First fractions · Usually met around P3
Simplifying fractions
Divide top and bottom by the H.C.F.
How to do it
Method
Divide top and bottom by the H.C.F.
1218 = 23, both ÷ 6
Another way
Step by step
1218 = 69 = 23
In full
To simplify a fraction, divide the top and the bottom by the same number. The fraction's size doesn't change. The quickest way is to divide once by their highest common factor (H.C.F.). 1218: the H.C.F. of 12 and 18 is 6. 12 ÷ 6 = 2 and 18 ÷ 6 = 3, so 1218 = 23. Short division finds the H.C.F. Or simplify in steps: ÷ 2 → 69, then ÷ 3 → 23. Stop when the top and bottom share no factor except 1. That's the simplest form, and you end up with the same answer.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
24 = ?
Answer in simplest form
Show the answer and working
Answer: 24 = 12
24: the H.C.F. of 2 and 4 is 2, 2 ÷ 2 = 1, 4 ÷ 2 = 2 → 12
Example 2
636 = ?
Answer in simplest form
Show the answer and working
Answer: 636 = 16
636: the H.C.F. of 6 and 36 is 6, 6 ÷ 6 = 1, 36 ÷ 6 = 6 → 16
Example 3
3054 = ?
Answer in simplest form
Show the answer and working
Answer: 3054 = 59
3054: the H.C.F. of 30 and 54 is 6, 30 ÷ 6 = 5, 54 ÷ 6 = 9 → 59
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