First fractions · Usually met around P3
Equivalent fractions
Multiply or divide top and bottom by the same number.
How to do it
Method
Multiply or divide top and bottom by the same number
12 = 24 = 36
Another way
Compare pictures
12 shaded is as big as 24 shaded
In full
Take two strips the same length: cut one into 2 equal parts and shade 1, cut the other into 4 and shade 2. The shaded parts are the same size, so 12 = 24: they are equivalent fractions. Multiply the top and the bottom by the same number and the fraction stays the same size: 12 = 24 = 36. Dividing both by the same number works too: 68 = 34. Only multiply or divide — adding the same number doesn't work: 12 and 23 are not equal. Or draw both and compare the shaded parts.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
The two strips are the same length and have the same amount shaded. 23 = □/6
Show the answer and working
Answer: 4
The lower strip has 6 equal parts with 4 shaded: 23 = 46.
Example 2
25 = 58
True or false?
Show the answer and working
Answer: False
Only multiplying or dividing the top and bottom by the same number keeps the size; adding doesn't.
Example 3
25 = □/10 = □/15
Fill in each box
Show the answer and working
Answer: 4，6
Bottom × 2, so top × 2: 4; bottom × 3, so top × 3: 6.
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