How to Compare and Order Fractions

Step-by-Step Guide

1. 1

   Step 1: List the fractions you are ordering in one column.

   Next to each fraction, write an equal sign.
   
   It doesn’t matter in what order you list the fractions.
   
   For example, if you are comparing 58{\displaystyle {\frac {5}{8}}}, 24{\displaystyle {\frac {2}{4}}}, and 37{\displaystyle {\frac {3}{7}}}, you could list the fractions like this:58={\displaystyle {\frac {5}{8}}=}24={\displaystyle {\frac {2}{4}}=}37={\displaystyle {\frac {3}{7}}=}
2. 2

   Step 2: Convert each fraction to a decimal.

   To do this, divide the numerator of each fraction by its denominator.
   
   Place each decimal to the right of its fraction, after the equal sign.
   
   The numerator is the number above the fraction bar; the denominator is the number below the fraction bar.
   
   You can complete the division using a calculator or by hand using the standard division algorithm.
   
   Either way, round to at least two or three decimal places.
   
   For example:5÷8=.625{\displaystyle 5\div 8=.625}, so 58=.625{\displaystyle {\frac {5}{8}}=.625}2÷4=.500{\displaystyle 2\div 4=.500}, so 24=.500{\displaystyle {\frac {2}{4}}=.500}3÷7=.429{\displaystyle 3\div 7=.429}, so 37=.429{\displaystyle {\frac {3}{7}}=.429}. , The tenths place is the first number to the right of the decimal point.
   
   The bigger the number in the tenths place, the bigger the decimal.
   
   For example, since 6>5>4{\displaystyle 6>5>4}, you know that .625>.500>.429{\displaystyle .625>.500>.429}.
   
   If all the numbers in the tenths place are the same, then compare the numbers in the hundredths place (the second number to the right of the decimal point). , The order of the fractions will be the same as the order of the decimals, since fractions and decimals are different ways to express the same value.
   
   For example, since .625>.500>.429{\displaystyle .625>.500>.429}, you know that58>24>37{\displaystyle {\frac {5}{8}}>{\frac {2}{4}}>{\frac {3}{7}}}.
3. 3

   Step 3: Compare and order the decimals

4. 4

   Step 4: beginning with the tenths place.

5. 5

   Step 5: Compare and order the fractions

6. 6

   Step 6: depending on the order of their corresponding decimals.

Detailed Guide

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