James uses the number fact 63 divided by seven equals nine to evaluate 0.63 divided by 0.07. What result does he find?
In this question, James has done what we often do when we’re faced with a problem that we might not know the answer to it in maths. He’s used a number fact that he knows to help find something that he doesn’t know. The tricky calculation that he’s been asked is a division involving two decimals, 0.63 divided by 0.07, or if we say it another way, 63 hundredths divided by seven hundredths.
Now, James has looked at this division and thought to himself, “I know a number fact that includes some of the digits here.” And he uses this number fact to help him divide these two decimals. And the number fact that we’re told he uses is 63 — we can see where the six and the three appear in the first calculation — divided by seven. And James knows the answer to this is nine. There are nine sevens in 63.
To help us link the number fact that James knows to the original calculation, we need to think about how each number changes. To begin with, how do we get from 63 to 0.63? Well, to begin with, we need our digit three to shift one, two places into the hundredths column. In other words, we want three ones to be now worth three hundredths. Shifting digits two places like this to the right is the same as dividing by 100. And the same thing needs to happen to our six tens, one, two. To show that these digits are now in their tenths and hundredths places, we need to add zero as a placeholder and put a decimal point there as well.
In other words, the decimal number in James’s original calculation is 100 times less than 63. Now, if this was all that changed, we’d be dividing a number 100 times less by the same amount. So, our answer would be 100 times less. But if we compare the divisor in both calculations — that’s the number we divide by — we can see that it doesn’t stay the same. It changes too. Seven becomes seven hundredths. And as we’ve seen already, to move a digit from the ones place to the hundredths place means shifting it two places. And shifting a digit two places to the right is the same as dividing it by 100 again.
The way that we changed the first number in our division is also the same way that we changed the second number in our division. And what happens when we do the same thing to both numbers in a division? Let’s pick a really simple example just to find out. 10 divided by two we know is five. And Let’s do the same thing to both numbers; let’s double them. 10 becomes 20 and two becomes four. What happens to the answer? 20 divided by four equals five. It stays the same. James obviously knew this when he thought of his number fact.
If we multiply or divide the dividend and the divisor in a division calculation by the same amount, in other words, if they both change in the same way, the answer will stay the same. And so we can say that 0.63 divided by 0.07 is going to be equal to nine.
At the start of the video, one of the ways that we read the question was 63 hundredths divided by seven hundredths. And this way of saying the calculation, we can almost hear that the answer’s going to be nine. How many lots of seven hundredths are in 63 hundredths? If we know there are nine lots of seven in 63, we know there are nine lots of seven hundredths in 63 hundredths.
James uses the number fact 63 divided by seven equals nine to evaluate 0.63 divided by 0.07. And the result he finds is that the answer’s nine.