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) 

\(\frac{2}{7}\) + \(\frac{4}{7}\) = \(\frac{ + }{7}\) = \(\frac{}{7}\) 
4th Grade Math Activities
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