Express a quantity as a mixed number and an improper fraction | Maths

Starter quiz

Which of the following are improper fractions?

${2} \over {4}$

${7} \over {5}$ ✓

${3} \over {5}$

${1} \over {4}$

${10} \over {4}$ ✓
Which of the following are mixed numbers?

$1{{2} \over {4}}$ ✓

${7} \over {5}$

${3} \over {5}$

$2{{1} \over {3}}$ ✓

${10} \over {4}$
Match the equation to its product.

3 × 7 =

⇔

21 ✓

4 × 7 =

⇔

28 ✓

7 × 5 =

⇔

35 ✓

6 × 7 =

⇔

42 ✓

7 × 7 =

⇔

49 ✓
Look at the part-part-whole model. What is the missing part?

3

5

${3} \over {7}$ ✓

${7} \over {3}$

7
How do we write the whole number eight as an improper fraction with a denominator of five?

${25} \over {5}$

${30} \over {5}$

${35} \over {5}$

${40} \over {5}$ ✓

${45} \over {5}$
Which of these represents the mixed number $1{{2} \over {4}}$ as an improper fraction?

${2} \over {4}$

${3} \over {4}$

${6} \over {4}$ ✓

${4} \over {6}$

Exit quiz

A whole has been divided into eight equal parts. Which unit do we need to think about?

sixths

sevenths

eighths ✓

ninths

tenths
Complete the sentence. The denominator of the fractional part of this mixed number, $4{{5} \over {7}}$ is seven. The unit we are working with is ______.

'sevenths' ✓
Complete the stem sentence to describe the image. There are three groups of five fifths, which is 15 fifths and one more fifth, so that is ______ fifths.

'16' ✓
Express four and three-ninths as an improper fraction.

$4{{3} \over {9}}$

${39} \over {9}$ ✓

${3} \over {9}$

${7} \over {9}$

${48} \over {9}$
Match the mixed number to the equivalent improper fraction.

$1{{3} \over {9}}$ =

⇔

${12} \over {9}$ ✓

$3{{5} \over {9}}$ =

⇔

${32} \over {9}$ ✓

$2{{4} \over {9}}$ =

⇔

${22} \over {9}$ ✓

$2{{8} \over {9}}$ =

⇔

${26} \over {9}$ ✓

$1{{7} \over {9}}$ =

⇔

${16} \over {9}$ ✓
Jacob has seven whole pizzas and a quarter of a pizza. If the whole pizzas are also cut into quarters, how many quarters will there be?

${1} \over {4}$

${8} \over {4}$

${28} \over {4}$

${29} \over {4}$ ✓

Worksheet

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Lesson Details

Key learning points

A mixed number can be written as an improper fraction of equal value.
The generalisation, ‘First we multiply the whole number by the denominator then we add the numerator’ can help.

Common misconception

Children may just add the whole number part of the mixed number to the numerator or may forget to add the fractional part of the mixed number.

Encourage children to check their work using the stem sentence or generalisation developed in the lesson, 'first we multiply the whole number by the denominator, then we add the numerator'.

Keywords

Mixed number - A mixed number is a whole number and a fraction combined. For example, one and a half is a mixed number.
Improper fraction - An improper fraction is a fraction where the numerator is greater than or equal to the denominator.