Equivalent fractions

What you will learn

• Recognise that different fractions can name the same amount
• Generate equivalent fractions by splitting every part
• Find a missing numerator or denominator

Models used: fraction strips, bar models, number sentences, stories.

Before you start

• Represent a fraction as part of a whole
• Compare unit fractions with denominators up to 12

Why both numbers change together

Half the strip is shaded.

1. Each strip is one whole of the same size. Count all the equal parts, then count the shaded parts.

   Half the strip is shaded.

   The size of a fraction depends on both numbers: how many equal parts make the whole, and how many of those parts we take.

2. Each strip is one whole of the same size. Count all the equal parts, then count the shaded parts.

   Cut each half into two equal pieces. We now call the shaded amount two quarters.

   1/2 = 2/4

   The size of a fraction depends on both numbers: how many equal parts make the whole, and how many of those parts we take.

   1/2 = 2/4: the same length, so the same amount.

3. Each strip is one whole of the same size. Count all the equal parts, then count the shaded parts.

   Another cut makes four eighths. The coloured length never changed.

   1/2 = 2/4 = 4/8

   The size of a fraction depends on both numbers: how many equal parts make the whole, and how many of those parts we take.

   1/2 = 2/4 · 1/2 = 4/8 · 2/4 = 4/8: the same length, so the same amount.

Worked example

2/3 = □/12

1. How many parts does the new whole have?

   The whole goes from 3 parts to 12 parts, so each part was split into…

   4

2. Each of the 3 parts was split into 4, giving 12 parts.

   2/3 = 8/12: the same length, so the same amount.

3. The 2 shaded parts were split into 4 as well.

   2 × 4 = ?

   How many shaded parts now?

   8

4. So the missing numerator is 8.

   2/3 = 8/12

5. Check on the wall: both rows end at the same place.

   2/3 = 8/12 ✓

Common mistakes to discuss

• Adding the same number to the top and bottom. 2/3 is not 3/4. Splitting every part multiplies both numbers: 2/3 = 4/6 = 6/9.
• Thinking a bigger denominator means a bigger fraction. More parts in the same whole means each part is smaller: 1/4 is bigger than 1/6.

Check your understanding

• show that 1/2 and 2/4 are the same amount
• make equivalent fractions by multiplying both numbers
• find the missing number in 2/3 = □/12
• explain why the amount does not change

Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.