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Write Mc019-1.jpg, Mc019-2.jpg, Mc019-3.jpg in Order From Least to Greatest.

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While it's easy to order whole numbers like 1, 3, and 8 by size, fractions can be hard to measure at a glance. If each lower number, or denominator, is the same, you can order them like whole numbers, for instance 1/5, 3/5, and 8/5. Otherwise, you can alter your list of fractions to use the same denominator, without changing the size of any fraction. This becomes easier with practice, and you can learn a couple "tricks" as well when comparing just two fractions, or when you're sorting top-heavy "improper" fractions like 7/3.

  1. 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 you can use to rewrite every fraction in the list, so you can easily compare them. This is called a common denominator, or the lowest common denominator if it is the lowest one possible:[1]

    • Multiply every different denominator together. For example, if you are comparing 2/3, 5/6, and 1/3, multiply the two different denominators: 3 x 6 = 18. This is a simple method, but will often result in a much larger number than the other methods, which can be difficult to work with.[2]
    • Or list the multiples of each denominator in a separate column, until you notice a number that shows up on every column. Use this number. For example, comparing 2/3, 5/6, and 1/3, list a few multiples of 3: 3, 6, 9, 12, 15, 18. Then list the multiples of 6: 6, 12, 18. Since 18 shows up on both lists, use that number. (You could also use 12, but the examples below will assume you are using 18.)
  2. 2

    Convert each fraction so it uses the common denominator. Remember, if you multiply a fraction's top and bottom by the same amount, the fraction is still the same size.[3] Use this technique on each fraction, one by one, so that each one uses the common denominator as the bottom number. Try it for 2/3, 5/6, and 1/3, using the common denominator 18:

    • 18 ÷ 3 = 6, so 2/3 = (2x6)/(3x6)=12/18
    • 18 ÷ 6 = 3, so 5/6 = (5x3)/(6x3)=15/18
    • 18 ÷ 3 = 6, so 1/3 = (1x6)/(3x6)=6/18

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  3. 3

    Use the top number to order the fractions. Now that they all have the same denominator, the fractions are easy to compare. Use their top number, or numerator, to rank them from least to greatest. Ranking the fractions we found above, we get: 6/18, 12/18, 15/18.

  4. 4

    Return each fraction to its original form. Keep the fractions in the same order, but return each one back to its original form. You can do this by remembering how each fraction transformed, or by dividing the top and bottom of each fraction again:

    • 6/18 = (6 ÷ 6)/(18 ÷ 6) = 1/3
    • 12/18 = (12 ÷ 6)/(18 ÷ 6) = 2/3
    • 15/18 = (15 ÷ 3)/(18 ÷ 3) = 5/6
    • The answer is "1/3, 2/3, 5/6"

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  1. 1

    Write the two 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: 3/5 on the left, and 2/3 on the right.

  2. 2

    Multiply the top of the first fraction with the bottom of the second 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 also 3. Multiply these together: 3 x 3 = ?

    • This method is called cross-multiplication, because you multiply numbers in a diagonal line across from each other.
  3. 3

    Write your answer next to the first fraction. Write the product, or answer to your multiplication problem, next to the first fraction on the page. In our example, 3 x 3 = 9, so you would write 9 next to the first fraction, on the left side of the page.

  4. 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 answer above with the answer to another multiplication problem. Multiply these two numbers together. For our example (comparing 3/5 and 2/3), multiply 2 x 5 together.

  5. 5

    Write this answer next to the second fraction. Write the answer to this second multiplication problem next to the second fraction. In this example, the answer is 10.

  6. 6

    Compare the values of the two cross-products. The answers to the multiplication problems in this method are called cross-products. If one 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, because 9 is less than 10, this means 3/5 must be less than 2/3.

    • Remember, always write the cross-product next to the fraction whose top number you used.
  7. 7

    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 cross-multiplication does![4] It just skips over actually writing the denominators, since once the two fractions have the same one, you only need to compare the top two numbers. Here's our same example (3/5 vs 2/3), written without the cross-multiplying "shortcut":

    • 3/5=(3x3)/(5x3)=9/15
    • 2/3=(2x5)/(3x5)=10/15
    • 9/15 is less than 10/15
    • Therefore, 3/5 is less than 2/3

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  1. 1

    Use this for fractions with a top number equal or larger than the bottom number. If a fraction has a top number, or numerator, that is larger than the bottom number, or denominator, it is larger than one. 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 9/9. Both of these fractions are examples of improper fractions.[5]

    • You can still use the other methods for these fractions. This method helps these fractions make sense, however, and might be faster.
  2. 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 = 1. Other times, use long division to find out how many times the numerator goes evenly into the denominator. The remainder in that long division problem, if any, gets "left over" as a fraction. For instance:

    • 8/3 = 2 + 2/3
    • 9/9 = 1
    • 19/4 = 4 + 3/4
    • 13/6 = 2 + 1/6
  3. 3

    Sort the mixed numbers by whole number. Now that there are no improper fractions, you have a better idea of how large each number is. Ignore the fractions for now, and sort the fractions into groups by whole number:

    • 1 is the smallest
    • 2 + 2/3 and 2 + 1/6 (we don't yet know which is larger than the other)
    • 4 + 3/4 is the largest
  4. 4

    If necessary, compare the fractions in each group. If you have multiple mixed numbers with the same whole number, such as 2 + 2/3 and 2 + 1/6, compare the fraction part of the number to see which is larger. You can use any of the methods in the other sections to do this. Here's an example comparing 2 + 2/3 and 2 + 1/6, converting the fractions to the same denominator:

    • 2/3 = (2x2)/(3x2) = 4/6
    • 1/6 = 1/6
    • 4/6 is greater than 1/6
    • 2 + 4/6 is greater than 2 + 1/6
    • 2 + 2/3 is greater than 2 + 1/6
  5. 5

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

  6. 6

    Convert the mixed numbers back to their original fractions. Keep the order the same, but undo the changes you made and write the numbers as the original improper fractions: 9/9, 8/3, 13/6, 19/4.

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Add New Question

  • Question

    How can I tell which fraction is greater?

    David Jia

    David Jia is an Academic Tutor and the Founder of LA Math Tutoring, a private tutoring company based in Los Angeles, California. With over 10 years of teaching experience, David works with students of all ages and grades in various subjects, as well as college admissions counseling and test preparation for the SAT, ACT, ISEE, and more. After attaining a perfect 800 math score and a 690 English score on the SAT, 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 as Larson Texts, Big Ideas Learning, and Big Ideas Math.

    David Jia

    Academic Tutor

    Expert Answer

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

  • Question

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

    Jasmine Tipping

    Jasmine Tipping

    Community Answer

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

  • Question

    Can I convert them into decimals while ordering them?

    Community Answer

    Yes you can, the order will be the same. Just make sure to convert back to fractions for your final answer if the original numbers are given as fractions.

  • Question

    How do I order fractions from least to greatest if the denominators are different?

    Community Answer

    Make them the same by multiplying both the numerator and the denominator of the smallest fraction, and if necessary, the largest one as well. For instance if you have 1/5 and 3/7, they are equivalent to 7/35 and 15/35 [ (7*1)/(7*5) and (5*3)/(5*7).

  • Question

    How can I put 2/3, 4/5, and 1/2 from least to greatest?

    Community Answer

    The smallest fraction is 1/2, then 2/3, then 4/5.

  • Question

    I have two equal fractions in a set. How should I arrange them?

    Donagan

    If you're ordering from least to greatest (or vice versa), list the equal fractions consecutively. You might want to list the fraction with the smaller denominator first, but it really wouldn't make any difference in terms of value.

  • Question

    How can I arrange 1/5, 2/3, and 5/8 from least to greatest?

    LyKaxandra Caimoy

    LyKaxandra Caimoy

    Community Answer

    You can try dividing it (or converting to decimal). Then you can start arranging it ascending. Also, you can try to find its LCD. If you do so, you will get 120. The fractions then will be 24/120, 80/120, and 75/120. If arranged: 24/120, 75/120, 80/120 or "1/5, 5/8, 2/3"

  • Question

    What is an easy way of ordering fractions with the same numerator?

    Donagan

    Look at the denominators. The fraction with the smaller denominator has a value greater than the fraction with the larger denominator.

  • Question

    How do I find out the percentage of the fraction?

    Community Answer

    To use an example, use 3 over 5, so take the top number and divide it by the bottom number and multiply it by 100. That will give you the percentage.

  • Question

    What do I do if my answers don't match?

    LyKaxandra Caimoy

    LyKaxandra Caimoy

    Community Answer

    Do it again to be sure of your answer.

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  • If the numerators are all the same, you can sort in reverse order of denominator. For instance, 1/8 < 1/7 < 1/6 < 1/5. Think of it as a pizza: if you go from 1/2 to 1/8, you're cutting the pizza into 8 slices instead of 2, and the 1 slice you get is now much smaller.

  • When ordering a large number of fractions, it may be helpful to compare and order smaller groups of 2, 3, or 4 fractions at a time.

  • While finding the lowest common denominator is helpful so you can work with smaller numbers, any common denominator will work. Try sorting 2/3, 5/6, and 1/3 using a common denominator of 36, and see if you get the same result.

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Article SummaryX

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 by the denominator and then multiplying the top and bottom of the fraction by your answer. Once all of the fractions have the same denominator, order 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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Write Mc019-1.jpg, Mc019-2.jpg, Mc019-3.jpg in Order From Least to Greatest.

Source: https://www.wikihow.com/Order-Fractions-From-Least-to-Greatest