New
New
Year 5

# Multiply a proper fraction by a whole number where the product is greater than a whole

I can multiply a proper fraction by a whole number where the product is greater than a whole.

New
New
Year 5

# Multiply a proper fraction by a whole number where the product is greater than a whole

I can multiply a proper fraction by a whole number where the product is greater than a whole.

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## Lesson details

### Key learning points

1. If 3 groups of 4 are equal to 12 then 3 groups of 4 fifths are equal to 12 fifths.
2. If the product is an improper fraction you can convert it to a mixed number.
3. The numerator of the fraction is multiplied by the whole number and the denominator remains the same.

### Common misconception

Pupils resort to a procedure with little understanding for how we convert between improper fractions and mixed numbers.

Encourage pupils to make connections between improper fractions and mixed numbers using both area models and number lines. Focus on reasoning by manipulating parts to complete wholes and where the wholes and parts are represented on the number line.

### Keywords

• Represent - To represent something is to show it in a different way.

• Unitise - Unitising means treating groups that contain or represent the same number of things as units or ones.

• Mixed number - A number which combines both a whole number and a fraction.

• Numerator - A numerator is the top number in a fraction. It shows how many parts we have.

• Denominator - A denominator is the bottom number in a fraction. It shows how many parts a whole has been divided into.

### Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

## Starter quiz

### 6 Questions

Q1.
Tick the non-unit fractions.
Correct answer: $$\frac{3}{10}$$
Correct answer: $$\frac{5}{6}$$
$$\frac{1}{9}$$
Correct answer: $$\frac{2}{7}$$
Q2.
What fraction of this shape is not shaded.
$$\frac{3}{3}$$
$$\frac{1}{3}$$
Correct answer: $$\frac{3}{4}$$
$$\frac{1}{4}$$
Q3.
Which expressions are represented by the number line.
$$\frac{2}{7}$$ × 6
Correct answer: $$\frac{2}{7}$$ × 3
Correct answer: $$\frac{2}{7}$$ + $$\frac{2}{7}$$ + $$\frac{2}{7}$$
$$\frac{3}{7}$$ × 2
Q4.
Which equation represents this image?
$$\frac{2}{9}$$ × 4 = $$\frac{8}{18}$$
Correct answer: $$\frac{2}{9}$$ × 4 = $$\frac{8}{9}$$
$$\frac{9}{2}$$ × 4 = $$\frac{36}{2}$$
Correct answer: 4 × $$\frac{2}{9}$$ = $$\frac{8}{9}$$
$$\frac{2}{9}$$ = 4 × $$\frac{8}{9}$$
Q5.
Match the equation to the correct product.
Correct Answer:$$\frac{1}{4}$$ × 3 = ,$$\frac{3}{4}$$

$$\frac{3}{4}$$

Correct Answer:$$\frac{1}{6}$$ × 2 = ,$$\frac{2}{6}$$

$$\frac{2}{6}$$

Correct Answer:$$\frac{1}{6}$$ × 4 = ,$$\frac{4}{6}$$

$$\frac{4}{6}$$

Correct Answer:$$\frac{1}{4}$$ × 2 =,$$\frac{2}{4}$$

$$\frac{2}{4}$$

Q6.
Order the expressions from largest to smallest.
1 - $$\frac{2}{9}$$ × 4
2 - $$\frac{2}{9}$$ × 2
3 - $$\frac{3}{9}$$ × 1
4 - $$\frac{1}{9}$$ × 2
5 - $$\frac{5}{9}$$ × 0

## Exit quiz

### 6 Questions

Q1.
Tick the fraction represented by the image.
Correct answer: $$\frac{6}{8}$$
$$\frac{6}{9}$$
$$\frac{7}{8}$$
$$\frac{8}{6}$$
Q2.
Which image matches the expression $$\frac{2}{3}$$ × 3?
Correct Answer: An image in a quiz
Correct Answer: An image in a quiz
Correct Answer: An image in a quiz
Q3.
Which equation represents this image?
$$\frac{5}{7}$$ × 3 = $$\frac{15}{21}$$
Correct answer: $$\frac{5}{7}$$ × 3 = $$\frac{15}{7}$$
$$\frac{5}{7}$$ × 3 = $$\frac{7}{15}$$
3 × $$\frac{5}{7}$$ = $$\frac{15}{21}$$
Correct answer: 3 × $$\frac{5}{7}$$ = $$\frac{15}{7}$$
Q4.
Tick the correct products for this equation. 4 × $$\frac{2}{10}$$ =
Correct answer: $$\frac{8}{10}$$
$$\frac{42}{10}$$
$$\frac{6}{10}$$
$$\frac{8}{40}$$
$$\frac{6}{14}$$
Q5.
Tick the correct products for this equation. 3 × $$\frac{3}{5}$$ =
$$\frac{33}{5}$$
Correct answer: $$\frac{9}{5}$$
Correct answer: $$1\frac{4}{5}$$
$$\frac{6}{5}$$
$$1\frac{9}{5}$$
Q6.
Which expression would be equal to this product? $$\frac{24}{6}$$
Correct answer: $$\frac{6}{6}$$ × 4
$$\frac{3}{6}$$ × 12
Correct answer: $$\frac{4}{6}$$ × 6
Correct answer: $$\frac{1}{6}$$ × 24
$$1\frac{8}{3}$$ × 6