7.2 Writing a quantity of an amount as a fraction
Sometimes you will need to show one amount as a fraction of another. This might sound complicated, but it’s actually very logical. Look at the examples below.
To express the fraction of Smarties that are red, you simply need to count the red Smarties (4) and the total number of Smarties (30). Since there are 4 red Smarties out of 30 altogether, the fraction is . It is worth noting here that this could also be written as 4/30.
You may well be asked to give your answer as a fraction in its simplest form, so always check to see if you can simplify your answer. In this case will simplify to .
Example 2: Fraction of an amount
250 g of flour is taken from a 1 kg bag. What fraction is this?
Hint: there are 1000 g in a kg.
To express quantities as fractions, the top and bottom numbers need to be in the same units, so here you need to make sure that you express both the top and bottom values in grams:
The flour removed is already expressed in grams: 250 g
The total amount is in kilograms so you need to convert to grams: 1 kg = 1000 g
Now write the amount taken over the total amount to express as a fraction:
(250 g of flour out of the 1000 g bag has been taken or used)
Then cancel down (or simplify) if possible:
=
So of the flour has been used.
Activity 15: Expressing one number as a fraction of another
What fraction of a kilogram is:
a.100 g
b.750 g
c.640 g
d.20 g
Answer
100 g = 1000 g, so:
a.100 g = of a kilogram
b.750 g = of a kilogram
c.640 g = of a kilogram
d.20 g = = of a kilogram
What fraction of an hour is:
a.15 minutes
b.20 minutes
c.35 minutes
d.48 minutes
Answer
1 hour = 60 minutes so:
a.15 minutes = = of an hour.
b.20 minutes = = of an hour.
c.35 minutes = = of an hour.
d.48 minutes = = of an hour.
A farmer takes 120 eggs to the local farmer’s market. She has 24 eggs left at the end of the day. What fraction of the eggs are left?
Answer
are left. This cancels down to , so of the eggs are left.
A class of students sit a test. 18 pass and 12 fail. What fraction passed the test?
Answer
Work out the total number of students by adding the number who passed to those who failed 18 + 12 = 30. Now work out the fraction that passed:
(18 out of 30 students passed)
Now cancel down:
= .
So passed the test.
Mary bought her car for £12 500. When she goes to trade it in she is offered £8750. What fraction of the original price is this?
Answer
=
30 people entered a raffle. 6 of these people won a prize. What fraction of people did not win a prize? Give your answer as a fraction in its simplest form.
Answer
As this question wants the number of people who did not win a prize we must first do:
30 − 6 = 24 people did not win a prize.
As a fraction this becomes which simplifies to .
Sometimes fractions will not cancel down easily. When this happens, you estimate the fraction by rounding the numbers to values that will cancel. Sometimes this means breaking the ‘rules’ of rounding.
Example: Estimating fractions
will not cancel.
By rounding 1347 up to 1400 and 2057 to 2100 we can cancel down the fraction to get:
=
Note: Round to numbers that are easy to cancel, but if you round off too much, you will lose the accuracy of your answer.
Now that you can express a quantity as a fraction, estimate and simplify fractions, the next step is to be able to work out fractions of amounts. For example, if you see a jacket that was priced at £80 originally but is in the sale with off, it’s useful to be able to work out how much you will be paying.