Q&A for How to Add and Multiply Fractions

Simplify by expressing the improper fraction as a mixed number. Divide the numerator by the denominator. That will yield a quotient consisting of a whole number and perhaps a remainder, expressed as a fraction with the same denominator as the one in the improper fraction. The whole number will be the whole number of the mixed number, and the remainder will be the fraction of the mixed number.

Simplify a fraction by dividing some whole number into both the numerator and the denominator. If necessary, do it again until there is no longer a whole number that will divide evenly into both the numerator and the denominator, at which point the fraction is fully simplified. For example, to simplify 42/54, divide 3 into both numbers of the fraction: 42 ÷ 3 = 14, and 54 ÷ 3 = 18. So the fraction becomes 14/18. We're not done, however, because 14 and 18 are both divisible by 2: 14÷2 = 7, and 18 ÷ 2 = 9. So the fraction becomes 7/9. That's fully simplified, because no whole number (besides 1) will evenly divide into both 7 and 9. So 42/54 simplifies to 7/9.

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Adding a negative fraction is the same as subtracting a positive fraction. For example, to add (-¼) to ¾, just subtract ¼ from ¾, which leaves ½.

If that concept doesn't make sense to you, all you can do is take it on faith: adding a negative number is the same as subtracting a positive number. Thus, ¾ + (-¼) = ¾ - ¼ = 2/4 = ½.