Video: KS2-M18 • Paper 1 • Question 34

28% of 650 = _.

06:26

Video Transcript

28 percent of 650 equals what?

How can we find 28 percent of a number? What percentages do we know that we could add or subtract to make 28 percent? One way we could think of 28 is 20 plus eight. So one method we could use to find the answer is to find 20 percent of 650, then eight percent, and then add the two to find the answer. We’ll call that method one. And we’ll come back to that in a second.

Another way we could think of 28 is as 30 take away two. What if we found 30 percent. We also worked out two percent. Then, we could subtract one from the other to find the answer. We’ll call this method two.

Let’s begin with our first strategy. Find 20 percent. Find eight percent. And then add the two together. What percentage do we know that could help us find 20 percent of a number? Well, we know that, to find 10 percent of a number, we have to divide that number by 10. So to find 10 percent of 650, we need to divide 650 by 10. The answer is 65. 10 percent of 650 is 65. 20 percent is double 10 percent. So 20 percent of 650 is double 10 percent of 650 or double 65. Double 60 is 120. Double five is 10. So double 65 is the same as 120 plus 10, which is 130. We’ve now found the first number we needed to find, which was 20 percent of 650.

Now we need to think about how to calculate eight percent. Eight is four lots of two. So if we can calculate two percent, we can multiply it by four to find out the value of eight percent. You could also work out 10 percent take away two percent. But for now, we’ll calculate two percent and then multiply it by four.

Two is equal to 20 divided by 10. And so two percent of 650 will be the same as 20 percent of 650 or 130 divided by 10, which is 13. We now know what two percent is. And so we can use this to calculate eight percent. Two times four is eight. So we need to multiply the answer to two percent of 650 or 13 by four to find eight percent of 650.

What is 13 multiplied by four? Well, multiplying by four is the same as doubling and then doubling again. 13 doubled equals 26. And then 26 doubled equals 52. So we’ve multiplied 13 by four to find that eight percent of 650 equals 52. Finally, we need to add our 20 percent and eight percent to find 28 percent. We said 20 percent was 130. And eight percent was 52. 130 plus 52 equals 182.

Remember the other method that we also could’ve used would be to find 30 percent, find two percent, and then take two from 30 to find 28 percent. Just like before, we start by using a percentage we already know. 10 percent of 650 equals 65. So if we want to find 30 percent, we need to multiply 65 by three, three lots of 10 percent. What’s 65 times three? Five threes are 15, six 10s times three is 18 10s plus the one 10 that we’ve exchanged underneath equals 19 10s. 65 times three, 30 percent of 650, equals 195.

Now we need to find two percent of 650. We already know this because we’ve looked at it in the first method. But pretend we haven’t used this first method. How could we find two percent quickly?

First, we could find one percent of 650 by dividing 10 percent by 10. So this means dividing 65 by 10, the digits move one place to the right. So the answer is 6.5 or six and a half. Two percent is double one percent. So we need to double 6.5 to find the answer. Double six is 12. And double 0.5 or double one-half equals one. 12 plus one equals 13. And so it’s another way of finding out what we knew already, which is two percent of 650 equals 13.

Now that we know 30 percent and two percent, we can take them away to find 28 percent, 195 take away 13. 195 take away 10 would be 185. And then, take away the three leaves us with 182. Two methods to find the same answer. The question is all about thinking how can I use what I know already to find 28 percent.

28 percent of 650 equals 182.

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