Content

• To step
• Method 1 of 3: Order any number of fractions
• Method 2 of 3: Order two fractions with cross multiplication
• Method 3 of 3: Order fractions greater than one
• Tips

While it is easy to size integers such as 1, 3, and 8, with fractions this is not always obvious. If each denominator is equal, then you can order them as well as integers, such as 1/5, 3/5 and 8/5. In other cases, you can convert the fractions to have the same denominator without changing the value of the fraction. This will be easier if you practice a lot and you can use some handy tricks, both comparing two fractions or ordering fractions where the numerator is greater than the denominator, the improper fractions such as 7/3.

To step

Method 1 of 3: Order any number of fractions

1. Find an equal denominator for all fractions. Use one of the following methods to find a denominator, or decrease the number of a fraction, which you can use to rewrite any fraction in the list for easy comparison. You call this one common denominator, or the least common denominator if this is the smallest possible:
   • Multiply each denominator. For example, if you're comparing 2/3, 5/6, and 1/3, multiply these denominators: 3 x 6 = 18. This is a simple method but one that often results in a much larger number than the other methods, which are a bit trickier.
   • Or List multiples of each denominator in a separate column until it pops out to a number that occurs more often. For example, for 2/3, 5/6, and 1/3, you have a list of multiples of 3: 3, 6, 9, 12, 15, 18. Then a list of multiples of 6: 6, 12, 18. Because 18 appears in both lists, use that number (You can also use 12, but the examples below assume that you use 18).
2. Convert each fraction so that they have an equal denominator. Remember, if you multiply the numerator and denominator of a fraction by the same number, the value of the fraction stays the same. Use this technique with each fraction, one at a time, so that each fraction has the same denominator. Try this for 2/3, 5/6, and 1/3, 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
3. Order the fractions by the numerators. Now that all fractions have the same denominator, they are easy to compare. Arrange them from smallest to largest according to the counter. This gives us the following list: 6/18, 12/18, 15/18.
4. Return each fraction to its original shape. Leave the fractions in this order, but convert them back to the original fraction. You do this by simply remembering which fraction belongs to or by dividing the top and bottom numbers of the 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"

Method 2 of 3: Order two fractions with cross multiplication

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: 3/5 left and 2/3 right.
2. Multiply the numerator of the first fraction by the denominator of the second. So: 3 x 3 = 9.
   • This is called cross multiplication, because you are multiplying numbers diagonally.
3. Write your answer next to the first fraction. Write the product of 3 x 3 = 9, next to the first fraction.
4. Multiply the numerator of the second fraction with the denominator of the first. Now to see which one is the largest, let's compare the answer with another multiplication. Multiply these two numbers together. In this example (we're comparing 3/5 and 2/3), we're multiplying 2 x 5.
5. Write the answer next to the second fraction. Write the result of 2 x 5 = 10 next to the second fraction.
6. Compare the values ​​of the results. If one value is greater than the other, the fraction next to the result is also the largest. So, because 9 is less than 10, 3/5 is less than 2/3.
   • Remember to always put the product of the multiplication next to the fraction whose numerator you used.
7. How exactly does this work? What you do is convert the fractions so that they both have the same denominator. So this is what cross multiplication actually does! It skips actually writing down the denominators, because in the case of like denominators, you just need to compare the numerators. So as follows, without the shortcut of cross multiplication:
   • 3/5 = (3x3) / (5x3) = 9/15
   • 2/3 = (2x5) / (3x5) = 10/15
   • 9/15 is less than 10/15
   • So 3/5 is less than 2/3

Method 3 of 3: Order fractions greater than one

1. Use this method for fractions where the numerator is greater than the denominator. If the numerator is greater than the denominator, this fraction is greater than 1.8 / 3 is an example.You can also use this for fractions with an equal numerator and denominator, such as 9/9. These are both examples of "improper" fractions.
   • You can still use the other methods for these fractions. This method will help you understand these fractions better and can be a bit faster.
2. Convert any improper fraction to a mixed fraction. Make it a combination of an integer and a fraction. Sometimes you can easily do this by heart. For example, 9/9 = 1. In trickier cases, use long division to find out how many times the denominator is divisible by the numerator. Any remainder of the long division remains as a fraction. For instance:
   • 8/3 = 2 + 2/3
   • 9/9 = 1
   • 19/4 = 4 + 3/4
   • 13/6 = 2 + 1/6
3. Sort the mixed numbers by the whole number. Now that there are no more improper fractions, you have a better idea of ​​the size of each number. Ignore the fractions first and sort each mixed number by the whole number:
   • 1 is the smallest
   • 2 + 2/3 and 2 + 1/6 (we don't know yet which one is greater than the other)
   • 4 + 3/4 is the largest
4. If necessary, compare the fractions in each group. If you have multiple mixed numbers with the same integer, such as 2 + 2/3 and 2 + 1/6, compare the fraction of both numbers to find which one is greater. In the example, we compare 2 + 2/3 and 2 + 1/6 by 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. Use the result to further sort the mixed numbers list. The order of the entire list now becomes: 1, 2 + 1/6, 2 + 2/3, 4 + 3/4.
6. Convert the mixed numbers back to the original fractions. Keep the order the same, but undo any changes and rewrite the fractions as the original improper fractions: 9/9, 8/3, 13/6, 19/4.

Tips

• When putting a large number of fractions in order, it can be useful to compare small groups of 2, 3 or 4 fractions.
• While finding the least common denominator can be useful, any common denominator will work. Try to rank 2/3, 5/6, and 1/3 with a common denominator of 36 and see if you get the same result.
• If the numerators are all the same, you can also quickly order the fractions. For example, 1/8 1/7 1/6 1/5. Think about this as if it were a pizza: if you go from 1/2 to 1/8, you cut the pizza into 8 pieces instead of 2 and the pieces are smaller.