Comparing Fractions

To compare two or more fractions. Those steps must be followed:

1) Find the LCD of the fractions

2) Change the fractions to higher terms using the LCD

3) Compare the numerator

Rules:

If  a/b = c/d, then ad = bc

If  a/(b  ) < c/d, then ad < bc

If  a/b > c/(d,)  then ad > bc

There are many ways to do this type of fraction.

1) Compare the size of the numerators, if the denominators are the same.

2) If one of the numerators is greater than the other one, then, the greater numerator represents the greater fraction.

Example: Use >, <, or = to compare  11/8  and 3/8

Solution

The numerators are 11 and 3. Because 11 is greater than 3,

Therefore, 11/8 > 3/8.

Let’s go the other way: Fractions not having the same denominator.

1) Multiply the numerator of the first fraction by the denominator of the second fraction, and you regard this answer as first fraction.

2) And then, multiply the numerator of the second fraction by the denominator of the first fraction, and this is the second fraction.

3) Compare the two numbers. The larger number represents the larger fraction. This type of multiplication is known as cross multiplication.

                Example:  Use >, < or = to compare  3/11, 4/7

Cross multiply:

                3 x 7 = 21          and        11 x 4 = 44

                                 21 < 44   or 44> 21

Based on the calculation, we can say:

                                3/11 < 4/7    or  4/7 > 3/11

The second way this second type of fraction can be done is as follow:    

1) Find the LCM

2) Write equivalent fractions, by using the LCD

3) Compare the numerators.

Example:  Use >, < or = to compare  3/8, and 1/4

Step 1) Multiples of 4 = 4, 8, 12, 16, 20, 24, 28, 32…

            Multiples of  8 = 8, 16, 24, 32, 40…

The LCM of 8, and 4 is 8. 8 is the LCD of   3/8, and 1/4

Step 2)

Write equivalent fractions for 3/8  and  1/4 using the LCD which is 8.

3/8 = 3/8 X 1/1 = 3/8

1/4 = 1/4 x 2/2 = 2/8

Step 3) Compare the numerators. The fact, is 3 is greater than 2, then  3/8 > 1/4

Example: Use >, <, or = to compare  2/3, and  5/8

Step 1) Find the LCM of 3 and 8 . The LCM of 3 and 8 is 24. 24 is the LCD of 2/3 and 5/8.

Step 2) Write equivalent fractions for   2/3 and 5/8 using the LCD, which is 24.

2/3  = 2/3 x 8/8 = 16/24

5/8  = 5/8 x 3/3 = 15/24

Step 3) Compare the numerators. The fact 16 is greater than 15, 2/3 > 5/8

Example:

Compare 4/6 and   6/9

Cross multiply:

                4 x 9 = 36                6 x 6 = 36

                                36 = 36, therefore,

                                                4/6 = 6/9