# Question Video: Ordering Multiplication Expressions Sharing a Factor Mathematics • 3rd Grade

Look at these cards. 2 × 9 0 × 9 8 × 9 9 × 4. Which expression has the smallest product? Which expression has the largest product?

03:09

### Video Transcript

Look at these cards: two times nine, zero times nine, eight times nine, and nine times four. Which expression has the smallest product? Which expression has the largest product?

In this question, we’re given four cards to look at. And on each one, there’s a multiplication expression. Now, we’re asked two very similar questions. We need to look at the expressions on the cards and decide which one has the smallest product and which one has the largest product. Remember that the word product is what we get when we multiply numbers together. It’s the answer to a multiplication. So really, our questions are asking us which multiplication has the smallest value or the smallest answer and which one has the largest.

Now, there are two ways we could solve this problem. Firstly, we could go through each card, multiply the numbers together, and then just compare all the answers. This would definitely be a way to solve the problem. But is there a quicker way to find the answer? If we look really carefully at these number cards, do you notice anything? Two times nine, zero times nine, eight times nine, nine times four. The number nine keeps cropping up a lot, doesn’t it? In fact, the number nine is a factor in each of the multiplications. They’ve all got it in. In fact, the first three multiplications are very easy to compare because the number nine is in the same position in each of them.

We can see straightaway which is the smallest out of two times nine, zero times nine, and eight times nine. But if we look at our last multiplication, the number nine is at the start. Does this make any difference to us? Not at all, because we know it doesn’t matter which order we multiply two numbers together. They give the same answer or the same product. So we know that nine times four is exactly the same as four times nine. And if it helps us, we could think of this last card as showing four times nine.

Now, all our cards show something times nine. So which has the smallest product? Two times nine, zero times nine, eight times nine, or four times nine. Because we’re multiplying by nine each time, we simply need to look for the smallest number that we’re multiplying by nine. And that’s zero. And the opposite is true. If we want to find the expression with the largest product, we need to find the one that has the largest number that we’re multiplying by nine. And that’s eight times nine.

Although we could’ve compared these multiplication expressions by working each one out individually and comparing all the answers, we noticed that they had something in common. And we used the fact that they were all to do with multiplying by nine to help us solve the problem without working out any of the answers. The expression that has the smallest product is zero times nine, and the expression that has the largest product is eight times nine.