Video: KS2-M16S • Paper 2 • Question 19

One gram of gold costs £32.94. What is the cost of half a kilogram of gold?

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Video Transcript

One gram of gold costs 32 pounds 94. What is the cost of half a kilogram of gold?

This problem asks us to find the cost of half a kilogram of gold. But if we read the first sentence carefully, we can see that we’re given the cost of gold in grams. One gram of gold costs 32 pounds 94. So we need to somehow convert the price in grams so that we can work out the price of half a kilogram.

We know that one kilogram equals 1000 grams. And so half a kilogram is half of this amount, 500 grams. We know that one gram costs 32 pounds 94. And 500 grams is 500 times larger than this. So to find the answer, we need to find a way of multiplying 32 pounds 94 by 500. How can we do this?

Well, as we’ve said already, 500 is half of 1000. So one way to multiply the price by 500 might be to multiply by 1000 and then find half or divide by two. We also know that 500 is 100 times five. So another method to multiply by 500 might be to multiply by 100 and then by five. Let’s go through both methods. We should get the same answer.

Let’s go through the first strategy. First, we need to multiply 32 pound 94 by 1000. Remember, when we multiply any number by 1000, the digits move three places to the left. And so 32 pounds 94 becomes 32940 pounds. Because we’ve multiplied by 1000, we know this is the cost of one kilogram of gold.

Now what we have to do is find half of this amount. Let’s partition 32940 to help us. We can partition it into 32000, 900, and 40. Half of 32000 is 16000, half of 900 equals 450, and half of 40 equals 20. And if we add these three amounts of money together, we get a total of 16470. And so 500 grams or half a kilogram of gold costs 16470 pounds.

We did say there was another method we could use to find the same answer. We could take the cost of one gram, multiply it by 100 and then by five. When we multiply a number by 100, the digits move two places to the left. And so 32 pounds 94 becomes 3294 pounds. This is the cost of 100 grams of gold. But we want to find the cost of 500 grams of gold. So we need to multiply this amount by five.

Let’s use a written method to multiply 3294 by five. Four times five equals 20. Nine fives are 45, plus the two underneath gives us 47. Two fives equals 10, plus the four underneath makes 14. And finally, three fives are 15, plus the one make 16.

And so we used two different methods but found the same answer. We knew what one gram of gold cost, but we knew we needed to find the cost of half a kilogram of gold. We knew that one kilogram was worth 1000 grams. So half a kilogram was 500 grams.

So to find the answer, we needed to take the cost of one gram and multiply it by 500. To multiply by 500 quickly, we tried multiplying by 1000 and then halving. And we also tried multiplying by 100 and then by five. Both methods found us the same answer.

In real life, the price of gold changes. But this question’s interesting because the cost of half a kilogram in the question is around about the cost of half a kilogram in real life. Half a kilogram of gold would cost you 16470 pounds.

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