Video: GCSE Mathematics Foundation Tier Pack 4 • Paper 1 • Question 15

GCSE Mathematics Foundation Tier Pack 4 • Paper 1 • Question 15

03:47

Video Transcript

Molly has a collection of magazines which she keeps in a pile. The pile has the following dimensions: height, 10 inches; width, 12 inches; depth, eight inches. Molly buys a box to store the magazines in. The inside of the box has a height of 26 centimeters, a width of 30 centimeters, and a depth of 21 centimeters. One inch is equal to 2.54 centimeters. Will Molly’s stack of magazines fit inside the box? You must show how you reached your answer.

To answer this question, we’ll need to either convert the dimensions of the magazines to centimeters or the dimensions of the box to inches. In fact, since we’re told the conversion between inches and centimeters in terms of one inch, it’s actually easier to change from inches to centimeters.

Let’s convert the dimensions of the box to centimeters. Since one inch is 2.54 centimeters. We can change inches into centimeters by multiplying by 2.54. The easiest dimension to convert is the height. Since to multiply by 10, we simply move the digits to the left once. 10 multiplied by 2.54 is 25.4. The height of the magazines then is 25.4 centimeters.

Since the height of the box is 26 centimeters, we can see that they will fit heightwise. Next, let’s calculate the width. We could use a formal written method to work out 12 multiplied by 2.54. But we did just calculate 10 multiplied by 2.54. We can, therefore, work out 12 multiplied by 2.54 by adding on two — two 2.54s — to 25.4.

Let’s use a column method to do this. Remember we need to line up the decimal points and add another zero where necessary. Zero plus four plus four is eight. Four plus five plus five is 14. So we put a four in this column and we carry the one. Five plus two plus two plus one is 10. So we put a zero here and carry the one. And two plus one is three. The width of the stack of magazines is 30.48 centimeters.

We can see that the width of the inside of the box is just 30 centimeters. So the magazines won’t fit widthwise into the box. Since we have already shown that the magazines won’t fit widthwise, we don’t actually need to calculate the depth of the magazines. The magazines will, therefore, be too wide to fit inside the box.

Now, you might have chosen to use a formal written method to work out 12 multiplied by 2.54. So let’s see what this might have looked like. We could have chosen the column method. When multiplying a decimal by an integer, we can line up the decimal point in our answer with the one in our question.

Four multiplied by two is eight. Five multiplied by two is 10. So we put a zero here and we carry the one. Two multiplied by two is four. And then, when we add one, we get five. Now, we’ll multiply all the digits on the top by the number one. But we’re not actually multiplying by one; we’re multiplying by 10.

So we add a zero here to show that all of our answers are gonna be 10 times bigger than we expect. Four multiplied by one is four, five multiplied by one is five, and two multiplied by one is two. Finally, we add these two numbers.

And you can see once again, we have worked out that 2.54 multiplied by 12 is 30.48. Either of these methods would have been suitable.

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