Multiplication and Division | Math Review
Multiplication and Division
In this video, we’re going to look at the last two of the basic operations: Multiplication and division. To start with, let’s take the case of integers. Let’s take 74, 41, and let’s multiply it by 7. All right. We want to line up the two numbers where the decimal point would be right there. Then, starting with the digit farthest to the right in the bottom number, in this case there’s only one, starting with that digit, we’ll multiply by all the digits in the top number starting with the one on the right.
We have 7 times 1, which is 7. 7 times 4, which is 28. Put an 8 here and write a 2 up here. 7 times 4 is, once again, 28. We have to add this 2, so we have 30. This becomes a zero, and we add a 3 up here. We have 7 times 7, which is 49. Adding three more, we get 52. We can put the 5 in there. That’s multiplication for integers.
If we had more digits in the bottom number, once we had finished multiplying the top number by this digit, we would then move on to this digit and multiply all those numbers but start in this digit place, then add up all the results at the end. We just had one, so that’s the answer. Division is a little bit more complicated. The way to do division (I’m going to be sharing a method called long division) is you write the number that you’re dividing.
Then, to the left of that, you write the number you’re dividing it by. In multiplication, we worked from right to left, but in division we work from left to right. We’re going to take the digits individually if we can and see how many times this number is going to fit into them.
First, we have 7 going into 7. 7 can go into 7 one time. 1 times 7 is equal to 7. When we subtract this number from that number, we just get a zero. Then, we move on to the next digit. I’ll write a 4 here. 7 cannot go into 4 any times, so we’ll at a zero here and we’ll add the next digit. 44 now. 7 can go into 44 six times. We’ll write a 6 here.
6 times 7 is 42 and when we subtract that out, that leaves us with the remainder of 2. Now we drag in the last digit, which is a 1. We have 21, and 7 goes into 21 three times. 3 times 7 is exactly 21. We have a remainder of 0. This is the full solution to this division problem.
If 7 had not evenly gone into the last number here, we would have had to put a decimal point here and keep on going until it either terminated or we found a repeating pattern of digits, at which point we could stop. This is multiplication and division for integers. I also want to demonstrate multiplication and division for fractions.
It’s much, much simpler than, particularly, than the long division here. It’s really just two different forms of multiplication. Let me demonstrate that. Let’s say we have 1/3 times 3/4. All we have to do to multiply fractions—we don’t have to worry about common denominator or any of that, like we do with addition and subtraction.
We just multiply that to numerators (1 times 3 gives us 3), and then we multiply the two denominators (3 times 4 gives us 12). It’s a lot easier in one sense to multiply two fractions than it is to add or subtract. That’s really all there is to fraction multiplication. Fraction division just requires one extra step.
What it’s going to look like is if you have 1/3 divided by 3/4, that you know you take the reciprocal of the second number and then change the division sign to a multiplication sign. This becomes 1/3 times—this was three over four—so we’ll take times 4/3.
We flipped the fraction and changed it to a multiplication. Then, all we have to do is just multiply numerator and denominator, like before. 1 times 4 is 4, and 3 times 3 is 9. That is a brief review of multiplication and division for integers and fractions.