Addition of Like Fractions

To add two or more like fractions we simplify add their numerators. The denominator remains same.

Let us find the sum of two fractions \(\frac{3}{7}\) and \(\frac{2}{7}\).

3 by 7

\(\frac{3}{7}\) is colored green.


2 by 7

\(\frac{2}{7}\) is colored yellow.

\(\frac{3}{7}\) + \(\frac{2}{7}\) is represented by 

5 by 7

\(\frac{3}{7}\) + \(\frac{2}{7}\)

= \(\frac{3 + 2}{7}\)

= \(\frac{5}{7}\) = \(\frac{\textrm{Sum of Numerators}}{\textrm{Common Denominator}}\)


Solved Examples on Addition of Like Fractions:

1. Find the sum of \(\frac{1}{9}\) and \(\frac{4}{9}\).

Solution:

Sum of \(\frac{1}{9}\) and \(\frac{4}{9}\)

= \(\frac{1}{9}\) + \(\frac{4}{9}\)

= \(\frac{1 + 4}{9}\)

= \(\frac{5}{9}\)


2. Find the sum of \(\frac{7}{27}\) and \(\frac{9}{27}\).

Solution:

Sum of \(\frac{7}{27}\) and \(\frac{9}{27}\)

= \(\frac{7}{27}\) + \(\frac{9}{27}\)

= \(\frac{7 + 9}{27}\)

= \(\frac{16}{27}\)


3. Find the sum of \(\frac{4}{29}\), \(\frac{5}{29}\) and \(\frac{8}{29}\).

Solution:

Sum of \(\frac{4}{29}\), \(\frac{5}{29}\) and \(\frac{8}{29}\).

= \(\frac{4}{29}\) + \(\frac{5}{29}\) + \(\frac{8}{29}\)

= \(\frac{4 + 5 + 8}{29}\)

= \(\frac{17}{29}\)

Addition of Like Fractions

4. Find the sum of \(\frac{31}{105}\), \(\frac{41}{105}\) and \(\frac{11}{105}\).

Solution:

Sum of \(\frac{31}{105}\), \(\frac{41}{105}\) and \(\frac{11}{105}\).

= \(\frac{31}{105}\) + \(\frac{41}{105}\) + \(\frac{11}{105}\).

= \(\frac{31 + 41 + 11}{105}\)

= \(\frac{83}{105}\)

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