Ordering Numbers

Ordering Numbers


Numbers can be sorted in ascending (increasing in value) or descending (decreasing in value) order.

To sort numbers with different formats - integers, fractions and percentages - re-write them in a single format. Often, the best choice is to write them as fractions, making sure that the denominator on each of the fractions is the same.


1. Arrange `frac(3)(5)`, 64%, -0.69, `frac(7)(10)` and 0.3 in ascending order.

Answer: -0.69, 0.3, `frac(3)(5)`, 64%, `frac(7)(10)`

Write each number as a fraction, using the same denominator:

`frac(3)(5)` is equivalent to `frac(60)(100)`

64% is `frac(64)(100)`

-0.69 is -`frac(69)(100)`

`frac(7)(10)`  is equivalent to `frac(70)(100)`

0.3 is `frac(3)(10)` which is equivalent to `frac(30)(100)`

Make sure that you use the original values in your answer.

2. Arrange 78%, `frac(57)(75)`, 0.77, `frac(18)(25)` in descending order.

Answer: 78%, 0.77, `frac(57)(75)`, `frac(18)(25)`

Change the numbers to fractions, then find equivalent fractions with the same denominator. The best denominator to use is 300, as this is the lowest common multiple of 25, 75 and 100.

78% is `frac(78)(100)` which is `frac(234)(300)`

`frac(18)(25)` is `frac(72)(100)`, which is `frac(216)(300)`

0.77 is `frac(77)(100)`, or `frac(231)(300)`

`frac(57)(75)` is `frac(114)(150)`, or `frac(228)(300)`

The answer needs to be in descending order.