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How would you order these fractions from smallest to largest: 5/6,2/3,1/4?

2 years ago

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3 Replies

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E

Eliseo Funk


3 Answers

Sharon S Profile Picture
Sharon S Verified Sherpa Tutor ✓

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Ordering fractions is much easier if all the denominators are the same. Then you will be comparing 'like' fractions instead of the unlike ones these currently are.

So first we need to find the lowest common multiple of the three denominators 6, 3 and 4. Although 3 goes into 6, 4 doesn't. 12 is a multiple of 6, 3 and 4 - this is our lowest common denominator (multiple).

To change the '6' into a 12, we multiply by 2. That means we need to multiply the top (numerator) by 2 as well to keep it being the same fraction. 5 x 2 = 10.

Therefore, 5/6 = 10/12

To change the '3' into a 12, we multiply by 4. That means we need to multiply the top (numerator) by 4 as well to keep it being the same fraction. 2 x 4 = 8.

Therefore, 2/3 = 8/12

To change the '4' into a 12, we multiply by 3. That means we need to multiply the top (numerator) by 3 as well to keep it being the same fraction. 1 x 3 = 3.

Therefore, 1/4 = 3/12

We are now dealing with: 10/12, 8/12 and 3/12.

Much easier to order. Smallest to biggest: 3/12, 8/12, 10/12

But write them in their original form: 1/4, 2/3, 5/6

Visually drawing squares and colouring in is also helpful to understand better.

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Elizabeth H Profile Picture
Elizabeth H Verified Sherpa Tutor ✓

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To solve this problem I would make the fractions more useable by finding equivalent fractions that all have the same denominator. In this case it would be 12 - 5/6 x2 = 10/12, 2/3 x4 = 8/12, 1/4 x3 = 3/12 then order them 2/12, 8/12 and 10/12


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Vicky Miller

First, you would need to convert all fractions to a common denominator.

All three fractions can be converted into 12ths as 6, 3 & 4 are all factors of 12.

Now convert the fractions:

5/6 = 10/12 because to convert to 12ths we needed to multiply the denominator (bottom number) by 2, therefore we must do the same with the numerator (top number).

2/3 = 8/12 (see above for explanation)

1/4 = 3/12

Now all of the fractions have the same denominator, we can put them in order from smallest to largest:

1/4 or 3/12, 2/3 or 8/12, 5/6 or 10/12


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