# Addition of Like Fractions

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

1. 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

$$\frac{3}{7}$$ + $$\frac{2}{7}$$

= $$\frac{3 + 2}{7}$$

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

Addition of Fractions with the Same (Like) Denominator

2. Observe the following figures:

What do we observe?

In the first figure $$\frac{1}{4}$$of the circle is shaded and in the second figure $$\frac{2}{4}$$ of the circle is shaded.

In all, we have Hence 3/4 of the circle is shaded.

$$\frac{1}{4}$$ + $$\frac{2}{4}$$ = $$\frac{1 + 2}{4}$$ = $$\frac{3}{4}$$

Thus, to add the fractions with the same denominator, we simply add their numerators and write the common denominator.

Sum of the fractions with like denominators = $$\frac{\textrm{Sum of the Numerators}}{\textrm{Common Denominator}}$$

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 $$\frac{11}{105}$$.

= $$\frac{31}{105}$$ + $$\frac{41}{105}$$ + $$\frac{11}{105}$$.

= $$\frac{31 + 41 + 11}{105}$$

= $$\frac{83}{105}$$

7. Find the sum of $$\frac{3}{7}$$ and $$\frac{2}{7}$$

Solution:

$$\frac{3}{7}$$ + $$\frac{2}{7}$$ = $$\frac{3 + 2}{7}$$ = $$\frac{5}{7}$$

2. Find the sum of $$\frac{1}{15}$$, $$\frac{4}{15}$$, $$\frac{7}{15}$$

Solution:

$$\frac{1}{15}$$ + $$\frac{4}{15}$$ + $$\frac{7}{15}$$ = $$\frac{1 + 4 + 7}{15}$$ = $$\frac{12}{15}$$

Worksheet 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$$\frac{7}{11}$$

2. Find the sum:

(i) $$\frac{1}{9}$$ + $$\frac{4}{9}$$

(ii) $$\frac{1}{4}$$ + $$\frac{2}{4}$$

(iii) $$\frac{5}{21}$$ + $$\frac{8}{21}$$

(iv) $$\frac{4}{15}$$ + $$\frac{7}{15}$$

(v) $$\frac{7}{16}$$ + $$\frac{8}{16}$$

(vi) $$\frac{13}{19}$$ + $$\frac{2}{19}$$

Answer:

2. (i) $$\frac{5}{9}$$

(ii) $$\frac{3}{4}$$

(iii) $$\frac{13}{21}$$

(iv) $$\frac{11}{15}$$

(v) $$\frac{15}{16}$$

(vi) $$\frac{15}{19}$$

3. Using the figures, fill in the blanks:

 (i) $$\frac{1}{8}$$ + $$\frac{2}{8}$$ = $$\frac{--- + ---}{8}$$ = $$\frac{---}{8}$$ (ii) $$\frac{1}{5}$$ + $$\frac{2}{5}$$ = $$\frac{--- + ---}{5}$$ = $$\frac{---}{5}$$ (iii) $$\frac{1}{8}$$ + $$\frac{2}{8}$$ + $$\frac{2}{8}$$ = $$\frac{--- + --- + ---}{8}$$ = $$\frac{---}{8}$$ (iv) $$\frac{2}{7}$$ + $$\frac{4}{7}$$ = $$\frac{--- + ---}{7}$$ = $$\frac{---}{7}$$

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