Fractions Decimals and Percentages

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

Mary eats:

1/3 (loaf per day) x 7 =

1 F 3 x 7 = 7/3

Matthew eats:

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

b) Save

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.…

This entry was posted in 2. Fractions Decimals and Percentages, Maths GCSE 2010 Syllabus, Unit 1 Statistics and Number. Bookmark the permalink.

One Response to Fractions Decimals and Percentages

  1. Clive says:

    If you’d like help with cal­cu­lat­ing per­cent­ages quickly you might find my per­cent­age cal­cu­la­tor page really useful.

    Its at

    Hope it helps

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