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Maths Year 4 Fractions, decimals & %

Year 4 families of equivalent fractions

The objective: Recognise and show, using diagrams, families of common equivalent fractions.

The explanation, example and questions are the ones Remelia uses in the app; the questions are not taken from any test paper.

The idea

Families of equivalent fractions come from multiplying the top and bottom by the same number. 1/2 = 2/4 = 3/6 = 4/8 is one family.

How to do it

  1. Pick a multiplier.
  2. Multiply numerator and denominator by it.
  3. To go the other way, divide both by a common factor.

A worked example

3/4 = 6/8 = 9/12 = 12/16. Each step multiplies both numbers by one more.

Watch for

Multiplying only one of the two numbers. Both, always, by the same amount.

Try four questions

  1. What fraction of the shape is shaded?

    Write it as a fraction with a denominator of 24.

    Grid of squares, some shadedA rectangle made of equal squares, three across and two down. Shaded: the first one square of the top row.
    Show the answer to question 1

    Answer: 4/24

    Why:

    1 of the 6 equal squares are shaded: 1/6.

    24 ÷ 6 = 4, so each part is 4/24. 1 × 4 = 4.

    So 1/6 = 4/24.

  2. What fraction of the shape is shaded?

    Write it as a fraction with a denominator of 2.

    Grid of squares, some shadedA rectangle made of equal squares, four across and two down. Shaded: the whole of the top row.
    Show the answer to question 2

    Answer: 1/2

    Why:

    4 of the 8 equal squares are shaded: 4/8.

    8 ÷ 2 = 4, so every 4 parts make 1/2. 4 ÷ 4 = 1.

    So 4/8 = 1/2.

  3. What fraction of the circle is shaded?

    Write it as a fraction with a denominator of 2.

    Circle in equal partsA circle cut into ten equal parts, like slices of a cake, all meeting at the centre. Five of the parts are shaded.
    Show the answer to question 3

    Answer: 1/2

    Why:

    5 of the 10 equal parts are shaded: 5/10.

    10 ÷ 2 = 5, so every 5 parts make 1/2. 5 ÷ 5 = 1.

    So 5/10 = 1/2.

  4. Yusuf says: In 1/4 = 2/8 = ☐/16, the number in the box is 10.

    Yusuf is wrong. Which reason shows why?

    • A Whatever is added to the bottom must be added to the top.
    • B 1/4 is less than 1, and so are the other fractions in the family.
    • C Equal fractions have the top and the bottom multiplied by the same number.
    • D The bottom goes up by 8, so the top goes up by 8 as well.
    Show the answer to question 4

    Answer: C · Equal fractions have the top and the bottom …

    Why:

    Equal fractions have the top and the bottom multiplied by the same number.

    "1/4 is less than 1, and so are the other fractions in the family." is true, but it does not show Yusuf is wrong.

Answers

  1. 1. 4/24
  2. 2. 1/2
  3. 3. 1/2
  4. 4. C · Equal fractions have the top and the bottom …

The mistakes Remelia names

When a wrong answer to a question like these matches one of these mistakes, the app says what the child seems to have done before they try again.

  • Question 1, the answer 1/5: It looks as if you put the parts not shaded as the denominator. The denominator is how many equal parts there are altogether; the numerator is how many are shaded.
  • Question 1, the answer 20/24: That is the fraction not shaded. The numerator counts the shaded parts.

More Year 4 maths

Year 4 fractions, decimals & %, every objective with a question, and six fractions questions with the common mistakes.

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