Multiply fractions (grade 5) · lesson

Tops times tops, bottoms times bottoms

💡 To multiply two fractions, multiply the tops and multiply the bottoms.

2/7 × 1/3: the top is 2 × 1 = 2. The bottom is 7 × 3 = 21. So the answer is 2/21.

You can simplify after, but you don't have to unless the problem asks.

🧠 Let's work it out

Find 2/7 × 1/3.

Tops: 2 × 1 = 2.
Bottoms: 7 × 3 = 21.
The answer is 2/21.

What do you think comes next?

product: the answer when you multiply
numerator: the top number of a fraction
denominator: the bottom number of a fraction

🔗 Multiply fractions · Khan Academy ↗

A fraction of a whole number

💡 To find a fraction of a number, find one part first, then take as many parts as the top says.

3/4 of 16: first find 1/4 of 16. That is 16 ÷ 4 = 4.

3/4 is 3 of those parts. 3 × 4 = 12.

🧠 Let's work it out

Find 3/4 × 16.

1/4 of 16 is 4.
3/4 of 16 is 3 × 4 = 12.

What do you think comes next?

part: a piece of the whole

"Of" means times

💡 A fraction of a fraction means multiply the two fractions.

"1/3 of 3/5" means 1/3 × 3/5.

Multiply the tops and the bottoms. 1 × 3 = 3 and 3 × 5 = 15, so it is 3/15. That is the same as 1/5.

🧠 Let's work it out

What is 1/2 of 3/7?

Write 1/2 × 3/7.
1 × 3 = 3 and 2 × 7 = 14.
The answer is 3/14.

What do you think comes next?

of: in math, a word that often means multiply

Bigger or smaller?

💡 Multiplying by a fraction less than 1 makes a number smaller, and by a fraction more than 1 makes it bigger.

2/3 × 9 means 2/3 of 9. That is only part of 9, so it is less than 9.

7/5 × 9 is more than 9, because 7/5 is more than 1. Times exactly 1 keeps the number the same.

🧠 Let's work it out

How does 4/9 × 30 compare to 30?

Is 4/9 more or less than 1? Less.
So the product is less than 30.

What do you think comes next?

scaling: making a number bigger or smaller by multiplying

Area with fraction sides

💡 The area of a rectangle with fraction sides is still length times width.

A rectangle 1/2 m by 5/6 m covers part of a square meter.

Multiply the sides: 1/2 × 5/6 = 5/12. The area is 5/12 of a square meter.

🧠 Let's work it out

A card is 2/3 ft long and 1/5 ft wide. What is its area?

Area = 2/3 × 1/5.
2 × 1 = 2 and 3 × 5 = 15.
The area is 2/15 square feet.

What do you think comes next?

area: how much flat space a shape covers

Multiply mixed numbers

💡 Change mixed numbers to fractions first, then multiply.

1 1/3 is 3/3 + 1/3 = 4/3. 1 1/2 is 3/2.

Now multiply the fractions as usual. Then make the answer simpler if you can.

🧠 Let's work it out

Find 1 1/3 × 1 1/2.

Change to fractions: 4/3 × 3/2.
4 × 3 = 12 and 3 × 2 = 6, so 12/6.
12/6 = 2.

What do you think comes next?

mixed number: a whole number and a fraction together