Video: Evaluating Numerical Expressions Using the Distributive Property

You know that 9 × 9 = 81, 9 × 8 = 72, and 9 × 3 = 27. Use this to find 9 × 17.

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Video Transcript

You know that nine times nine equals 81, nine times eight equals 72, and nine times three equals 27. Use this to find nine times 17.

This problem is all about a skill that’s very useful in maths, using facts that we know already to help us find out information that we don’t. We’re given three facts from the nine times table. These are three facts that we should know already. Nine nines are 81. Nine eights are 72. And nine threes are 27. We need to use these facts to help us find a fact we don’t know, nine times 17.

There are several different ways we could answer this question, and they’re all to do with how to partition the number 17 to help. Let’s think of this rectangle as representing nine multiplied by 17. The height will be worth nine, and the width will be worth 17. So, we can see how we could represent the calculation nine multiplied by 17 in this way. But how can we use these calculations to help us?

We need to think about the number 17. How can we split up the number 17 into smaller numbers? Perhaps numbers that are linked to times tables facts that we already know. We know 17 is the same as nine plus eight. And so, we could partition our diagram like this. Now, we can use the facts we know to help.

Nine multiplied by nine, we know, is 81. And nine multiplied by eight is 72. So, nine multiplied by 17 is the total of the two parts, 81 plus 72. One plus two equals three. And eight plus seven equals 15. So, we know nine multiplied by 17 must equal 153.

How else can we make 17 using these numbers here? Well, double nine is 18. So, we could say nine multiplied by 17 is the same as nine multiplied by nine doubled, which gives us 18 nines. And so, if we take away one lot of nine, that will give us nine lots of 17, or 17 nines. We know already that nine nines are 81. So, our calculation becomes 81 doubled take away nine, 81 plus 81 take away nine. 81 plus 81 equals 162. And then, if we take away nine from this, we get the answer 153.

Another method we could use is to use the number eight to help. Eight plus eight equals 16. So, if we have 16 nines, we only have to add one more nine to find 17 nines. So, we can say that nine multiplied by 17 is the same as nine multiplied by eight plus another lot of nine multiplied by eight plus one more nine. We know that eight lots of nine are 72. So, our calculation becomes 72 plus 72 plus nine. 72 doubled is 144. That’s the same as 16 nines. But, remember, we need to find 17 nines. So, we need to add one more nine onto 144, which equals 153.

The lesson here is that whenever we’re faced with a calculation that perhaps we don’t know how to work out the answer, there’s nearly always a way to find the answer using facts that we do know. Any of these three methods is correct. They all find the answer 153. We’ll draw green answer boxes around all three examples because any one of them would be correct. They all show us how to use known facts to help us find a fact that we don’t know. Nine multiplied by 17 equals 153.

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