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Ordering Fractions

Ordering Fractions

To place fractions in order, find equivalent fractions for each one, making sure that the denominators are the same.

Then compare the numerators to order the fractions.

Example 1

Put these fractions in ascending order: `-frac(1)(3), frac(1)(3), -frac(2)(3), frac(2)(3), -frac(5)(3)`

The denominator is the same for each fraction, so examine the numerators, taking the negative sign into account.

Answer: `-frac(5)(3), -frac(2)(3), -frac(1)(3), frac(1)(3), frac(2)(3) `

Example 2

Put these fractions in ascending order: `frac(3)(4), 2, frac(1)(2), frac(5)(12), 1frac(1)(3)`

To compare the fractions, find equivalent fractions where the denominator is the same. The common denominator is 12, as 4, 2, 3, 12 are all factors of 12.

Convert each fraction into an equivalent fraction, each with a denominator of 12:

`frac(3)(4)` becomes `frac(9)(12)` (multiply top and bottom by 3)

2 is the same as `frac(2)(1)` and becomes `frac(24)(12)` (convert 2 to a fraction, multiply by 12)

`frac(1)(2)` becomes `frac(6)(12)` (multiply by 6)

`frac(5)(12)` is left as it is and

1`frac(1)(3)` is `frac(4)(3)` which becomes `frac(16)(12)` (convert to a top-heavy fraction, multiply by 4)

Compare the numerators and place in order.

Answer: `frac(5)(12), frac(1)(2), frac(3)(4), 1frac(1)(3), 2`

See also Terminating Decimals and Fractions and Ordering Numbers