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How do you add mixed numbers?

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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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