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KS2 Maths · Fractions · Year 4

Equivalent fractions

Different-looking fractions can be exactly the same amount.

About 20 minutes

Step 1 · Wonder why it matters

Hook

Same chocolate, different pieces

Maya breaks her chocolate bar into 2 big pieces and eats 1. Leo breaks the same size bar into 8 small pieces and eats 4.

Who ate more? Leo says he did because 4 is more than 1. Is he right? By the end of this lesson you will be able to prove the answer.

Step 2 · See it

Picture

See the same amount

All four bars are the same length. The shaded part is the same size in every bar, even though it is cut into a different number of pieces.

1/2
2/4
3/6
4/8
1/2 = 2/4 = 3/6 = 4/8

Step 3 · Understand how it works

Logic

Multiply top and bottom by the same number

Equivalent fractions are fractions that are worth the same amount.

To make one, multiply the numerator (top) and the denominator (bottom) by the same number. This cuts each piece into smaller pieces without changing how much is shaded.

To simplify, do the opposite: divide the top and bottom by the same number.

Numerator
The top number — how many parts you have.
Denominator
The bottom number — how many equal parts make the whole.
Equivalent
Worth the same amount.
Simplify
Write a fraction using the smallest possible numbers.

Worked example

Find the missing number: 3/4 = ?/12

  1. 1Look at the denominators: 4 has become 12.
  2. 24 × 3 = 12, so we multiplied by 3.
  3. 3Do the same to the numerator: 3 × 3 = 9.

Answer: 3/4 = 9/12

Step 4 · Have a go

Do

Have a go

Use paper strips, or draw bars of the same length with a ruler.

  1. 1Draw four bars, each 12 cm long, one under the other.
  2. 2Split them into 2, 3, 4 and 6 equal parts.
  3. 3Shade 1/2 of the first bar. Which of the other bars can you shade to show the same amount?
  4. 4Write each equivalent fraction you found, then check it by multiplying.
  5. 5Back to the hook: did Leo eat more than Maya? Use 1/2 = 4/8 to explain.

Step 5 · Remember it

Recall

Quick quiz

Five questions with an explanation for each.

0 of 5 answered

  1. 1.Which fraction is equivalent to 1/2?

  2. 2.2/5 = ?/10

  3. 3.Simplify 6/8.

  4. 4.Which of these is NOT equivalent to 2/3?

  5. 5.Maya ate 1/2 of a bar. Leo ate 4/8 of the same size bar. Who ate more?

Step 6 · Link it to your world

Reflect

Think about it

Equivalent fractions appear in recipes, music and sharing.

A recipe needs 1/2 a cup of milk but you only have a 1/4 cup. How would you measure it, and why does that work?

Saved to your notebook on this device only.

Finished all six steps?

Mark it complete to collect 3 stars. Next up: Area and perimeter of rectangles.