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Why say four-eighths (
4
8
) when we really mean half (
1
2
) ?
4
8
=
2
4
=
1
2
(Four-Eighths) (Two-Quarters) (One-Half)
pizza 4/8 = pizza 2/4 = pizza 1/2
How do I Simplify a Fraction ?
There are two ways to simplify a fraction:
Method 1
Try to exactly divide (only whole number answers) both the top and bottom of the fraction by 2, 3, 5, 7 ,... etc, until we can't go any further.
Example: Simplify the fraction
24
108
:
÷ 2 ÷ 2 ÷ 3
right over arrow right over arrow right over arrow
24
108
=
12
54
=
6
27
=
2
9
right under arrow right under arrow right under arrow
÷ 2 ÷ 2 ÷ 3
That is as far as we can go. The fraction simplifies to
2
9
Example: Simplify the fraction
10
35
:
Dividing by 2 doesn't work because 35 can't be exactly divided by 2 (35/2 = 17½)
Likewise we can't divide exactly by 3 (10/3 = 3
1
3
and also 35/3=11
2
3
)
No need to check 4 (we checked 2 already, and 4 is just 2×2).
But 5 does work!
÷ 5
right over arrow
10
35
=
2
7
right under arrow
÷ 5
That is as far as we can go. The fraction simplifies to
2
7
Notice that after checking 2 we didn't need to check 4 (4 is 2×2)?
We also don't need to check 6 when we have checked 2 and 3 (6 is 2x3).
In fact, when checking from smallest to largest we use prime numbers:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, ...
Method 2
Divide both the top and bottom of the fraction by the Greatest Common Factor (you have to work it out first!).
Example: Simplify the fraction
8
12
:
The largest number that goes exactly into both 8 and 12 is 4, so the Greatest Common Factor is 4.
Divide both top and bottom by 4:
÷ 4
right over arrow
8
12
=
2
3
right under arrow
÷ 4
That is as far as we can go. The fraction simplifies to
2
3
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