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 \(\frac{2}{7}\).

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

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

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

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

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

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

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 \(\frac{8}{29}\).

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

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

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

More Examples on Addition of Like Fractions:

(Fractions having same denominator)

4. Add \(\frac{5}{17}\) + \(\frac{4}{17}\)

Solution:

\(\frac{5}{17}\) + \(\frac{4}{17}\)

= \(\frac{5 + 4}{17}\)

= \(\frac{9}{17}\)  (in lowest terms)

5. Add \(\frac{3}{23}\) + \(\frac{13}{23}\) + \(\frac{4}{23}\)

Solution:

\(\frac{3}{23}\) + \(\frac{13}{23}\) + \(\frac{4}{23}\)

= \(\frac{3 + 13 + 4}{23}\)

= \(\frac{20}{23}\)  (in lowest terms)

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

Solution:

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

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

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

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

Questions and Answers on Addition of Like Fractions:

1. Add the following Like Fractions:

(i) \(\frac{2}{5}\) + \(\frac{3}{5}\)

(ii) \(\frac{1}{8}\) + \(\frac{3}{8}\) + \(\frac{7}{8}\)

(iii) \(\frac{11}{23}\) + \(\frac{10}{23}\) + \(\frac{5}{23}\)

(iv) \(\frac{2}{10}\) + \(\frac{1}{10}\) + \(\frac{3}{10}\)

(v) \(\frac{5}{11}\) + \(\frac{7}{11}\) + \(\frac{4}{11}\) + \(\frac{2}{11}\)

Answer:

1. (i) 1

(ii) 1\(\frac{3}{8}\)

(iii) 1\(\frac{3}{23}\) 

(iv) \(\frac{3}{5}\) 

(v) 1\(\frac{7}{11}\) 

4th Grade Math Activities

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