Cross-cancellation is a nifty trick that makes multiplying fractions a breeze. Let me break it down for you. When you multiply fractions, you typically multiply the numerators (top numbers) and the denominators (bottom numbers) separately. But sometimes, those numbers can be simplified before you even start multiplying. That’s where cross-cancellation comes in.
Here’s how it works. Let’s say we have the fraction 2/3 multiplied by 4/5. Normally, we would multiply 2 by 4 to get 8 as the numerator, and 3 by 5 to get 15 as the denominator. But with cross-cancellation, we can simplify things right off the bat.
You see, if there are common factors between any of the numerators and denominators, we can cancel them out. In this case, both the 2 and the 5 have a common factor of 1, so we can cancel them out. Similarly, the 3 and the 4 have a common factor of 1 as well. So instead of multiplying 2 by 4 and 3 by 5, we can simply multiply 1 by 1, which gives us 1 as the numerator, and 1 by 1, which gives us 1 as the denominator.
So, in this example, the simplified fraction after cross-cancellation is 1/1. Now, you might be thinking, “But wait, 1/1 is just 1. Isn’t that the same as not doing anything at all?” And you’re absolutely right! In this case, cross-cancellation didn’t really make a difference. But there are plenty of cases where it can save you some extra steps.
Let’s take another example. Say we have 6/8 multiplied by 9/12. Normally, we would multiply 6 by 9 to get 54 as the numerator, and 8 by 12 to get 96 as the denominator. But with cross-cancellation, we can simplify things once again.
The number 6 has a common factor of 3 with the number 9, and the number 8 has a common factor of 4 with the number 12. So we can cancel out those common factors before we even start multiplying. After canceling out the 3 and the 9, we’re left with 2 as the numerator. And after canceling out the 4 and the 12, we’re left with 3 as the denominator.
So, the simplified fraction after cross-cancellation is 2/3. And if we had gone through the regular process, we would have ended up with the same result. But cross-cancellation saved us some extra steps and made the multiplication easier.
Cross-cancellation is a handy shortcut that allows you to simplify fractions before multiplying them. By canceling out common factors between the numerators and denominators, you can make the arithmetic easier and potentially save yourself some time. It may not always make a big difference, but it’s definitely a useful tool to have in your math toolbox.