How do you add mixed numbers?


Quick Answer

Mixed numbers can be added either by first converting them to improper fractions and then adding, or by adding the fractional part and the whole-number part of the mixed numbers separately and carrying or regrouping as necessary. In either case, the fractions can only be added after a common denominator has been found.

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Full Answer

Any mixed number can be written as an improper fraction. For example, the mixed number 3 1/8 is equal to three times 8/8 plus 1/8, or 25/8. When adding 3 1/8 to 2 5/6, first convert 3 1/8 to 25/8 and 2 5/6 to 17/6. Using the common denominator of 24, convert 25/8 to 75/24 and 17/6 to 68/24, and add the numbers, producing a sum of 143/24. Since 143/24 is irreducible, the only step remaining is to convert the improper fraction to a mixed number. Since 24 divides into 143 five times with a remainder of 23, the result is 5 23/24.

The other way to add mixed numbers is to add the parts separately and regroup. For example, to add 3 2/3 to 4 3/4, first add the whole numbers 3 and 4 for a sum of 7. Then, using the common denominator of 12, convert 2/3 to 8/12 and 3/4 to 9/12, and add, producing the sum of 17/12. Since 17/12 equals 12/12 plus 5/12, or 1 5/12, regroup by adding the one to the whole number seven, producing a final sum of 8 5/12.

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