Did you notice where we used the word systematic to describe that step-by-step way of doing cross-cancellation? Some people probably ignored that word, and some other people might have wondered what it meant, and had a sinking feeling that we’re using fancy words, and things might soon stop making sense. Multiply all factors on the top of both fractions to form the numerator of the answer, and multiply all factors on the bottom of both fractions to form the denominator of the answer.ĭo you always have to do all that? No, not always.Repeat the previous step on the other diagonal.If multiple copies of any factor are present, deal with them by canceling only as many copies as are present in the opposite location (the same as when simplifying fractions). In fact, it’s because these factors are located diagonally from each other, that we call it cross-cancellation. Cancel any factors found both in a numerator and the opposite denominator.If either factor was not in simplest form, perform the simplification now.Find the prime factorization of both the numerator and denominator of both fractions.If a division problem is being converted into multiplication, first rewrite it converting the divisor into its reciprocal.
Here’s the systematic way to cross-cancel: You can cross-cancel systematically, but there’s also some shortcuts. The divisor is the number that you are dividing by. Taking the reciprocal of a fraction just means swapping the numerator and the denominator (put the top on the bottom, and the bottom on the top). That’s because you can always convert a fraction division problem to a fraction multiplication problem. In addition to multiplication, cross-cancellation can be used to make math easier when fractions are divided. The most common examples of operations are adding, subtracting, multiplying, and dividing (there’s others, but let’s not get into that right now). In mathematics, we use the word operation for something basic that you do to a number. That’s great, because simplifying before means when you do multiply, you’ll have smaller numbers, and smaller numbers are easier to work with.ĭid you catch that? Cross-cancellation makes fractions easier.īut what operation can you use cross-cancellation on? Multiplication of fractions. Cross-cancellation is a simplification that can be done before. Sometimes you have to simplify fractions after doing arithmetic with them. Cross-cancellation is a shortcut that you can use to make multiplying fractions easier.
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