Multiplying a Fraction and a Whole Number

Learn to find a fraction OF a number using bar models and multiplication

1. Understanding "Fraction OF" a Number

Key Concept

When we say "fraction OF a number", the word OF means multiplication.

For example: $\frac{3}{4}$ of 12 means $\frac{3}{4} \times 12$

Example: What is $\frac{3}{4}$ of 12?

Bar Model Method:

Step 1: Divide 12 into 4 equal parts (since denominator = 4)

12 ÷ 4 = 3 (each part equals 3)

Step 2: Take 3 parts (since numerator = 3)

3 × 3 = 9

$\frac{3}{4}$ of 12 = 9

Calculation Method

Rule: Multiply the numerator by the whole number and keep the denominator. Then simplify.

$\frac{3}{4}$ of 12 = $\frac{3 \times 12}{4} = \frac{36}{4} = 9$

2. More Examples

Example: What is $\frac{2}{5}$ of 15?

Bar Model:

15 ÷ 5 = 3 per unit

2 units = 2 × 3 = 6

Calculation:

$\frac{2}{5} \times 15 = \frac{30}{5} = 6$

Example: Find $\frac{2}{5} \times 12$

$\frac{2}{5} \times 12 = \frac{2 \times 12}{5} = \frac{24}{5}$

Convert improper fraction: $\frac{24}{5} = 4\frac{4}{5}$

(24 ÷ 5 = 4 remainder 4)

Remember: When You Multiply, Order Doesn't Matter!

$\frac{2}{5} \times 12 = 12 \times \frac{2}{5}$

Both give the same answer: $4\frac{4}{5}$

3. Word Problems

Example: Painted Pole

A pole is 15 m long. $\frac{2}{5}$ of the pole is painted red. What is the length of the pole that is painted red?

Solution:

5 units = 15 m

1 unit = 15 ÷ 5 = 3 m

2 units = 2 × 3 = 6 m

The length of the pole painted red is 6 m.

Example: Buttons

Mrs Lee has 120 buttons. $\frac{4}{5}$ of the buttons are red. How many red buttons does she have?

Solution: $\frac{4}{5}$ × 120

= $\frac{4 \times 120}{5} = \frac{480}{5} = 96$

She has 96 red buttons.

4. Practice Problems

Practice 1: Find $\frac{3}{7}$ of 28

ShowHide solution

Method 1: 28 ÷ 7 = 4 (one unit), 3 × 4 = 12

Method 2: $\frac{3 \times 28}{7} = \frac{84}{7} = 12$

Answer: 12

Practice 2: $20 \times \frac{7}{10}$

ShowHide solution

$20 \times \frac{7}{10} = \frac{20 \times 7}{10} = \frac{140}{10} = 14$

Answer: 14

Practice 3: A block of butter has a mass of $\frac{3}{10}$ kg. Sarah needs 3 blocks. How much butter does she need? Give your answer in kilograms.

ShowHide solution

Total butter = 3 × $\frac{3}{10}$ kg

= $\frac{9}{10}$ kg

Sarah needs $\frac{9}{10}$ kg of butter.

Practice 4: There are 12 glasses, each containing $\frac{2}{5}$ litre of water. How much water is there in total?

ShowHide solution

Total water = 12 × $\frac{2}{5}$

= $\frac{12 \times 2}{5} = \frac{24}{5} = 4\frac{4}{5}$ litres

There are $4\frac{4}{5}$ litres of water in total.

Key Takeaways

"OF" means multiply: $\frac{3}{4}$ of 12 = $\frac{3}{4} \times 12$
Bar model method: Divide the total into as many equal parts as the denominator, then take as many parts as the numerator
Calculation method: Multiply the numerator by the whole number and keep the denominator: $\frac{2}{5} \times 12 = \frac{2 \times 12}{5} = \frac{24}{5}$
Order does not matter when you multiply: $\frac{2}{5} \times 12 = 12 \times \frac{2}{5}$
Convert improper fractions to mixed numbers when needed
Include units in word problem answers (metres, kg, litres, etc.)

Multiplying a Fraction and a Whole Number

1. Understanding "Fraction OF" a Number

Key Concept

Example: What is 34\frac{3}{4}43​ of 12?

Calculation Method

2. More Examples

Example: What is 25\frac{2}{5}52​ of 15?

Bar Model:

Calculation:

Example: Find 25×12\frac{2}{5} \times 1252​×12

Remember: When You Multiply, Order Doesn't Matter!

3. Word Problems

Example: Painted Pole

Example: Buttons

4. Practice Problems

Practice 1: Find 37\frac{3}{7}73​ of 28

Practice 2: 20×71020 \times \frac{7}{10}20×107​

Practice 3: A block of butter has a mass of 310\frac{3}{10}103​ kg. Sarah needs 3 blocks. How much butter does she need? Give your answer in kilograms.

Practice 4: There are 12 glasses, each containing 25\frac{2}{5}52​ litre of water. How much water is there in total?

Key Takeaways

Example: What is $\frac{3}{4}$ of 12?

Example: What is $\frac{2}{5}$ of 15?

Example: Find $\frac{2}{5} \times 12$

Practice 1: Find $\frac{3}{7}$ of 28

Practice 2: $20 \times \frac{7}{10}$

Practice 3: A block of butter has a mass of $\frac{3}{10}$ kg. Sarah needs 3 blocks. How much butter does she need? Give your answer in kilograms.

Practice 4: There are 12 glasses, each containing $\frac{2}{5}$ litre of water. How much water is there in total?