Learn about Multiplication and Division Facts

This track covers the topic of multiplication and division facts and the problem is for us to use the fact family of 8, 9 and 72 to form two multiplication and two division facts. Let’s learn how to do this.

First, we need to remember that multiplication and division are inverse operations. What that means is I can undo one of them by using the other. I can undo a multiplication by dividing or dividing the product by one of the factors. If I have a multiplication that’s been performed, I can unto it by dividing the end result which is the product by one of the factors. Similarly, we can undo division by multiplying the quotient with the divisor. We will cover a couple of these facts.

Let’s start with the problem which says for to find two multiplication and two division facts. So fact one is let’s look at multiplication facts. What are we given? The fact family that we are given is 8, 9 and 72. The first multiplication fact that we know is 8 × 9 = 72. The second multiplication fact is the fact that 9 × 8 is also equal to 72. This is called a commutative property of multiplication. I can exchange the numbers to give me the same result. I can rearrange the order of the factors to give me the same product. Those are two multiplication facts.

Let’s quickly do the division facts, creating a little bit of extra space. Division facts basically tell us that fundamentally, a division fact can be formed by a multiplication fact. As we said in the section above, a product equals factor one times factor two; we just did that right here. Because division and multiplication are inverse of each other, the product divided by factor one will give me factor two. This is a fact. I can use the same exact thing we did above. We can say 72 divided by one of the factors which is 8 gives me the other factor which is 9. This is fact one.

Similarly, 72 which is the product divided by factor 2 which is 9 will give me factor one which is the second fact. This is again the same property that we used in multiplication. I can rearrange the order, except here what we’re doing is we’re saying that the final product is divided by one of the factors, it gives you the other factor. I just replaced 72 divided by factor one gives me factor two and 72 divided by factor two gives me factor one.

Another thing to remember, these are the two facts where we’ve solved the problem but what we need to remember is in this scenario 9, if I’m dividing 72 ÷ 9 to give me 8, 9 is the divisor, 8 is the quotient and 72 is the product. What that means is I can use this as a division fact or I can use this as a multiplication fact because dividend which is the product equals quotient times the divisor. Dividend or the product equals quotient times the divider. The product or dividend is the same thing. Simple facts about multiplication and division, we found two and two above.

Quickly recapping what we’ve learned. Multiplication and division are inverse operations. I can undo multiplication by dividing the product by one of the factors and I can undo division by multiplying the quotient with the divisor. The multiplication facts from the fact family of 8, 9 and 72 is 9 × 8 = 72, 8 × 9 = 72 and I can use the commutative property to say just rearrange the order 9 × 8 = 72 as well. Division fact stems from the fact that the product equals factor one time factor two, that’s what we just did which means a product divided by factor one equals factor two and vice versa. Product which is the dividend divided by factor one gives me factor two and the same product divided by factor two gives me factor one. These are the two division facts.

Key to remember, if the product or the dividend is the divisor multiplied by the quotient or the product equals the divisor multiplied by the quotient or the product or the dividend divided by the divisor gives us the quotient, these are the facts of multiplication and division.