Question Video: Comparing Multiplication Expressions Involving Multiplication by Zero

Use <, =, or > to fill in the blank: 9 × 1 × 0 _ 9 × 10.


Video Transcript

Use the symbol for is less than, is equal to, or is greater than to fill in the blank. Nine times one time zero what nine times 10.

Here we have an expression that contains two multiplications. In the first, we have three numbers being multiplied together, nine times one times zero. And interestingly, the second multiplication contains the same digits though we have a different calculation. This time it’s nine times 10. We need to use the correct symbol to fill in the blank between the two multiplications. Should we say that nine times one times zero is less than nine times 10, is equal to nine times 10, or is greater than nine times 10? Now, the way that we’d normally answer a question like this is to work out the value of both multiplications and then just compare them.

But there’s a quicker way to find the answer here. And we can just use reasoning to help. In the multiplication on the right-hand side, we can see two numbers that we’re multiplying together. They’re both greater than one, nine times 10. So this is going to make a total that’s a whole number. It doesn’t matter what it is. We’ll come to the answer in a second. But it actually doesn’t matter what that total is. Because in our first multiplication, there’s a digit that we’re multiplying by that makes everything pointless.

The third digit that we’re multiplying by is a zero. And we know that anything multiplied by zero equals zero. So it doesn’t matter at all what these first two numbers are that we’re multiplying by. Because we’re multiplying them then by zero, the answer to the first multiplication is going to be zero. And so, we can predict that the first multiplication is going to be less than the second one.

Let’s test our prediction by working out the actual values. In our first calculation, we know that nine multiplied by one equals nine. And so, our calculation becomes nine times zero. As we’ve said already, any number multiplied by zero is zero. Nine lots of nothing equals nothing. Our second calculation asks us to find nine times 10. We know that 10 10s are 100. So nine 10s is 10 less than 100. Nine times 10 is 90. And we know that 90 is greater than zero. Because we read from left to right, we need to say this the other way around. Zero is less than 90. We need to use the symbol for “is less than” to complete the blank. Nine times one times zero is less than nine times 10.

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