Fractions From Smallest To Biggest

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While it's easy to order whole numbers like 1, 3, and viii past size, fractions tin exist difficult to measure at a glance. If each lower number, or denominator, is the same, you can lodge them like whole numbers, for example 1/5, 3/five, and 8/5. Otherwise, you can modify your list of fractions to use the same denominator, without changing the size of any fraction. This becomes easier with do, and you tin can learn a couple "tricks" likewise when comparing simply two fractions, or when you lot're sorting top-heavy "improper" fractions like vii/3.

1
Notice a common denominator for all the fractions. Use one of these methods to find a denominator, or lower number of a fraction, that y'all can employ to rewrite every fraction in the list, so you can hands compare them. This is called a common denominator, or the lowest common denominator if information technology is the lowest i possible:^[1]
- Multiply every different denominator together. For case, if you lot are comparing 2/iii, 5/vi, and 1/3, multiply the two different denominators: 3 10 6 = eighteen. This is a simple method, but will oft issue in a much larger number than the other methods, which tin can be hard to work with.^[2]
- Or list the multiples of each denominator in a separate column, until you lot notice a number that shows upwardly on every column. Use this number. For instance, comparing 2/3, 5/6, and one/iii, list a few multiples of three: 3, half-dozen, 9, 12, 15, xviii. So list the multiples of half-dozen: vi, 12, 18. Since 18 shows up on both lists, utilise that number. (You could also employ 12, but the examples below volition presume you are using 18.)
2
Convert each fraction and then it uses the common denominator. Think, if you multiply a fraction's top and lesser by the same amount, the fraction is withal the aforementioned size.^[three] Use this technique on each fraction, i by one, so that each one uses the common denominator as the bottom number. Try information technology for two/3, 5/6, and i/iii, using the common denominator xviii:
- 18 ÷ 3 = 6, so two/3 = (2x6)/(3x6)=12/18
- 18 ÷ 6 = 3, so 5/six = (5x3)/(6x3)=15/18
- 18 ÷ 3 = 6, and so 1/3 = (1x6)/(3x6)=vi/18
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iii

Employ the top number to order the fractions. Now that they all have the same denominator, the fractions are piece of cake to compare. Apply their height number, or numerator, to rank them from least to greatest. Ranking the fractions we found higher up, nosotros go: half dozen/xviii, 12/18, fifteen/18.
iv
Return each fraction to its original form. Keep the fractions in the same social club, but render each one back to its original course. You tin can do this by remembering how each fraction transformed, or by dividing the superlative and bottom of each fraction once more:
- 6/18 = (6 ÷ half dozen)/(18 ÷ 6) = one/3
- 12/xviii = (12 ÷ 6)/(18 ÷ 6) = 2/3
- 15/xviii = (xv ÷ 3)/(xviii ÷ iii) = 5/6
- The reply is "1/3, two/3, 5/6"

1

Write the 2 fractions next to each other. For example, compare the fraction 3/5 and the fraction 2/3. Write these next to each other on the page: iii/5 on the left, and two/3 on the correct.
ii
Multiply the top of the beginning fraction with the bottom of the second fraction. In our example, the top number, or numerator, of the starting time fraction (3/v) is 3. The bottom number, or denominator, of the second fraction (2/iii) is also 3. Multiply these together: 3 x iii = ?
- This method is called cross-multiplication, considering you multiply numbers in a diagonal line across from each other.
3

Write your answer next to the beginning fraction. Write the product, or answer to your multiplication problem, next to the first fraction on the page. In our example, iii 10 iii = ix, so you would write 9 side by side to the first fraction, on the left side of the page.
4

Multiply the top of the second fraction with the bottom of the kickoff. To discover out which fraction is larger, we'll need to compare our answer above with the answer to another multiplication problem. Multiply these two numbers together. For our example (comparing three/five and 2/3), multiply two x 5 together.
five

Write this answer side by side to the second fraction. Write the answer to this 2d multiplication problem side by side to the second fraction. In this example, the answer is 10.
half-dozen
Compare the values of the two cross-products. The answers to the multiplication problems in this method are chosen cross-products. If 1 cross-product is larger than the other, then the fraction next to that cross-product is also larger than the other fraction. In our example, considering 9 is less than ten, this means 3/5 must be less than two/3.
- Recollect, always write the cross-production side by side to the fraction whose top number you used.
seven
Understand why this works. To compare two fractions, typically you transform them to give them the same denominator, or lower part of the fraction. Secretly, this is what cantankerous-multiplication does!^[4] Information technology just skips over actually writing the denominators, since once the ii fractions have the same ane, you but demand to compare the tiptop ii numbers. Here'due south our aforementioned example (3/5 vs two/iii), written without the cantankerous-multiplying "shortcut":
- 3/five=(3x3)/(5x3)=9/15
- two/iii=(2x5)/(3x5)=10/15
- 9/15 is less than 10/15
- Therefore, 3/5 is less than two/3

1
Utilise this for fractions with a summit number equal or larger than the bottom number. If a fraction has a elevation number, or numerator, that is larger than the bottom number, or denominator, it is larger than i. 8/3 is one example of this type of fraction. You can also use this for fractions with an equal numerator and denominator, such as 9/ix. Both of these fractions are examples of improper fractions.^[5]
- Y'all tin nevertheless use the other methods for these fractions. This method helps these fractions make sense, still, and might be faster.
2
Convert each improper fraction into a mixed number. Turn them into a mix of whole numbers and fractions. Sometimes, you might be able to do this in your head. For example, 9/9 = ane. Other times, utilise long division to find out how many times the numerator goes evenly into the denominator. The rest in that long division problem, if any, gets "left over" as a fraction. For instance:
- 8/3 = 2 + 2/3
- 9/9 = one
- xix/iv = 4 + 3/4
- xiii/half dozen = 2 + 1/six
three
Sort the mixed numbers by whole number. At present that at that place are no improper fractions, yous have a improve idea of how big each number is. Ignore the fractions for now, and sort the fractions into groups by whole number:
- 1 is the smallest
- 2 + two/three and 2 + i/6 (we don't yet know which is larger than the other)
- 4 + 3/4 is the largest
four
If necessary, compare the fractions in each group. If you have multiple mixed numbers with the aforementioned whole number, such as 2 + ii/3 and 2 + ane/6, compare the fraction office of the number to see which is larger. You can utilize any of the methods in the other sections to do this. Here's an instance comparing 2 + 2/three and 2 + 1/half dozen, converting the fractions to the aforementioned denominator:
- ii/three = (2x2)/(3x2) = 4/six
- 1/half-dozen = i/6
- 4/6 is greater than 1/6
- 2 + 4/half-dozen is greater than 2 + 1/6
- two + 2/3 is greater than 2 + 1/6
v

Use your results to sort your whole list of mixed numbers. Once you've sorted the fractions in each grouping of mixed numbers, you can sort your entire listing: 1, 2 + 1/6, two + 2/3, four + 3/4.
6

Convert the mixed numbers back to their original fractions. Continue the guild the same, only undo the changes you fabricated and write the numbers as the original improper fractions: 9/nine, viii/3, 13/six, 19/4.

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How tin can I tell which fraction is greater?

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Expert Answer

Look for a common denominator between the fractions, then multiply the numerators and denominators past the same value. Then you lot can see which fraction is greater just by the numerator.
Question

Which is the lowest: three/5, 3/4, 4/7, or 2/3?

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Community Answer

4/7 is the lowest, then 3/5, 2/iii and 3/4.
Question

Can I convert them into decimals while ordering them?

Yes y'all can, the guild will be the aforementioned. Just make sure to convert back to fractions for your concluding answer if the original numbers are given as fractions.

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If the numerators are all the aforementioned, you can sort in contrary lodge of denominator. For case, 1/8 < one/seven < i/6 < 1/5. Think of it as a pizza: if you become from 1/2 to 1/eight, you lot're cutting the pizza into viii slices instead of 2, and the i slice you get is now much smaller.

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When ordering a large number of fractions, it may be helpful to compare and order smaller groups of 2, three, or four fractions at a time.

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While finding the lowest common denominator is helpful so you can piece of work with smaller numbers, whatever common denominator volition piece of work. Attempt sorting ii/3, five/6, and ane/3 using a common denominator of 36, and see if yous get the same upshot.

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To order fractions from least to greatest, start by finding the lowest common denominator for all of the fractions. Next, convert each of the fractions by dividing the lowest common denominator past the denominator and and then multiplying the tiptop and bottom of the fraction by your answer. Once all of the fractions accept the same denominator, order them from least to greatest using the numerators. To learn how to social club fractions that are greater than i, scroll down!

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