In Grade 3, multiplication meant equal groups: $3 \times 4$ is 3 groups of 4. The same meaning works when each group is a fraction, and you already know how to add like fractions.
Key idea
$3 \times \dfrac{2}{5}$ means 3 groups of $\dfrac{2}{5}$: $\dfrac{2}{5} + \dfrac{2}{5} + \dfrac{2}{5} = \dfrac{6}{5}$. Multiply the whole number by the numerator and keep the denominator: $3 \times \dfrac{2}{5} = \dfrac{3 \times 2}{5} = \dfrac{6}{5}$.
Why it works
$\dfrac{2}{5}$ is 2 pieces of size $\dfrac{1}{5}$. Three groups of 2 pieces is 6 pieces, and each piece is still a fifth. So $3 \times \dfrac{2}{5} = 6 \times \dfrac{1}{5} = \dfrac{6}{5}$. Nothing makes the pieces smaller, so the denominator does not change.
Worked example: Multiply
Find $3 \times \dfrac{2}{5}$.
- 3 groups of 2 fifths is $3 \times 2 = 6$ fifths.
- As a mixed number, $\dfrac{6}{5} = 1\dfrac{1}{5}$.
Answer: $\dfrac{6}{5}$, or $1\dfrac{1}{5}$
Worked example: A recipe
Each batch of muffins uses $\dfrac{3}{4}$ cup of milk. How much milk do 5 batches use?
- 5 equal groups of $\dfrac{3}{4}$: multiply.
- $5 \times \dfrac{3}{4} = \dfrac{15}{4}$.
- $15 \div 4 = 3$ R 3, so $\dfrac{15}{4} = 3\dfrac{3}{4}$.
Answer: $3\dfrac{3}{4}$ cups
Common mistake
Multiplying the denominator too: $3 \times \dfrac{2}{5} = \dfrac{6}{15}$. But $\dfrac{6}{15}$ is the same as $\dfrac{2}{5}$, so that would mean 3 groups equal 1 group. Only the number of pieces grows.