The 100% Challenge
Your challenge was to
give your personal 100% to a maths topic that is not difficult -
but trips more people up than any other topic - percentages (and of course
fractions and decimals).
YOU AVOID THE MOST COMMON TRIPS?
DID YOU REMEMBER
4% MEANS ... 4 IN EVERY
100 ... or 4 OUT OF
10% means 10 out of 100 = 10/100 =
1/10 ... OR DIVIDE BY 10
20% is TWICE as big
... and 5% is HALF as big ... as 10%
had any Problems ...
remember that you can Ask an
You're on a shopping mission for a new
outfit and you've just found that everything is on special
Can you work out the sale prices?
50% of original price
50% of £23 means 1/2
Half of 23 =
Miss Shellfish bomber jacket
Sale price: Now one third of original price
one third means 'divide by 3'.
57 / 3 = 19
Weaver Ireland winter
Sale price: 10% of original
'one tenth' or 'divide by 10' :
170 / 10 = 17
TipTop Shop trouser suit
Sale price: 20% of
20% means '20 out of 100' or 'one fifth' or 'divide by 5'
Shortcut: Find 10% and double it:
10% of 150 = 150 / 10 = 15
20% = 2 x 15 =
Next Stop silk T-shirt
£70, which is 50% of THE ORIGINAL PRICE
£70 is 50% (HALF) OF THE ORIGINAL
So original price is TWO TIMES £70:
2 x 70 = 140
you've finished your clothes shopping and you're off to buy wood for your
need four fifths of a metre (4/5 m) of 20mm by 20mm wood.
The wood is
labelled using decimal lengths.
Which of these is the correct
B. 0.8 metre
C. 0.45 metre
1: Write 4/5 as tenths
4/5 = ?/10
4/5 = 8/10 (you
can make both 4 and 5 two times
changing the size of the
A fifth is twice as
big as a tenth (Why? Because:
If you divide 1 piece of wood
into 10 equal
each part = 1/10.
If you divide the same wood into 5 equal parts,
each part = 1/5.
SO - YOU GET HALF AS
MANY FIFTHS BUT THEY'RE TWICE AS
Step 2; Write tenths as a
8/10 = 0.8 (1st
digit after the decimal point =
Q7. You also need seven tenths of a metre (7/10
m) of slightly thicker wood (30 mm by 30 mm).
Which of these is the
B. 70 metre
Seven tenths = 7/10 = 0.7 metre
(1st digit after the decimal point =
Q8. Right - you're home with the shopping.
But you didn't finishing cleaning your room did you?
mum says you only tidied your room on three Saturdays out of five, so
you're only getting three fifths of your £35 monthly pocket money.
Sounds logical doesn't it?
much do you pick up?
three fifths =
USE A GENERAL RULE TO FIND ANY FRACTION:
'Divide by the
denominator and multiply by the numerator'
('Divide by the bottom
and times by the top'):
35 / 5 =
7 x 3 = 21
OR METHOD 2: USE TENTHS AS A
1/10 of £35 =
3.50 So, 6/10 = 6 x
3.50 = 21
Q9. Your sister shows you her clothes
She says she paid £12 for her TeenGear wool jumper - and it
was 40% of the original price.
was the original price?
Clue: the original amount = £100% of the
You know: 40% of original amount = £12
want: 100% of the original amount = £ ?
How do you go from 40% to 100%? Here's one
4) ( x by
Q10. She also says she bought her JBC
all-weather trainers with airsoles in the ' 10% Off ' sale.
trainers were £80 before the sale, how much did she
A10. A: £72
£10% means 1/10 or
'divide by 10'
So, 10% Off means
'find 1/10 and subtract it from £80' :
of 80 = 1/10 of 80 = 8
Sale Price: 80 - 8 =
How well did your shopping trip go?
- Did you calculate your bargain prices
- Did you pay more than you bargained for?
0 - 1
It looks like painful percentages and fractious
fractions gave you a lot of shopping hassle - and they are a pain at
first - but don't give in just yet! Why not go and read the
answers to the first three questions and see if they make sense?
2 - 4
Not a bad start
at all - to one of the trickiest topics in the history of maths. Your
score also shows that you're working to at least Level 4 ... keep turning
up to those fantastic Year 9 maths lessons: you'll be working at Level 5 in
5 - 8
brilliant score, indicating dazzling Year 9 success - well
9 - 10
Congratulations! You're clearly a
high-ranking mathematician, and your excellent Level 6
understanding of percentages, fractions and decimals promises a
heartwarming success in both your SATs - and later on in your GCSE
What Next? - You
- Leave this challenge
... and come back later if you want to see
if you can improve your score
- Or clicjk here to try the next SatsMuncher: the SizeWise