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

Arjun painted $\dfrac{3}{8}$ of a classroom wall in the morning, and his friend Meera painted another $\dfrac{1}{4}$ of it in the afternoon. How much of the wall did they paint together?

Solution: With a common denominator of 8, $\dfrac{1}{4} = \dfrac{2}{8}$, so $\dfrac{3}{8} + \dfrac{2}{8} = \dfrac{5}{8}$. Together they painted five-eighths of the wall, leaving $\dfrac{3}{8}$ still to do.

2. Sharing cake

At a party, Kabir ate $2\dfrac{1}{4}$ slices of cake and Riya ate $1\dfrac{2}{3}$ slices. How much cake did the two of them eat altogether?

Solution: Convert to improper fractions: $2\dfrac{1}{4} = \dfrac{9}{4}$ and $1\dfrac{2}{3} = \dfrac{5}{3}$. With a common denominator of 12: $\dfrac{9}{4} = \dfrac{27}{12}$ and $\dfrac{5}{3} = \dfrac{20}{12}$, so $\dfrac{27}{12} + \dfrac{20}{12} = \dfrac{47}{12} = 3\dfrac{11}{12}$ slices of cake in total.

3. Buying ribbon

For a craft project, Tara bought $\dfrac{3}{10}$ meter of red ribbon and $\dfrac{5}{6}$ meter of blue ribbon. What is the total length of ribbon she bought?

Solution: The LCM of 10 and 6 is 30: $\dfrac{3}{10} = \dfrac{9}{30}$ and $\dfrac{5}{6} = \dfrac{25}{30}$, so $\dfrac{9}{30} + \dfrac{25}{30} = \dfrac{34}{30} = \dfrac{17}{15} = 1\dfrac{2}{15}$ meters of ribbon.

4. Find the missing number

$? - \dfrac{3}{10} = \dfrac{2}{5}$

Solution: Rearranging, $? = \dfrac{2}{5} + \dfrac{3}{10} = \dfrac{4}{10} + \dfrac{3}{10} = \dfrac{7}{10}$.

5. Find the missing number

$? - \dfrac{1}{6} = \dfrac{3}{4}$

Solution: Rearranging, $? = \dfrac{3}{4} + \dfrac{1}{6} = \dfrac{9}{12} + \dfrac{2}{12} = \dfrac{11}{12}$.