Ordering fractions comes down to finding the Least Common Multiple (LCM) within the denominators in a series of fractions. We’ll walk you through a simple way of finding the LCM, so you can order your fractions with ease and solve any math problem that comes your way. Plus, we'll share other methods for ordering fractions and provide tips, tricks, and example problems.
How to Order Fractions from Least to Greatest
Find the Least Common Multiple (LCM) among the fractions, then convert the fractions so they all have the same denominator. Next, order the converted fractions from least to greatest, using the numerators as a guide. Divide by the same number you multiplied by to convert the fractions to their original forms.
Steps
Ordering Fractions from Least to Greatest
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Identify the least common multiple for the fractions. According to math tutor David Jia, the first thing you have to do is find a common denominator. [1] X Expert Source David Jia
Academic Tutor Expert Interview. 23 February 2021. List out the multiples of each denominator in the problem until you find a number that all the fractions have in common. [2] X Research source- Let’s say you’re comparing three fractions: , , and . You’d list of several multiples of 8 (8, 16, 24), 3 (3, 6, 9, 12, 15, 18, 21, 24), and 4 (4, 8, 12, 16, 20, 24). In this example, 24 would be the least common denominator.
- Alternative: Multiply all the denominators together to get the LCM. For example, if you’re comparing , , and , you’d multiply 6 and 3 to get 18 as the LCM (you’d only need to multiply by 3 once).
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Convert any mixed numbers to improper fractions. Mixed numbers are a combination of whole numbers and fractions, like . To order them properly with other fractions, you need to convert them to an improper fraction (a fraction with a higher numerator than denominator):
- Separate the whole number from the fraction. In our example, that would be 3 and 2/3.
- Multiply the whole number by the denominator of the fraction. In our example, you’d multiply by , giving you .
- Add the numerators of the improper fraction and leftover fraction together. In our example, would become .
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Adjust the fractions so they all have the same denominator. Now that you know the LCM, multiply the numerator and denominator by the same number—whichever number turns the denominator into the LCM. In our example, for instance, would be multiplied by to make , with 24 being the LCM. [3] X Research source
- To continue with the previous example, we’d multiply by to get and by to get .
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Use the numerators to order the fractions from least to greatest. Now that the denominators are the same, list the fractions from the smallest numerator to the largest numerator. You’ve now successfully ordered fractions!
- The correct order of fractions from our previous example would be: .
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Divide by the original number to convert the fractions to their original numbers. According to Jia, you can “simplify by dividing the top and bottom by whatever their common factors are.” [4] X Expert Source David Jia
Academic Tutor Expert Interview. 23 February 2021. Let’s go back to the example of , which we converted to by multiplying the original fraction by . Now that we’ve successfully ordered the fractions, we can convert by dividing both the numerator and denominator by 3, which gives us again.
Ordering Fractions with Cross Multiplication
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Write the two fractions next to each other. For example, let’s compare the fraction and the fraction . Write these next to each other on the page: on the left, and on the right.
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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 ( ) is 3 . The bottom number, or denominator , of the second fraction ( ) is also 3 . Multiply these together: [7] X Research source
- This method is called cross-multiplication because you multiply numbers in a diagonal line across from each other.
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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, , so you would write 9 next to the first fraction, on the left side of the page.
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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 together. [8] X Research source
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Write this answer next to the second fraction. In this example, the answer is 10.
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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 must be less than . [9] X Research source
- Remember, always write the cross-product next to the fraction whose top number you used.
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Order the fractions based on your results. Cross-multiply fractions all the fractions within the series to figure out which ones are the biggest and smallest. Place the fractions in correct order to finish the puzzle.
Expert Q&A
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QuestionHow 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 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.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.
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QuestionWhich is the lowest: 3/5, 3/4, 4/7, or 2/3?Jasmine TippingCommunity Answer4/7 is the lowest, then 3/5, 2/3 and 3/4.
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QuestionCan I convert them into decimals while ordering them?Community AnswerYes 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.
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Tips
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Thanks
References
- ↑ David Jia. Academic Tutor. Expert Interview. 23 February 2021.
- ↑ https://flexbooks.ck12.org/cbook/ck-12-cbse-maths-class-6/section/5.3/primary/lesson/comparing-and-ordering-fractions/
- ↑ https://flexbooks.ck12.org/cbook/ck-12-cbse-maths-class-6/section/5.3/primary/lesson/comparing-and-ordering-fractions/
- ↑ David Jia. Academic Tutor. Expert Interview. 23 February 2021.
- ↑ https://flexbooks.ck12.org/cbook/ck-12-cbse-maths-class-6/section/5.3/primary/lesson/comparing-and-ordering-fractions/
- ↑ https://flexbooks.ck12.org/cbook/ck-12-cbse-maths-class-6/section/5.3/primary/lesson/comparing-and-ordering-fractions/
- ↑ https://flexbooks.ck12.org/cbook/ck-12-cbse-maths-class-6/section/5.3/primary/lesson/comparing-and-ordering-fractions/
- ↑ https://flexbooks.ck12.org/cbook/ck-12-cbse-maths-class-6/section/5.3/primary/lesson/comparing-and-ordering-fractions/
- ↑ https://flexbooks.ck12.org/cbook/ck-12-cbse-maths-class-6/section/5.3/primary/lesson/comparing-and-ordering-fractions/
About This Article
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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