Primary 3 maths · Fractions · About 12 minutes
Equivalent fractions
Recognise that different fractions can name the same amount
Start the interactive lesson →Related practice: Equivalent-fraction bridge
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
Why both numbers change together
Half the strip is shaded.
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.
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.
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.
Why can’t I just add the same number to the top and bottom?
Adding changes the shaded parts and the whole by different proportions. 2/3 and 3/4 do not reach the same place on the wall. Splitting each part keeps the relationship between the shaded amount and the whole, which is what a fraction records.
Worked example
2/3 = □/12
How many parts does the new whole have?
The whole goes from 3 parts to 12 parts, so each part was split into…
4
Each of the 3 parts was split into 4, giving 12 parts.
2/3 = 8/12: the same length, so the same amount.
The 2 shaded parts were split into 4 as well.
2 × 4 = ?
How many shaded parts now?
8
So the missing numerator is 8.
2/3 = 8/12
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.
Try this lesson →Related Primary 3 lessons
- Simplest formFind a common factor of the numerator and denominator · About 10 minutes
- Generate equivalent fractionsGenerate equivalent fractions · About 10 minutes
- Simplify fractionsSimplify fractions · About 10 minutes
- Compare unlike fractions with denominators up to 12Compare unlike fractions with denominators up to 12 · About 10 minutes
- Find a missing numerator or denominatorFind a missing numerator or denominator · About 10 minutes
- Add and subtract related fractions within one wholeAdd and subtract related fractions within one whole · About 10 minutes