Master multiplying fractions by whole numbers using repeated addition and area models!
Scenario: You're helping your family bake cookies for a school fundraiser. Each batch of cookies requires 3/4 cup of flour. If you need to make 8 batches, how much flour will you need in total?
When we multiply a fraction by a whole number, we're essentially adding that fraction to itself multiple times. This is just like repeated addition!
3/4 + 3/4 + 3/4 + 3/4 + 3/4 + 3/4 + 3/4 + 3/4 = ?
(8 times)
3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 = 24
The denominator stays 4: 24/4
24/4 = 6
(24 ÷ 4 = 6)
Answer: You need 6 cups of flour total for 8 batches of cookies!
From our repeated addition example, we can derive a general algorithm:
Fraction × Integer = (Numerator × Integer) / Denominator
A bag of rice weighs 2/3 kilograms. If you have 5 bags, what is the total weight?
2/3 × 5 = (2 × 5)/3 = 10/3 = 3 1/3 kilograms
Answer: 3 1/3 kilograms total
Calculate: 5/6 × 12
5/6 × 12 = (5 × 12)/6 = 60/6 = 10
Calculate: 3/8 × 4
3/8 × 4 = (3 × 4)/8 = 12/8 = 3/2 = 1 1/2
We can also think of 3/4 × 8 using an area model. Imagine 8 rectangles, each representing 3/4:
When we combine all 8 pieces of 3/4, we get 8 × 3/4 = 24/4 = 6 whole units.