Master multiplying fractions by fractions using area models and simplification techniques!
Scenario: You're helping your grandmother make a quilt. She has a piece of fabric that is 3/5 meters long and 2/3 meters wide. What is the area of this fabric piece?
To find 3/5 × 2/3, we can use an area model. Imagine a rectangle representing 1 square meter, divided into a 5×3 grid (15 equal parts).
3/5 × 2/3 = 6/15 = 2/5 square meters
Divide 1 square meter into 5×3 = 15 equal parts
Shade 3 rows × 2 columns = 6 parts out of 15
6/15 = 2/5
(Both numerator and denominator ÷ 3)
Answer: The fabric piece has an area of 2/5 square meters!
From our area model, we can derive the algorithm for multiplying fractions:
a/b × c/d = (a × c)/(b × d)
Sometimes we can simplify before multiplying to avoid large numbers:
2/4 × 3/5 = 1/2 × 3/5 = 3/10
(Simplify 2/4 to 1/2 first)
Find numbers that divide both numerator and denominator
Reduce fractions before multiplying to make calculations easier
Always check if your final answer can be simplified:
4/7 × 2/3 = 8/21 (already simplified)
6/8 × 4/9 = 24/72 = 1/3 (simplified)
Just like with whole numbers, the order of multiplication doesn't change the result:
4/7 × 2/3 = 8/21
(4 × 2)/(7 × 3)
2/3 × 4/7 = 8/21
(2 × 4)/(3 × 7)
Both give the same result! This property helps us choose the easier order to multiply.
You eat 3/4 of a pizza, and your friend eats 2/3 of what's left. What fraction of the original pizza did your friend eat?
(1 - 3/4) × 2/3 = 1/4 × 2/3 = 2/12 = 1/6
Answer: Your friend ate 1/6 of the original pizza.
Calculate: 5/6 × 3/4
5/6 × 3/4 = 15/24 = 5/8
Calculate: 2/3 × 9/10
2/3 × 9/10 = 18/30 = 3/5