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
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
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
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
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
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.