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Here are two methods:
1) Divide the numerator by the denominator. Compare the decimals. This can be done quickly with a calculator.
2) Convert both fractions to a common denominator. This need not be the least common denominator; for example, simply multiplying the two denominators gives you a common denominator, which is not necessarily the least common denominator. Then compare the numerators.
The denominator of the fractions need to all be equal. Then you can just compare the numerator:
Example:
Which is bigger: 4/9 or 5/12
36 would be the least common multiple, but often times it's just easier to use the product of the denominators, especially by this case:
12 x 9 = 108
For 4/9 = ???/108, wemultipliedthe 9 by 12, and need to also multiply the 4 by 12.
4 x 12 = 48
Therefore: 4/9 = 48/108
For 5/12 = ???/108, wemultipliedthe 12 by 9, and need to also multiply the 5 by 9.
5 x 9 = 45
Therefore: 5/12 = 45/108
48/108 > 45/108, because 48 > 45
Therefore: 4/9 > 5/12
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lets us use this, we use fraction strips and stack them. Then compare them!
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