Video: GCSE Mathematics Foundation Tier Pack 3 • Paper 1 • Question 15

GCSE Mathematics Foundation Tier Pack 3 • Paper 1 • Question 15

04:56

Video Transcript

This is a scaled, accurate image of a rectangular wall. On the image, one centimeter represents 0.5 meters. Liam wants to paint the wall. Each pot of paint contains enough paint to paint exactly 1.5 meters squared of wall. Liam has eight pots of paint. Does he have enough paint to paint the entire wall? You must show how you reached your answer.

We are told that the wall is drawn to scale with a scale of one centimeter on the diagram, representing 0.5 or half a meter in real life. Let’s begin then by using a ruler to accurately measure the dimensions of the wall. Assuming your paper has been printed on the A4, you should be able to see that the width of the wall is nine centimeters. The height of the wall is 4.5 centimeters.

Since one centimeter on the diagram is equal to 0.5 or half a meter in real life, we can scale these measurements up to the real-life measurements by multiplying each by one-half. Multiplying nine by a half is the same as dividing by two. Now, you might know this value off by heart. But if not, we can use the bus stop method with an extra zero after the decimal point. Nine divided by two is four with a remainder of one and 10 divided by two is five. So the real-life width of the wall is 4.5 meters.

To find the real-life height of the wall, we can multiply 4.5 by one-half. And again, that’s the same as dividing by two. Four divided by two is two with no remainder. Five divided by two is two with a remainder of one. And you can see we can add a zero here since it’s after the decimal point, it doesn’t change the size of our number. 10 divided by two is five. And we’ve worked out that the real-life height of the wall is 2.25 meters.

We need to calculate the exact amount of paint that’s required to cover the wall. When we’re thinking about covering the space made by this rectangle, that’s it’s area. And the area of a rectangle is simply width multiplied by height. In this case, that’s 4.5 multiplied by 2.25.

In order to work this out, we first calculate 45 multiplied by 225. We can use any formal written method for multiplication to do this. Let’s look at the grid method. Two multiplied by four is eight. So 200 multiplied by 40 is 8000. 20 multiplied by 40 is 800. And five multiplied by four is 20. So five multiplied by 40 is 200.

We can fill out the rest of the grid as shown. Then, we add all of the numbers in our grid. We get 10125. So, 45 multiplied by 225 is 10125. 4.5 is 10 times smaller than 45 and 2.25 is 100 times smaller than 225. So our answer is going to be 10 times smaller and then another 100. That’s the same as it being 1000 times smaller. So we can divide 10125 by 1000. And that’s tells us that 4.5 multiplied by 2.25 is 10.125.

A nice way to remember this though is to count the total number of digits in the question, which are after the decimal point. In our question, we have one two and three numbers that are after the decimal point. So in our answer, we also need to have three numbers after the decimal point. The area of the wall is 10.125 meters squared.

Now, Liam has eight pots of paint. And we know each pot covers 1.5 meters squared of wall. What we could do is divide the area that we calculated, 10.125, by 1.5 to see how many pots of paint he would require. It’s much easier though to work out the total area of wall that Liam can cover with his eight pots of paint. To do this, we multiply eight by 1.5.

We could once again use a formal written method for multiplication. However, finding 1.5 of a number is the same as finding one and a half of it. One-half of eight is four. So we can say that one and a half lots of eight is eight plus four, which is equal to 12. He has enough paint to cover 12 meters squared of wall.

We mustn’t forget to include a conclusion. Yes, he does have enough paint. He has enough to cover 12 meters squared of wall, which is greater than the amount required, 10.125 meters squared.

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