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Chapter Overview

Learning Goals

Maths

Multiplying fractions and mixed numbers

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Multiplying fractions and mixed numbers

In a nutshell

Fractions and mixed numbers can be multiplied by whole numbers.

Example 1

At a restaurant three people choose pizza from the menu. Each person eats $\frac{3}{4}$ of a pizza. How much pizza do they eat altogether?

Maths; Fractions; KS2 Year 5; Multiplying fractions and mixed numbers

Maths; Fractions; KS2 Year 5; Multiplying fractions and mixed numbers

Maths; Fractions; KS2 Year 5; Multiplying fractions and mixed numbers

Three lots of three quarters totals nine quarters.

$\frac{3}{4}\times3 = \underline{\frac{9}{4}}$

Multiplying fractions by whole numbers

procedure

1.	Multiply the numerator of the fraction by the whole number. Note: The denominator does not change.
2.	Simplify the fraction if possible.

Example 2

Multiply $\frac{3}{12}$ by $3$ . Give your answer as a fraction in its simplest form.

Multiply the numerator of the fraction by the whole number:

$\frac{3\times3}{12} = \frac{9}{12}$ 

Simplify the fraction:

$\frac{9\div3}{12\div3}=\underline{\frac{3}{4}}$ 

Multiplying mixed numbers by whole numbers

procedure

1.	Convert the mixed number into an improper fraction.
2.	Multiply the numerator of the fraction by the whole number.
3.	Convert the answer to Step 2 back into a mixed number.
4.	Simplify the fraction if possible.

Example 3

Multiply $2\frac{1}{4}$ by $4$ . Give your answer as a mixed number in its simplest form.

Convert the mixed number into an improper fraction:

$2\frac{1}{4} = \frac{2\times4+1}{4} = \frac{9}{4}$ 

Multiply the numerator of the fraction by the whole number:

$\frac{9}{4}\times4=\frac{36}{4}$ 

Convert the fraction back into a mixed number:

$36\div4=\underline{9}$ 

Note: This question has no remainder, so the answer is a whole number with no fraction part.

Multiplying fractions and mixed numbers

In a nutshell

Fractions and mixed numbers can be multiplied by whole numbers.

Example 1

At a restaurant three people choose pizza from the menu. Each person eats $\frac{3}{4}$ of a pizza. How much pizza do they eat altogether?

Maths; Fractions; KS2 Year 5; Multiplying fractions and mixed numbers

Maths; Fractions; KS2 Year 5; Multiplying fractions and mixed numbers

Maths; Fractions; KS2 Year 5; Multiplying fractions and mixed numbers

Three lots of three quarters totals nine quarters.

$\frac{3}{4}\times3 = \underline{\frac{9}{4}}$

Multiplying fractions by whole numbers

procedure

1.	Multiply the numerator of the fraction by the whole number. Note: The denominator does not change.
2.	Simplify the fraction if possible.

Example 2

Multiply $\frac{3}{12}$ by $3$ . Give your answer as a fraction in its simplest form.

Multiply the numerator of the fraction by the whole number:

$\frac{3\times3}{12} = \frac{9}{12}$ 

Simplify the fraction:

$\frac{9\div3}{12\div3}=\underline{\frac{3}{4}}$ 

Multiplying mixed numbers by whole numbers

procedure

1.	Convert the mixed number into an improper fraction.
2.	Multiply the numerator of the fraction by the whole number.
3.	Convert the answer to Step 2 back into a mixed number.
4.	Simplify the fraction if possible.

Example 3

Multiply $2\frac{1}{4}$ by $4$ . Give your answer as a mixed number in its simplest form.

Convert the mixed number into an improper fraction:

$2\frac{1}{4} = \frac{2\times4+1}{4} = \frac{9}{4}$ 

Multiply the numerator of the fraction by the whole number:

$\frac{9}{4}\times4=\frac{36}{4}$ 

Convert the fraction back into a mixed number:

$36\div4=\underline{9}$ 

Note: This question has no remainder, so the answer is a whole number with no fraction part.

Want to find out more? Check out these other lessons!

Mixed numbers and improper fractions

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Frequently Asked Questions (FAQ)

FAQs

Question: Can fractions be multiplied?

Answer: Fractions and mixed numbers can be multiplied by whole numbers.
Question: How do I multiply mixed numbers by a whole number?

Answer: 1. Convert the mixed number into an improper fraction. 2. Multiply the numerator of the fraction by the whole number. 3. Convert the answer to Step 2 back into a mixed number. 4. Simplify the fraction if possible.
Question: How do I multiply fractions by whole numbers?

Answer: 1. Multiply the numerator of the fraction by the whole number. Note: The denominator does not change. 2. Simplify the fraction if possible.

Theory

Exercises

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