Learn about Division of Decimals Learn how to use fractions to divide decimals. We’ll try two problems. The first problem is 7.48 ÷ 0.4. I’m going to write this as 7.48 ÷ 0.4. So, both of these are decimals. First, what we have to do is convert both of these two fractions. 7.48 becomes—and the way we convert this to fractions is we put the denominator as one followed by as many zeroes as there are digits to the right of the decimal point. So, we put two zeroes because there are two digits to the decimal point or to the right of the decimal point and then the numerator becomes 748. We removed the decimal point altogether. Similarly, 0.4 becomes—the denominator is 10 because it’s only one digit to the right of decimal point and the numerator becomes four. So, if I’m dividing these two numbers, I might as well divide these two which becomes (748/100)/(100/4/10). Since I’m dividing these, it’s the same as multiplying with the reciprocal of the second fraction which is 748/100 x 10/4. Now, what we can do is 10, so it’s 748 x 10. Multiply the numerators together and multiply the denominators together, 100 x 4. That’s the ultimate value. Now, let’s simplify this a little bit. 10 in a hundred, we can divide both by the GCF. So I can put 748 x 10/10 and here we have 100/10 x 4. I’m dividing both 10 and a hundred by their GCF which is 10. This gives me 748 on top. 10/10 is one, 1 x 748 is the same. 100/10 is 10 x 4. Again, 748 and 4 share a GCF of four in common. So, let’s divide both by four, 748/4 is 187 and 4/4 is one so the denominator is 10. Now that I get the answers of 187/10, I can convert this back to a decimal. And the way we do that is at this one zero in the denominator, we move the decimal spot, one digit here. So, 187/10 becomes 18.7. That’s the answer we we’re looking for. Quickly, let’s try the second problem which is to solve or evaluate the expressions 7.2/N when N equals 0.24 or -0.24. So, the second problem is N=(-0.24) and we have to solve for 7.2 ÷ N. So first, let’s substitute instead of N, let’s put down -0.24 so it becomes 7.2 ÷ -0.24. Again, I put two decimals. Let’s convert them to fractions. 7.2 becomes 72/10, 10 at the denominator because there’s one digit divided by -24/100, two digits, two zeroes. This is the same as 72/10 multiplied by the reciprocal which is -100/24. Again, so the final answer becomes 72 x -100/10 x 24. Let’s take away some GCFs. So 72, I can divide by 24 because I can divide 24/24 as well. This is their GCF and a 100-100, we can divide it by 10 and this we can divide it by 10 because 10 is the GCF of 10 and -100. So, when I do this all out, 72/24 is 3 x -10/1 x 1. It becomes -30. The answer we we’re looking for is -30.