3
A fraction times a fraction
Discover Mathematics P5: Term 2, Unit 9, Lessons 1–4
GoalMultiply two fractions with an area model and with the rule, and simplify the product.
New words
area model · a rectangle cut into rows and columns to show a productof · in fractions, “of” means multiply: 1/2 of 3/4 is 1/2 × 3/4product of fractions · multiply the numerators, multiply the denominators
Explanation
To take a fraction of a fraction, think of a rectangle. 1/2 × 3/4: cut the rectangle into 4 columns and shade 3 of them (3/4). Cut it into 2 rows and keep 1 row (1/2). The part that is shaded in both ways is 3 small boxes out of 8, so 1/2 × 3/4 = 3/8. The rule is the same: multiply the numerators (1 × 3 = 3) and multiply the denominators (2 × 4 = 8). Always simplify the answer: 2/3 × 3/4 = 6/12 = 1/2. The product of two fractions that are both less than 1 is less than both of them.
Worked examples
Work out 1/2 × 3/4 with an area model. The rectangle has 2 rows and 4 columns, so 8 boxes. Half of the rows and 3 of 4 columns give 3 boxes. 1/2 × 3/4 = 3/8.
Work out 2/3 × 3/4. Multiply the numerators: 2 × 3 = 6. Multiply the denominators: 3 × 4 = 12. 6/12 = 1/2.
Work out 5/6 × 3/10. (5 × 3)/(6 × 10) = 15/60. Divide top and bottom by 15: 1/4.
Class activity
Fold and shade. Fold a sheet of paper into 3 equal columns and shade 2 of them (2/3). Fold the sheet across into 4 equal rows and shade 3 rows with a different colour (3/4). Count the boxes shaded twice and the total boxes. Write 2/3 × 3/4 = 6/12 = 1/2.
Practice
1
Work out 1/3 × 1/4.
1/12.
2
Work out 2/5 × 3/4 and simplify.
6/20 = 3/10.
3
Work out 3/4 × 8/9 and simplify.
24/36 = 2/3.
4
Work out 5/8 × 4/15.
20/120 = 1/6.
5
Salma has 3/4 of a pizza and eats 1/3 of that. What fraction of the whole pizza does she eat?
3/4 × 1/3 = 3/12 = 1/4 of the pizza.