fractions

 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

  1.  \frac{5}{4}- \frac{6}{7}
  2. 4\frac{1}{5}- 2\frac{1}{4}
  3. 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?
  4. 2\frac{2}{7}+ \frac{2}{3}
  5. 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
  1. \frac{11}{28}
  2. 1\frac{19}{20}
  3. \frac{94}{63} or 1\frac{31}{63} mile
  4. \frac{20}{21}
  5. \frac{17}{8} or 2\frac{1}{8} cups

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