Maths
Equivalent fractions: why 1/2 equals 2/4
Equivalent fractions describe the same amount of the same whole using different numbers of equal parts. Half a bar can be one of two pieces, two of four pieces, or three of six pieces.
Why 1/2 and 2/4 mean the same amount
- Draw two rectangles of the same size.
- Split the first into two equal parts and shade one.
- Split the second into four equal parts and shade two.
- The shaded areas match. The pieces are smaller in the second rectangle, but you have more of them.
What happens to the numbers?
The denominator tells you how many equal parts make the whole. The numerator tells you how many of those parts you have. Multiplying both by the same nonzero number changes how you count the pieces without changing the amount: 1/2 × 2/2 = 2/4.
For another example, multiply both numbers in 2/3 by 3 to get 6/9. Dividing both numbers in 6/9 by 3 takes you back to 2/3.
A common mix-up
More pieces does not necessarily mean more food. Equal fractions compare equal-sized wholes: half a small bar and half a large bar are both one half, but they are different amounts of chocolate. The pieces within each whole must also be equal.
Have a go
Try explaining your answer before opening the hint.
Which fraction equals 1/2: 3/6 or 3/5?
3/6. Divide the numerator and denominator by 3 to get 1/2.
Fill in the gap: 2/3 = ?/12.
8. The denominator was multiplied by 4, so multiply the numerator by 4 too.
Is 2/4 the same as 2/8?
No. With the same whole, 2/4 is one half and 2/8 is one quarter. Changing only the denominator changes the amount.
Try it together
Fold a sheet of paper into four equal sections and shade two. Fold it again to make eight equal sections. Count the shaded sections. What changed, and what stayed the same?
Compare different amounts next in our one-quarter and one-third guide. You can also see how a lesson with Edny works.