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This article was co-written by David Jia. David Jia is a tutoring teacher and founder of LA Math Tutoring, a private tutoring facility based in Los Angeles, California. With over 10 years of teaching experience, David teaches a wide variety of subjects to students of all ages and grades, as well as college admissions counseling and prep for SAT, ACT, ISEE, etc. scoring 800 in math and 690 in English on the SAT, David was awarded a Dickinson Scholarship to the University of Miami, where he graduated with a bachelor’s degree in business administration. Additionally, David has worked as an instructor in online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math.
This article has been viewed 113,131 times.
While sorting integers such as 1, 3, and 8 by large or small is simple, sorting fractions can seem difficult at first glance. If the denominators are the same, you can sort them as whole numbers, for example 1/5, 3/5 and 8/5. Otherwise, you can convert the fractions to the same denominator without changing their values. This gets easier with practice, and you may learn a few “tricks” when comparing two fractions, or when sorting “unordinary” fractions with a larger numerator than a denominator like 7/ 3.
Steps
Sort any number of fractions
- Multiply different denominators together. For example, if you are comparing three fractions 2/3, 5/6 and 1/3, multiply the two different denominators: 3 x 6 = 18 . This is a simple method, but will usually result in a much larger number than the other methods.
- Or list the multiples of each denominator in a separate column until you find a common multiple between the columns. This is the number you are looking for. For example, comparing 2/3, 5/6, and 1/3, list several multiples of 3: 3, 6, 9, 12, 15, 18. Then list multiples of 6: 6, 12, 18. Since 18 appears in both lists, we will use this number. (You can also use 12, but 18 is assumed to be used in the examples below.)
- 18 3 = 6, so 2/3 = (2×6)/(3×6)=12/18
- 18 6 = 3, so 5/6 = (5×3)/(6×3)=15/18
- 18 3 = 6, so 1/3 = (1×6)/(3×6)=6/18
- 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”
Sort two fractions by cross multiplying
- This method is called cross multiplication , because you multiply the numbers diagonally between two fractions.
- Remember, always write the cross product next to the numerator of the fraction you’re comparing.
- 3/5=(3×3)/(5×3)=9/15
- 2/3=(2×5)/(3×5)=10/15
- 9/15 is less than 10/15
- Therefore, 3/5 is less than 2/3
Sort fractions greater than 1
- You can still use other methods for this type of fraction. However this method makes it easier to understand, and possibly faster.
- 8/3 = 2 + 2/3
- 9/9 = 1
- 19/4 = 4 + 3/4
- 13/6 = 2 + 1/6
- 1 is the smallest
- 2 + 2/3 and 2 + 1/6 (we don’t know which is greater than the other)
- 4 + 3/4 is the largest
- 2/3 = (2×2)/(3×2) = 4/6
- 1/6 = 1/6
- 4/6 is bigger than 1/6
- 2 + 4/6 is greater than 2 + 1/6
- 2 + 2/3 is greater than 2 + 1/6
Advice
- If the numerators are the same, you can sort in reverse order of the denominators. For example, 1/8 < 1/7 < 1/6 < 1/5. Think of a pizza: if you go from 1/2 to 1/8, that means you’ll cut the pie into 8 pieces instead of 2, and the piece you have now is much smaller.
- When sorting a large number of fractions, you should compare and sort small groups of 2, 3, or 4 fractions at a time.
- While the least common denominator helps you work with small numbers, any common denominator is useful. Try sorting 2/3, 5/6, and 1/3 using the common denominator of 36, and see if you get the same result.
This article was co-written by David Jia. David Jia is a tutoring teacher and founder of LA Math Tutoring, a private tutoring facility based in Los Angeles, California. With over 10 years of teaching experience, David teaches a wide variety of subjects to students of all ages and grades, as well as college admissions counseling and prep for SAT, ACT, ISEE, etc. scoring 800 in math and 690 in English on the SAT, David was awarded a Dickinson Scholarship to the University of Miami, where he graduated with a bachelor’s degree in business administration. Additionally, David has worked as an instructor in online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math.
This article has been viewed 113,131 times.
While sorting integers such as 1, 3, and 8 by large or small is simple, sorting fractions can seem difficult at first glance. If the denominators are the same, you can sort them as whole numbers, for example 1/5, 3/5 and 8/5. Otherwise, you can convert the fractions to the same denominator without changing their values. This gets easier with practice, and you may learn a few “tricks” when comparing two fractions, or when sorting “unordinary” fractions with a larger numerator than a denominator like 7/ 3.
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