MIXED NUMBERS - ADDITION

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. To add or subtract mixed numbers, work with each part separately and then combine the results.

Mixed Number

Steps for Adding Mixed Numbers

Step 1 | Determine the lowest common denominator for the fractions in both numbers.
| 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.)
| Next, list the multiples of the second denominator.
| Finally, compare the two lists of multiples. The smallest number that is found in both lists is the lowest common denominator
Step 2 | Convert the fraction in the first number to a new fraction using the lowest common denominator.
Step 3 | Convert the fraction in the second number to a new fraction using the lowest common denominator.
Step 4 | Add the fractions together.
Step 5 | Reduce the sum of the fractions, if necessary. (If both the numerator and the denominator can be divided by the same number, the fraction can be reduced.)
Step 6 | If the sum of the fractions 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 7 | Add the original whole numbers together.
Step 8 | Combine the sum of the fractions and the sum of the original whole numbers.
Step 9 | Write the final answer.

Example 1 Add the mixed numbers and reduce the answer to the lowest term:

and

Step 1 | Determine the lowest common denominator for the fractions in both numbers. |
| 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, etc
| Next, list the multiples of the second denominator. | Multiples of 3: 3, 6, 9, 12, etc
| Finally, compare the two lists of multiples. The smallest number that is found in both lists is the lowest common denominator. | 6
Step 2 | Convert the fraction in the first number to a new fraction using the lowest common denominator. |
Step 3 | Convert the fraction in the second number to a new fraction using the lowest common denominator. |
Step 4 | Add the fractions together. |
Step 5 | Reduce the sum of the fractions, if necessary. (If both the numerator and the denominator can be divided by the same number, the fraction can be reduced.) |
Step 6 | If the sum of the fractions 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.) | Does not apply in this problem.
Step 7 | Add the original whole numbers together. | 5 + 7 = 12
Step 8 | Combine the sum of the fractions and the sum of the original whole numbers. |
Step 9 | Write the final answer. |