Video: KS2-M16 • Paper 1 • Question 26

15 × 6.1 = _.


Video Transcript

15 multiplied by 6.1 equals what?

This question involves multiplying a two-digit number by a decimal number. Is there something we can do to one of those numbers to make the calculation easier? Well, one strategy we could use is to partition the number 15 into more manageable chunks. We can split 15 into 10 and five.

We know that we can multiply numbers by 10 quite quickly. So we can find the answer to 10 multiplied by 6.1. We can use this to find the answer to five multiplied by 6.1 and then combine our two answers together to find the answer to 15 multiplied by 6.1. So let’s go through these calculations one at a time.

What is 10 multiplied by 6.1 or, if we look at it the other way, 6.1 times 10? We know that when any number is multiplied by 10, the digits in that number become 10 times larger. To help us understand this, let’s draw a place value grid. 6.1 is made up of six ones and one-tenth. When we multiply this by 10, the number of ones in our number, six ones, are going to become 10 times as large. Six ones become six tens or 60. And we can see that that digit, six, has shifted one place to the left.

What happens to a number of tenths if we multiply it by 10? Well, ten-tenths are one whole. And so if we make one-tenth 10 times as large, it will become one whole. The digit once again has shifted one place to the left. And so we know 10 times 6.1 or 6.1 times 10 equals 61.

Now we need to find five multiplied by 6.1. We already know that 10 lots of 6.1 are 61. So how can we use this to help? Five is half of 10. And so if we halve 61, we can find the answer to five lots of 6.1. What’s half of 61? Half of 60 is 30, and half of one is 0.5. So half of 61 must be 30.5.

So now we have all the information we need to be able to say what 15 multiplied by 6.1 is. Because we know 15 is made up of 10 and five, we can add 10 lots of 6.1 and five lots of 6.1 to find the overall answer. What’s 61 plus 30.5? 91.5, which is the same as saying 91 and a half.

This is not the only way we could’ve found the answer. Remember, at the start, we talked about how we could break up 15 to make it more manageable. Well, we could also do the same to 6.1. We can partition 6.1 into six and 0.1. Then just like before, we can work out the answer to both parts, 15 multiplied by six and then 15 multiplied by 0.1 or one-tenth, and then as before combine them to find the overall answer.

What’s 15 multiplied by six? Well, there are lots of strategies we could use. One way is to partition 15 once again. 10 lots of six plus five lots of six equals 15 lots of six. We know that 10 lots of six is 60. Five lots of six must be half of this, which is 30. And the total of 60 and 30 equals 90. So 15 multiplied by six must be 90.

What’s 15 multiplied by 0.1? This isn’t as hard as it looks. 0.1 is the same as one-tenth. And so multiplying 15 by one-tenth is really the same as saying what’s one-tenth of 15. When we find one-tenth of a number, the digits shift one place to the right. They become 10 times less. And so one-tenth of 15 is 1.5.

So now all we need to do is to combine the two parts back together. 90 plus 1.5 equals 91.5. Really, the way we’ve found the answer is to use the same strategy. We started off by partitioning one of the numbers to make it easier. Then we multiplied both parts, one by one, using known facts to help us. Then we combined the answers to both parts back together again to find the overall total. 15 multiplied by 6.1 equals 91.5.

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