Video: GCSE Mathematics Foundation Tier Pack 3 • Paper 1 • Question 26

GCSE Mathematics Foundation Tier Pack 3 • Paper 1 • Question 26


Video Transcript

Sarah is filling bags with rice. The capacity of each bag is two-thirds of a cubic decimeter. One cubic decimeter of rice has a mass of 1.45 kilograms. Work out the mass of 30 bags filled with rice. The mass of the bags can be neglected.

Let’s begin by highlighting the important pieces of information in this question. We’re told that each bag has a capacity of two-thirds of a cubic decimeter. That’s how much rice each bag can hold. We know that one cubic decimeter has a mass of 1.45 kilograms although that’s not going to be hugely useful just yet. We also know that Sarah is going to be filling 30 bags with rice.

To answer this question then, we’ll begin by calculating the total amount of rice that will fit into those 30 bags. Then, we’ll calculate the mass of all of the rice that fits into those bags. One bag has a capacity of two-thirds of a cubic decimeter. We can, therefore, work out the total amount of rice that 30 bags will hold by multiplying two-thirds by 30.

Remember when working with a mixture of fractions and integers, those are whole numbers, it’s sensible to turn the integers into a fraction. We do that by adding the denominator of one since 30 is the same as 31 wholes. Next, we could multiply the numerator of each fraction and the denominator of each fraction and then simplify our answer.

We could, however, do something called cross cancelling. This is where we look diagonally to see if the numbers have any common factors. In fact, both 30 and three have a factor of three. So we can simplify our problem by dividing each of these by three. 30 divided by three is 10 and three divided by three is one. The only common factor that two and one have is one. They’re called coprime. So we can’t simplify these two numbers any further.

Now, we perform the multiplication as normal. Two multiplied by 10 is 20 and one multiplied by one is one. We can spot that 21 wholes is just 20. So the total capacity of all 30 bags is 20 cubic decimeters.

Next, we’ll use the information that one cubic decimeter of rice weighs 1.45 kilograms. Once again, we can scale this information up to work out the mass of 20 cubic decimeters. This time, we’ll multiply by 20. So to work out the total mass of the 20 cubic decimeters and therefore the 30 bags of rice, we’ll multiply 20 by 1.45. 20 is two multiplied by 10. So it’s actually easier to work out two multiplied by 1.45 and then multiply that by 10.

We can use a number of formal written methods to multiply 1.45 by two. And in fact, you might be able to do it in your head. But it’s certainly useful to check with a written method of thoughts. Let’s look at the column method. When multiplying a decimal by an integer, we can include a decimal point in the answer directly below the one in the question. Then, we multiply as normal.

Five multiplied by two is 10. So we put a zero in the units column and we carry the one. Four multiplied by two is eight. And then, when we add that carried one, we get nine. And one multiplied by two is two. So 1.45 multiplied by two is 2.90, which is actually just 2.9. We’re going to now need to multiply this by 10.

Remember to multiply by 10, we move each of the digits to the left one space. The two moves from the units into the tens column and the nine moves from the tenths into the units column. That tells us that 2.9 multiplied by 10 is 29 and 1.45 multiplied by 20 is 29.

We’re assuming the mass of the bags themselves can be neglected. So we’re done. The mass of 30 bags filled with rice is 29 kilograms.

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