Question

How do you order these fractions: `4/5, 1/2, 9/10 and 3/4` from least to greatest?

Answer 1

First, we need to make all of their denominators the same. We do this by finding the 'LCD', or Lowest Common Denominator. This means the lowest number that all of these numbers multiply to.

20 is the LCD since they all multiply to it.

Let's look at `4/5`. What times `5` multiplies to `20`? `4`.
So we multiply the whole fraction by `4`, like this:
`(4 * 4)/(5 * 4) = 16/20`

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And we do the same thing for the other fractions:

For `1/2`, What times `2` multiplies to `20`? `10`.
So we multiply the whole fraction by `10`, like this:
`(1 * 10)/(2 * 10) = 10/20`

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`(9 * 2)/(10 * 2) = 18/20`

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`(3 * 5)/(4 * 5) = 15/20`

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Now that we've got our fractions all with denominators of 20, let's list them out again.
`16/20, 10/20, 18/20`, and `15/20`.

Let's just focus on the numerators now, and list them out from least to greatest.
We can see that `10` is the smallest, then `15`, then `16`, then `18`.
So the fractions from least to greatest is `10/20, 15/20, 16/20`, and `18/20`.

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We should now put them back into their original form before they were multiplied to the LCD.
`10/20` was `1/2`
`15/20` was `3/4`
`16/20` was 4/5# and #18/20`was`9/10#

So the least to greatest is `1/2`, `3/4`, `4/5`, and `9/10`.

If you still need help with ordering fractions from least to greatest, feel free to watch this video: https://www.khanacademy.org/math/arithmetic/fraction-arithmetic/arith-review-comparing-fractions/v/order-fractions

Hope this helps!