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Year 4

Express a quantity as a mixed number and an improper fraction

I can express a quantity as a mixed number and an improper fraction.

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New
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Year 4

Express a quantity as a mixed number and an improper fraction

I can express a quantity as a mixed number and an improper fraction.

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Share activities with pupils
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Lesson details

Key learning points

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

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.

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'.

A secure recall of multiplication facts is beneficial in this lesson. If pupils are less secure consider providing a multiplication square. If children choose to use the generalisation, ensure they have a secure understanding of the structure behind it.
Teacher tip

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).

Lesson video

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Starter quiz

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6 Questions

Q1.
Which of the following are improper fractions?
$$ {2} \over {4}$$
Correct answer: $$ {7} \over {5}$$
$$ {3} \over {5}$$
$$ {1} \over {4}$$
Correct answer: $$ {10} \over {4}$$
Q2.
Which of the following are mixed numbers?
Correct answer: $$1{{2} \over {4}}$$
$$ {7} \over {5}$$
$$ {3} \over {5}$$
Correct answer: $$ 2{{1} \over {3}}$$
$$ {10} \over {4}$$
Q3.
Match the equation to its product.
Correct Answer:3 × 7 =,21

21

Correct Answer:4 × 7 =,28

28

Correct Answer:7 × 5 =,35

35

Correct Answer:6 × 7 =,42

42

Correct Answer:7 × 7 =,49

49

Q4.
Look at the part-part-whole model. What is the missing part?
An image in a quiz
3
5
Correct answer: $$ {3} \over {7}$$
$$ {7} \over {3}$$
7
Q5.
How do we write the whole number eight as an improper fraction with a denominator of five?
$$ {25} \over {5}$$
$$ {30} \over {5}$$
$$ {35} \over {5}$$
Correct answer: $$ {40} \over {5}$$
$$ {45} \over {5}$$
Q6.
Which of these represents the mixed number $$1{{2} \over {4}}$$ as an improper fraction?
$$ {2} \over {4}$$
$$ {3} \over {4}$$
Correct answer: $$ {6} \over {4}$$
$$ {4} \over {6}$$

Exit quiz

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6 Questions

Q1.
A whole has been divided into eight equal parts. Which unit do we need to think about?
sixths
sevenths
Correct answer: eighths
ninths
tenths
Q2.
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 .
Correct Answer: sevenths
Q3.
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.
An image in a quiz
Correct Answer: 16
Q4.
Express four and three-ninths as an improper fraction.
$$ 4{{3} \over {9}}$$
Correct answer: $$ {39} \over {9}$$
$$ {3} \over {9}$$
$$ {7} \over {9}$$
$$ {48} \over {9}$$
Q5.
Match the mixed number to the equivalent improper fraction.
Correct Answer:$$ 1{{3} \over {9}}$$ =,$$ {12} \over {9}$$

$$ {12} \over {9}$$

Correct Answer:$$ 3{{5} \over {9}}$$ =,$$ {32} \over {9}$$

$$ {32} \over {9}$$

Correct Answer:$$ 2{{4} \over {9}}$$ =,$$ {22} \over {9}$$

$$ {22} \over {9}$$

Correct Answer:$$ 2{{8} \over {9}}$$ =,$$ {26} \over {9}$$

$$ {26} \over {9}$$

Correct Answer:$$ 1{{7} \over {9}}$$ =,$$ {16} \over {9}$$

$$ {16} \over {9}$$

Q6.
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?
$$ {1} \over {4}$$
$$ {8} \over {4}$$
$$ {28} \over {4}$$
Correct answer: $$ {29} \over {4}$$