Whether you are multiplying fractions that include negative numbers, mixed numbers, or improper fractions you’ll find that it’s a lot easier to simplify the problem before you do the actual multiplication step.
Cross cancelling is one powerful tool for making fraction multiplication easier. If you don’t know how, this post will have you multiplying fractions so much faster!
What is Cross Cancelling?
You know that many fractions can be reduced to more simple forms by finding a number that divides both the numerator and the denominator. If you’re not familiar with reducing fractions, be sure to check out that post.
If you don’t know exactly what number might divide both the numerator and denominator of a fraction, a good strategy is to find the prime factorizations of the numbers and then look at the fraction again with the factorizations in place of their composed numbers. You can reduce the fraction by cancelling factors that appear in both the top and the bottom.
Cross cancelling can be thought of as a slightly more advanced version of reducing fractions, but the mechanics are the same.
You’ll recall that to multiply fractions, you separately multiply the numerators on top and the denominators on the bottom to get to the final product. Because this multiplication step produces a number that has factors from both parts of the problem, those factors can be cancelled in the problem itself just like the cancelling process using prime factors.
Because the numbers being cancelled are two different fractions in the problem, those factors are “across” from each other and we use the term “cross cancelling” to describe this technique. But in reality, it’s really no more complicated than reducing a fraction.
Why Do We Use Cross Cancelling?
Cross cancelling may seem like an extra step when multiplying fractions. So why do we use it?
One reason is that cross cancelling makes the values that have to be multiplied smaller, so the actual multiplication step is less complicated. In fact you, can often multiply the numerators and denominators in your head after cross cancelling makes them smaller.
Another reason is to avoid having to reduce the final product. If you’re able to simplify a fraction problem using cross cancelling, you know if you didn’t do the cross cancelling step, you would definitely wind up with a product that needs to be reduced.
So not only does cross cancelling make the multiplication process easier, it also saves work reducing the final fraction! Cross cancelling isn’t extra work at all… It saves lots of arithmetic!
