Is 8/10 Greater Than 3/5

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While information technology's easy to order whole numbers like 1, 3, and 8 by size, fractions tin be hard to mensurate at a glance. If each lower number, or denominator, is the aforementioned, you can guild them similar whole numbers, for instance 1/5, three/five, and 8/5. Otherwise, you tin can alter your list of fractions to utilize the same denominator, without irresolute the size of any fraction. This becomes easier with exercise, and yous tin learn a couple "tricks" every bit well when comparison just 2 fractions, or when you're sorting top-heavy "improper" fractions similar 7/3.

1
Find 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, and then y'all can easily compare them. This is chosen a common denominator, or the lowest common denominator if it is the lowest i possible:^[ane]
- Multiply every different denominator together. For example, if you are comparing 2/3, five/6, and i/3, multiply the ii different denominators: 3 x 6 = xviii. This is a simple method, but will often issue in a much larger number than the other methods, which can be difficult to work with.^[two]
- Or listing the multiples of each denominator in a separate column, until you discover a number that shows upwardly on every cavalcade. Use this number. For example, comparison 2/three, v/half dozen, and 1/3, list a few multiples of 3: 3, half-dozen, 9, 12, fifteen, 18. Then list the multiples of 6: 6, 12, 18. Since eighteen shows up on both lists, use that number. (You could as well use 12, but the examples below will assume you are using 18.)
2
Catechumen each fraction so it uses the mutual denominator. Recollect, if you multiply a fraction's height and bottom past the same corporeality, the fraction is still the same size.^[3] Use this technique on each fraction, one past one, then that each one uses the common denominator equally the bottom number. Try information technology for 2/three, five/6, and 1/three, using the common denominator xviii:
- eighteen ÷ 3 = 6, so 2/3 = (2x6)/(3x6)=12/eighteen
- xviii ÷ 6 = 3, so 5/6 = (5x3)/(6x3)=15/18
- 18 ÷ iii = six, and so 1/three = (1x6)/(3x6)=6/18
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iii

Employ the top number to club the fractions. Now that they all accept the same denominator, the fractions are piece of cake to compare. Use their elevation number, or numerator, to rank them from to the lowest degree to greatest. Ranking the fractions we found above, nosotros go: vi/18, 12/xviii, fifteen/18.
4
Return each fraction to its original course. Keep the fractions in the same social club, but return each 1 dorsum to its original form. You can exercise this past remembering how each fraction transformed, or by dividing the tiptop and lesser of each fraction again:
- 6/xviii = (6 ÷ vi)/(18 ÷ 6) = 1/3
- 12/18 = (12 ÷ 6)/(18 ÷ 6) = ii/3
- 15/18 = (15 ÷ 3)/(18 ÷ 3) = 5/6
- The reply is "1/3, ii/three, 5/vi"

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1

Write the two fractions next to each other. For example, compare the fraction 3/5 and the fraction 2/iii. Write these next to each other on the page: 3/v on the left, and 2/3 on the correct.
2
Multiply the height of the first fraction with the lesser of the 2d fraction. In our example, the top number, or numerator, of the first fraction (3/5) is 3. The bottom number, or denominator, of the second fraction (2/3) is likewise 3. Multiply these together: 3 ten three = ?
- This method is called cross-multiplication, because yous multiply numbers in a diagonal line beyond from each other.
iii

Write your respond side by side to the first fraction. Write the product, or answer to your multiplication problem, next to the kickoff fraction on the page. In our example, iii x 3 = ix, then you would write nine side by side to the commencement fraction, on the left side of the folio.
4

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

Write this answer adjacent to the second fraction. Write the answer to this 2d multiplication problem next to the 2d fraction. In this example, the answer is x.
6
Compare the values of the ii cantankerous-products. The answers to the multiplication problems in this method are called cross-products. If one cross-product is larger than the other, and so the fraction next to that cross-product is also larger than the other fraction. In our example, because ix is less than 10, this means 3/five must be less than two/3.
- Remember, e'er write the cross-product side by side to the fraction whose peak number y'all used.
7
Understand why this works. To compare ii fractions, typically you lot transform them to give them the aforementioned denominator, or lower part of the fraction. Secretly, this is what cross-multiplication does!^[four] It but skips over really writing the denominators, since once the 2 fractions have the same 1, you only need to compare the summit ii numbers. Here's our same example (3/5 vs 2/iii), written without the cross-multiplying "shortcut":
- 3/5=(3x3)/(5x3)=9/15
- 2/3=(2x5)/(3x5)=10/15
- 9/fifteen is less than 10/15
- Therefore, 3/five is less than 2/3

i
Utilise this for fractions with a top number equal or larger than the lesser number. If a fraction has a top number, or numerator, that is larger than the lesser number, or denominator, it is larger than 1. 8/3 is one instance of this type of fraction. You tin also use this for fractions with an equal numerator and denominator, such every bit ix/ix. Both of these fractions are examples of improper fractions.^[5]
- Yous tin can notwithstanding use the other methods for these fractions. This method helps these fractions brand sense, however, and might be faster.
two
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 caput. For case, 9/nine = 1. Other times, apply long division to notice out how many times the numerator goes evenly into the denominator. The remainder in that long division problem, if any, gets "left over" equally a fraction. For instance:
- eight/3 = 2 + two/iii
- ix/nine = i
- nineteen/4 = iv + 3/iv
- xiii/6 = ii + 1/6
3
Sort the mixed numbers by whole number. Now that in that location are no improper fractions, you accept a better idea of how big each number is. Ignore the fractions for now, and sort the fractions into groups by whole number:
- ane is the smallest
- 2 + 2/3 and 2 + 1/6 (we don't yet know which is larger than the other)
- iv + 3/four is the largest
iv
If necessary, compare the fractions in each grouping. If you have multiple mixed numbers with the aforementioned whole number, such as ii + two/three and two + 1/6, compare the fraction part of the number to see which is larger. You tin can utilize any of the methods in the other sections to practice this. Here'southward an example comparison 2 + two/3 and two + 1/half dozen, converting the fractions to the aforementioned denominator:
- 2/iii = (2x2)/(3x2) = 4/6
- ane/vi = one/6
- 4/6 is greater than i/6
- ii + 4/vi is greater than 2 + i/half dozen
- 2 + two/3 is greater than two + 1/6
five

Use your results to sort your whole list of mixed numbers. One time you've sorted the fractions in each group of mixed numbers, you tin can sort your entire list: i, 2 + i/six, 2 + 2/3, 4 + 3/4.
six

Convert the mixed numbers back to their original fractions. Keep the guild the same, but undo the changes you lot made and write the numbers as the original improper fractions: 9/nine, eight/3, 13/half-dozen, nineteen/four.

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Question

How can I tell which fraction is greater?

David Jia is an Academic Tutor and the Founder of LA Math Tutoring, a private tutoring company based in Los Angeles, California. With over ten years of educational activity feel, David works with students of all ages and grades in various subjects, as well equally college admissions counseling and test preparation for the Sabbatum, Human action, ISEE, and more. Later on attaining a perfect 800 math score and a 690 English score on the Sabbatum, David was awarded the Dickinson Scholarship from the University of Miami, where he graduated with a Bachelor's degree in Business Administration. Additionally, David has worked as an instructor for online videos for textbook companies such equally Larson Texts, Big Ideas Learning, and Big Ideas Math.

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Expert Answer

Look for a mutual denominator between the fractions, so multiply the numerators and denominators past the same value. Then you lot tin can see which fraction is greater merely past the numerator.
Question

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

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Customs Answer

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

Can I convert them into decimals while ordering them?

Yes you tin can, the gild volition be the same. Just make sure to convert dorsum to fractions for your concluding answer if the original numbers are given equally fractions.

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If the numerators are even so, you can sort in reverse gild of denominator. For case, 1/8 < 1/7 < 1/6 < i/five. Think of information technology as a pizza: if you become from 1/2 to 1/8, you're cutting the pizza into 8 slices instead of 2, and the 1 slice yous get is now much smaller.
When ordering a large number of fractions, information technology may be helpful to compare and order smaller groups of ii, 3, or 4 fractions at a time.
While finding the everyman mutual denominator is helpful and then you tin can work with smaller numbers, any common denominator will work. Try sorting two/3, 5/6, and 1/3 using a common denominator of 36, and meet if yous become the same result.

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Article Summary X

To gild fractions from least to greatest, commencement by finding the everyman common denominator for all of the fractions. Adjacent, catechumen each of the fractions by dividing the everyman mutual denominator past the denominator and then multiplying the tiptop and lesser of the fraction past your respond. In one case all of the fractions have the same denominator, guild them from least to greatest using the numerators. To learn how to order fractions that are greater than 1, scroll down!

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