Addition of Fractions

To add two fractions, first give them a common denominator, then add the numerators. For mixed numbers, convert to an improper fraction first (or add the whole-number parts and fractional parts separately). Here are a few worked practice questions.

1. Painting a wall together

Shubham painted $\dfrac{2}{3}$ of the wall space in his room. His sister Madhavi helped and painted $\dfrac{1}{3}$ of the wall space. How much did they paint together?

Solution: $\dfrac{2}{3} + \dfrac{1}{3} = \dfrac{3}{3} = 1$. Together they painted the whole wall.

2. Sharing cake

Naina was given $1\dfrac{1}{2}$ pieces of cake and Najma was given $1\dfrac{1}{3}$ pieces of cake. Find the total amount of cake given to both of them.

Solution: Convert to improper fractions: $1\dfrac{1}{2} = \dfrac{3}{2}$ and $1\dfrac{1}{3} = \dfrac{4}{3}$. With a common denominator of 6: $\dfrac{3}{2} = \dfrac{9}{6}$ and $\dfrac{4}{3} = \dfrac{8}{6}$, so $\dfrac{9}{6} + \dfrac{8}{6} = \dfrac{17}{6} = 2\dfrac{5}{6}$ pieces of cake in total.

3. Buying ribbon

Sarita bought $\dfrac{2}{5}$ meter of ribbon and Lalita bought $\dfrac{3}{4}$ meter of ribbon. What is the total length of ribbon they bought?

Solution: With a common denominator of 20: $\dfrac{2}{5} = \dfrac{8}{20}$ and $\dfrac{3}{4} = \dfrac{15}{20}$, so $\dfrac{8}{20} + \dfrac{15}{20} = \dfrac{23}{20} = 1\dfrac{3}{20}$ meters of ribbon.

4. Find the missing number

$? - \dfrac{5}{8} = \dfrac{1}{4}$

Solution: Rearranging, $? = \dfrac{1}{4} + \dfrac{5}{8} = \dfrac{2}{8} + \dfrac{5}{8} = \dfrac{7}{8}$.

5. Find the missing number

$? - \dfrac{1}{5} = \dfrac{1}{2}$

Solution: Rearranging, $? = \dfrac{1}{2} + \dfrac{1}{5} = \dfrac{5}{10} + \dfrac{2}{10} = \dfrac{7}{10}$.