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. Don’t hesitate to also check our 236 free and powerful practice tests
The next lesson to learn: Integers, Decimals, and Fractions
The following transcript is provided for your convenience.
Let’s take 7441 and let’s multiply it by 7. Alright, so we want to line up the two numbers at where the decimal point would be right there, and then starting with the digit farthest to the right and the bottom number, in this case, there’s only 1 starting with that digit, we’ll multiply by all the digits from the top numbers starting with the one on the right.
So we have 7 times 1, which is 7; 7 times 4, which is 28; so we 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. So this becomes a 0 and we have 3 up here. We have 7 times 7, which is 49. Adding 3 more, we get 52. So we could put the 5 in there. So that’s multiplication for integers.
If we have more digits in the bottom number, once we have 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. But we just have 1 so that’s the answer.
The division is a little bit more complicated.
The way to do division, I’m going to be showing a method called long division. You write the number that you’re dividing and then to the left of that, you write the number you’re dividing it by. And so in multiplication, we worked from right to left, but in division, we worked from left to right. So 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 going into 7 one time, and 1 times 7 is equal to 7. So, when we subtract this number from that number, we just get a 0. Then we move on to the next digit, and I’ll write a 4 here; 7 cannot go into 4 many times, so we’ll write a 0 here and we’ll add the next digit, so 44 now.
Seven can go into 44 six times, so we’ll write a 6 here; 6 times 7 is 42. When we subtract that out, that leaves us with a remainder of 2, so now we drag in the last digit, which is a 1. So we have 21, and 7 goes into 21 three times, so 3 times 7 is exactly 21 and so we have a remainder of 0. So, 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 we 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 simpler particularly than the long division here. It’s really just two different forms of multiplication, so let me demonstrate that. Let’s say we have 1 over 3 times 3 over 4. Now all we have to do to multiply fractions, we don’t have to worry about common denominator any of that like we do with addition and subtraction. We just multiply the two 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. And so, that’s really all there is to fraction multiplication.
Fraction division just requires one extra step.
And so what it’s going to look like is if you have 1/3 divided by 3/4, that you take the reciprocal of the second number and then change the division sign to a multiplication sign. This becomes 1/3 times – this is 3/4 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.
And so that is a brief review of multiplication and division for integers.