# 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) $$\frac{5}{11}$$ + $$\frac{7}{11}$$ + $$\frac{4}{11}$$ + $$\frac{2}{11}$$

1. (i) 1

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

(iii) 1$$\frac{3}{23}$$

(iv) $$\frac{3}{5}$$

(v) 1$$\frac{7}{11}$$