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 

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

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

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

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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)

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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)		$\frac{2}{7}$ + $\frac{4}{7}$ = $\frac{--- + ---}{7}$ = $\frac{---}{7}$

4th Grade Math Activities

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