Equivalent Fractions
Equivalent Fractions have the same value, even though they may look different.
These fractions are really the same:
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Why are they the same? Because when you multiply or divide both the top and bottom by the same number, the fraction keeps it's value.
The rule to remember is:
What you do to the top of the fraction
you must also do to the bottom of the fraction !
So, here is why those fractions are really the same:
| × 2 | × 2 | |||
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| 1 | = | 2 | = | 4 |
| 2 | 4 | 8 | ||
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| × 2 | × 2 | |||
| 1/2 | 2/4 | 4/8 | ||
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See the AnimationSee Fractions on the Number Line ... it shows you many equivalent fractions We also have a Chart of Fractions with many examples of equivalent fractions. |
Dividing
Here are some more equivalent fractions, this time by dividing:
| ÷ 3 | ÷ 6 | |||
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| 18 | = | 6 | = | 1 |
| 36 | 12 | 2 | ||
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| ÷ 3 | ÷ 6 | |||
If we keep dividing until we can't go any further, then we have simplified the fraction (made it as simple as possible).
Important:
- The top and bottom of the fraction must always be a whole number.
- So, what you divide by must divide evenly (ie no remainders) for both the top and bottom numbers.
- You only multiply or divide, never add or subtract, to get an equivalent fraction.