Q&A for How to Add Mixed Numbers

There is always a lowest common denominator, even if it's just the product of the denominators.

The easiest way is Method 1 above. In that example, you first add the whole numbers: 1 + 2 = 3. Remember the 3. We'll need it later. Next add together the two fractions: ½ + ¾. Before you can add fractions, their denominators must be made equal to each other. The easiest thing to do here is double the first denominator (2) to make it the same as the second denominator (4). So we double the denominator in the fraction ½. In order not to change the value of that fraction, we must also double the numerator. Thus, ½ becomes 2/4. Now we can add the two fractions together: 2/4 + 3/4 = 5/4. 5/4 = 1¼. Get the final answer by adding 1¼ to the 3 we got earlier. 1¼ + 3 = 4¼.

If you're asking about first dividing mixed numbers, you must convert both mixed numbers to improper fractions, invert the divisor, and multiply the two fractions together. Then subtract the proper fraction from the product you just found. Do this by converting one or both fractions until they have the same denominator. Perform the subtraction and then (if the difference is an improper fraction) convert the difference to a mixed number if you wish.

See Divide a Whole Number With a Fraction .

Divide the denominator of the improper fraction into its numerator. The quotient will be a whole number (and perhaps a remainder, too). The whole number becomes the whole number of the mixed fraction (the "mixed number"), and the remainder (if there is one) becomes the numerator of the fractional part of the mixed fraction. The denominator is the same as the denominator in the original improper fraction. For example, take the improper fraction 25/6. First divide 6 into 25. The quotient is 4 with a remainder of 1. So the improper fraction is 4 1/6.