Overview Fractions, Decimals and Percentages
For me, this is one of the key sections. An understanding of fractions, decimals and percentages will give you a headstart in many other areas within Maths GCSE. Just one small example, stratified sampling (see data collection) becomes simple if you understand percentages. In addition this is one of the subjects that really helps in everyday life. For example, you currently pay £62 per month for electricity and your electricity company announces a price increase of 20%, how much will this cost you per month? Answer 20% of £62 = £12.40.
The other key point seems to be to learn how to use your calculator. Practice using decimals and percentages. Make sure you have a scientific calculator with a fraction key, you may have to refer to your instruction book!
Questions and Answers
The only way to get really comfortable with fractions, decimals and percentages is to answer questions. Some of the questions can be quite wordy and almost sound like riddles or trick question but you just need to keep calm and work through the question step by step. So here goes!
Fraction of an amount
You can use your calculator to make this easy. I will call the fraction button “F” when I am showing its use in the following question and answer.
Mary and Matthew have 6 children. On average each of her children eat 1/4 of a loaf per day, Mary eats 1/3 of a loaf per day and Matthew eats 1/2 a loaf per day. How many loaves to do Mary, Matthew and their children eat per week.
There are quite a few words but it just needs to be broken down and use the fraction key on your calculator. So you need to calculate how many loaves per week the children eat, Mary eats and Matthew eats and then just add them all up.
The children eat:
6 (number of children) x 1/4 (fraction of loaf eaten per child per day) x 7 (days of week)=
6 x 1/4 x 7
So the calculator entry is:
6 x 1 F 4 x 7 = 21/2
1/3 (loaf per day) x 7 =
1 F 3 x 7 = 7/3
1/2 (loaf per day) x 7 =
1 F 2 x 7 = 7/2.
Therefore between them all, the family eats:
21/2 + 7/3 + 7/2 =
21 F 2 + 7 F 3 + 7 F 2 = 49/3 Divide top and bottom by 3 = 16 1/3 loaves per week.
A quantity as a Fraction of another Quantity
Joe earns £45 per week from his paper round. He gives £15 per week to his Mum for housekeeping, he saves £10 per week and he spends $3.50 on magazines.
What fraction of his earnings does Joe:
a) Give to his Mum for housekeeping
c) On magazines
d) Have left over?
When writing a fraction first convert both numbers to the same units (in this example we have a mixture of Pounds and Pence) and then simplify the fraction.
a) Joe gives £15/£45 to his Mum for housekeeping = 1/3
b) Joe saves £10/£45 = 2/9
c) Joe spends 350p/4500p on magazines = 35/450 = 7/90
NB you can this simplification yourself OR you can use the fraction function on your calculator:-
350 F 4500 = 7/90
d) Joe has left over £45 — £15 — £10 — £3.50 = £16.50
= £16.50/£45 = 1650/4500 = 165/450 = 33/90 = 11/30
NB using the calculator you get:
1650 F 4500 = 11/30
So a key learning point is that you can use the fraction key on your calculator to simplify fractions (this may save you time in the exam).
to be continued.…