PROPER FRACTIONS - DIVISION

Concept: A fraction describes a part of a whole. A fraction is written as two numbers, separated by a fraction bar. The bottom number, or denominator, tells the number of equal parts into which the whole is divided. The top number, or numerator, tells the number of equal parts of the whole being considered. The numerator and denominator are the terms of the fraction. A proper fraction is a quantity less than 1, in which the numerator is less than the denominator. An improper fraction is a quantity equal to or greater than 1. The numerator of an improper fraction is equal to or greater than the denominator. When an improper fraction is reduced to its lowest terms it becomes a mixed number, containing a whole number and a proper fraction.

Numerator 1 2 Denominator

Steps for Dividing Fractions

Step 1 | Convert whole numbers into improper fractions, if necessary, by placing a 1 under the fraction bar.
Step 2 | Invert, or turn over, the divisor (the fraction you are dividing by) and change the operation to multiplication.
Step 3 | Cross-cancel if possible. Compare the numerator of the first fraction with the denominator of the second fraction. If they can be divided by the same number (other than 1), do so.
Step 4 | Compare the denominator of the first fraction with the numerator of the second fraction. If they can be divided by the same number (other than 1), do so.
Step 5 | Multiply one numerator by the other numerator.
Step 6 | Multiply one denominator by the other denominator.
Step 7 | Reduce the product fraction if necessary.
Step 8 | If the answer is an improper fraction, rewrite it as a whole or mixed number. (Divide the numerator by the denominator.)
Step 9 | Write the final answer.

Example 1 Divide the fractions and reduce the answer to the lowest term:

Step 1 | Convert whole numbers into improper fractions, if necessary, by placing a 1 under the fraction bar. | Not necessary for this problem.
Step 2 | Invert, or turn over, the divisor (the fraction you are dividing by) and change the operation to multiplication. |
Step 3 | Cross-cancel if possible. Compare the numerator of the first fraction (1) with the denominator of the second fraction (3). If they can be divided by the same number (other than 1), do so. |
x
1 2 No cancelation 6 3 possible! There is no number other than 1 that will divide both 1 and 3 .
Step 4 | Compare the denominator of the first fraction with the numerator of the second fraction. |
x
1 2 Both 6 and 2 can be 6 3 divided by 2. Proceed with canceling.
| If they can be divided by the same number (other than 1), do so. |
X
1 . 2 ÷ 2 = 1 6 ÷ 2 = 3 3
Step 5 | Multiply one numerator by the other numerator. | 1 x 1 = 1 3 3
Step 6 | Multiply one denominator by the other denominator. | 1 1 1 3 x 3 = 9
Step 7 | Reduce the product fraction if necessary. | Not necessary in this case.
Step 8 | If the answer is an improper fraction, rewrite it as a whole or mixed number. (Divide the numerator by the denominator.) | Not necessary in this case.
Step 9 | Write the final answer. | 1 9

Example 2 Divide the fractions and reduce the answer to the lowest term:

Step 1 | Convert whole numbers into improper fractions, if necessary, by placing a 1 under the fraction bar. | Not necessary for this problem.
Step 2 | Invert, or turn over, the divisor (the fraction you are dividing by) and change the operation to multiplication. |
Step 3 | Cross-cancel if possible. Compare the numerator of the first fraction with the denominator of the second fraction. |
X
2 3 15 8
| If they can be divided by the same number (other than 1), do so. |
X
2 ÷ 2 = 1 . 3 . 15 8 ÷ 2 = 4
Step 4 | Compare the denominator of the first fraction with the numerator of the second fraction. If they can be divided by the same number (other than 1), do so. |
X
2 ÷ 2 = 1 3 ÷ 3 = 1 15 ÷ 3 = 5 8 ÷ 2 = 4
Step 5 | Multiply one numerator by the other numerator. |
X
=
1 1 1 5 4
Step 6 | Multiply one denominator by the other denominator. |
X
=
1 1 . 1 . 5 4 20
Step 7 | Reduce the product fraction if necessary. | Not necessary in this case.
Step 8 | If the answer is an improper fraction, rewrite it as a whole or mixed number. (Divide the numerator by the denominator.) | Not necessary in this case.
Step 9 | Write the final answer. | 1 20