PROPER FRACTIONS - SUBTRACTION

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 Subtracting Fractions

Step 1 | Determine if the denominators are the same. If the denominators are the same, proceed to Step 2. If the denominators are different, proceed to Step 4.
Step 2 | If the denominators are the same, you have like fractions. Simply subtract the smaller numerator from the larger numerator.
Step 3 | Write the difference of the numerators over the common denominator. Now proceed to Step 11.
Step 4 | The denominators are different, so you have unlike fractions. You must convert the unlike fractions into like fractions before you can subtract. To do this you must first find the lowest common denominator.
Step 5 | Begin by listing the multiples of the first denominator. (The multiples of a number are found by going through the times tables for the number. For instance, the multiples of 3 are 3, 6, 9, 12, 15, 18, and so on.)
Step 6 | Next, list the multiples of the second denominator.
Step 7 | Finally, compare the two lists of multiples. The smallest number that is found in both lists is the lowest common denominator.
Step 8 | Make one or both of the original unlike fractions into like fractions, using the newly determined lowest common denominator. Whatever was done to the denominator to convert it into the lowest common denominator must also be done to the numerator.
Step 9 | Subtract the smaller numerator from the larger numerator.
Step 10 | Write the difference of the numerators over the common denominator.
Step 11 | Reduce the fraction if necessary. (If both the numerator and the denominator can be divided by the same number, the fraction can be reduced.)
Step 12 | If the fraction is an improper fraction, rewrite it as a whole or mixed number. (If the numerator is larger than the denominator, you must divide the numerator by the denominator.)
Step 13 | Write the final answer.

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

from .

Step 1 | Determine if the denominators are the same. If the denominators are the same, proceed to Step 2. If the denominators are different, proceed to Step 4. |
and
11 2 12 12
Step 2 | If the denominators are the same, you have like fractions. Simply subtract the smaller numerator from the larger numerator. | 11 - 2 = 9
Step 3 | Write the difference of the numerators over the common denominator. Now proceed to Step 11. | 11 - 2 = 9 12 12 12
Step 4 | The denominators are different, so you have unlike fractions. You must convert the unlike fractions into like fractions before you can subtract. To do this you must first find the lowest common denominator. | Does not apply in this problem.
Step 5 | Begin by listing the multiples of the first denominator. (The multiples of a number are found by going through the times tables for the number. For instance, the multiples of 3 are 3, 6, 9, 12, 15, 18, and so on.) | Does not apply in this problem.
Step 6 | Next, list the multiples of the second denominator. | Does not apply in this problem.
Step 7 | Finally, compare the two lists of multiples. The smallest number that is found in both lists is the lowest common denominator. | Does not apply in this problem.
Step 8 | Make one or both of the original unlike fractions into like fractions, using the newly determined lowest common denominator. Whatever was done to the denominator to convert it into the lowest common denominator must also be done to the numerator. | Does not apply in this problem.
Step 9 | Subtract the smaller numerator from the larger numerator. | Does not apply in this problem.
Step 10 | Write the difference of the numerators over the common denominator. | Does not apply in this problem.
Step 11 | Reduce the fraction if necessary. (If both the numerator and the denominator can be divided by the same number, the fraction can be reduced.) |
Step 12 | If the fraction is an improper fraction, rewrite it as a whole or mixed number. (If the numerator is larger than the denominator, you must divide the numerator by the denominator.) | This is not an improper fraction.
Step 13 | Write the final answer. |

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

Step 1 | Determine if the denominators are the same. If the denominators are the same, proceed to Step 2. If the denominators are different, proceed to Step 4. |
and
1 2 6 3
Step 2 | If the denominators are the same, you have like fractions. Simply subtract the smaller numerator from the larger numerator. | Does not apply in this problem.
Step 3 | Write the difference of the numerators over the common denominator. Now proceed to Step 11. | Does not apply in this problem.
Step 4 | The denominators are different, so you have unlike fractions. You must convert the unlike fractions into like fractions before you can subtract. To do this you must first find the lowest common denominator. | 6 and 3 are different denominators
Step 5 | Begin by listing the multiples of the first denominator. (The multiples of a number are found by going through the times tables for the number. For instance, the multiples of 3 are 3, 6, 9, 12, 15, 18, and so on.) | Multiples of 6: 6, 12, 18, 24, etc
Step 6 | Next, list the multiples of the second denominator. | Multiples of 3: 3, 6, 9, 12, etc
Step 7 | Finally, compare the two lists of multiples. The smallest number that is found in both lists is the lowest common denominator. | 6 is the lowest common denominator.
Step 8 | Make one or both of the original unlike fractions into like fractions, using the newly determined lowest common denominator. Whatever was done to the denominator to convert it into the lowest common denominator must also be done to the numerator. |
Step 9 | Subtract the smaller numerator from the larger numerator. | 4 – 1 = 3
Step 10 | Write the difference of the numerators over the common denominator. | 4 – 1 = 3 6 6 6
Step 11 | Reduce the fraction if necessary. (If both the numerator and the denominator can be divided by the same number, the fraction can be reduced.) |
Step 12 | If the fraction is an improper fraction, rewrite it as a whole or mixed number. (If the numerator is larger than the denominator, you must divide the numerator by the denominator.) | The fraction is not as improper fraction.
Step 13 | Write the final answer. | 1 2