Video: GCSE Mathematics Foundation Tier Pack 3 • Paper 1 • Question 5

GCSE Mathematics Foundation Tier Pack 3 • Paper 1 • Question 5

06:15

Video Transcript

Tim makes a drink. The recipe requires 1.5 liters of water and 250 milliliters of juice. Tim uses 3.75 liters of water to make his drink. How much drink does he make?

Now, we’re going to need to be a little bit careful in this question as we notice that we’ve been given the quantities of water and juice in different units: one is in liters and one is in milliliters. We’ll need to bear this in mind later on.

First though, we notice that Tim has used 3.75 liters of water to make his drink, which is more than the original recipe required. This means that Tim has scaled the recipe up. And we need to know how many times he scaled it up by.

To work this out, we can compare the two quantities of water. And we want to know how many times does 1.5 go into 3.75 because this will tell us what Tim has multiplied the quantities in the original recipe by. If we want to work out how many times one number goes into another, this means we’re doing a division calculation.

So we’re actually working out 3.75 divided by 1.5. Then, you may be thinking, “How am I supposed to do this without a calculator?” And it is actually a little bit easier than it first looks. Remember that the horizontal line in a fraction means divide. So we can write 3.75 divided by 1.5 as 3.75 over 1.5.

Now, at this stage, we’re still dividing by a decimal, which is tricky. And we would much prefer to be dividing by an integer or whole number. What we want to do is find an equivalent fraction where the number that we’re dividing by — the number in the denominator — is an integer. And to do this, we need to multiply both the numerator and denominator by the same number.

Now, there are a couple of possibilities for what we could use. For example, we could multiply by 10, which would take 1.5 to 15. But actually, the smallest then therefore easiest number to multiply it by is two as 1.5 multiplied by two is three.

We can work out what 3.75 multiplied by two is using a column multiplication method. First, we multiply five by two giving 10. So we put a zero in the units column and carry the one. Then, we can work out seven multiplied by two which is 14 and adding the one we’ve carried gives 15. Finally, we have three multiplied by two which is six and then adding the one we’ve carried gives seven.

So 3.75 multiplied by two is 7.50 or just 7.5. Now, we still have a decimal in the numerator of this fraction. But that’s okay as dividing into a decimal is a lot easier than dividing by a decimal. We can work out 7.5 divided by three using a short division method.

We put the decimal point for our answer directly above the decimal point in 7.5. Threes into seven go twice with a remainder of one and threes into 15 go five times exactly. So 7.5 divided by three is equal to 2.5.

So this tells us that Tim has scaled the recipe up 2.5 times.

Next, we need to work out how much juice has used. And as there were 250 milliliters of juice in the original recipe, Tim would have used 2.5 times this amount. So we need to work out 2.5 multiplied by 250.

There are different ways that we could do this. For example, we could use a column multiplication method to work out 250 multiplied by 25 first of all and then divide the answer of this by 10 as we should have been multiplying by 2.5 not 25. However, I think there’s an easier way.

If we want to find two and a half times a number, this means we want to find twice that number and then half of that number and add them together. So I think the easiest thing to do is to add 250 to 250, which gives two lots of 250, and then add half of 250, which is 125. 250 plus 250 is 500. And adding 125 gives 625.

So this tells us that Tim has used 625 milliliters of juice in the drink that he has made.

Now, remember we said we’re going to have to be careful of the units as the juice has been given in milliliters, whereas the water was given in liters. And we need the same units for the two. If we remember that one liter is equivalent to 1000 milliliters, then we can convert our answer from milliliters into liters by dividing by 1000. And it gives 0.625.

We can see this using place value. To divide a number by 1000, we keep the decimal point fixed and move all of the digits three places to the right. So the five that was in the units column is now in the thousandths column. The two that was in the tens column is now in the hundredths column. And the six that was in the hundreds column is now in the tenths column. We can fill in a zero before the decimal point and it gives our answer of 0.625.

Finally, to find the total amount of drink that Tim has made, we need to add together the number of liters of water, which is 3.75, and the number of liters of juice, which is 0.625. We can work this out using a column addition method making sure that we line up the decimal points.

You can include a zero in the empty space of the thousandths column of 3.75 if this helps you. We can then add up in columns starting from the right. Zero plus five is five, five plus two is seven, seven plus six is 13. So we carry a one into the next column. Three plus zero is three and adding the one we’ve carried gives four.

The units for this are liters as that’s what the quantities of water and juice that we were using were measured in. So the total amount of drink that Tim has made is 4.375 liters.

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