SatsMuncher 3: 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).  DID YOU AVOID THE MOST COMMON TRIPS?   DID YOU REMEMBER THAT: 4% MEANS ... 4 IN EVERY 100 ... or 4 OUT OF 100 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% If you had any Problems ... did you remember that you can Ask an Expert ?

Fantastic!  You're on a shopping mission for a new outfit and you've just found that everything is on special offer! Can you work out the sale prices? Q1.  Gape jeans Were £23 Sale Price: 50% of original price Sale price? A1.  £11.50 50% of £23 means 1/2 of £23 Half of 23 = 11.50   Q2.  Miss Shellfish bomber jacket Was £57 Sale price: Now one third of original price Sale price? A2.  £19 one third means 'divide by 3'. 57 / 3 = 19   Q3.  Weaver Ireland winter coat  Was £170 Sale price: 10% of original price Sale price? A3.  £17 10% means 'one tenth' or 'divide by 10' : 170 / 10 = 17

Q4.  TipTop Shop trouser suit Was £150 Sale price: 20% of original price. Sale price? A4.  £30 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 So, 20% = 2 x 15 = 30   Q5.  Next Stop silk T-shirt Sale price: £70, which is 50% of THE ORIGINAL PRICE Original price? A5.  £140 £70 is 50% (HALF) OF THE ORIGINAL PRICE So original price is TWO TIMES £70: 2 x 70 = 140     Q6.  Now you've finished your clothes shopping and you're off to buy wood for your technology project.  You 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 length? A.  0.4 metre B.  0.8 metre C.  0.45 metre D.  0.08 metre A6.  B: 0.8 metre Step 1: Write 4/5 as tenths Number Smart:  4/5 = ?/10  4/5 = 8/10  (you can make both 4 and 5 two times bigger                     without changing the size of the fraction) OR: Word Smart:  A fifth is twice as big as a tenth  (Why? Because: If you divide 1 piece of wood into 10 equal parts,    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 BIG! Step 2;  Write tenths as a decimal: 8/10 = 0.8  (1st digit after the decimal point = tenths)      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 correct length? A.   0.07 metre B.  70 metre C.  0.7 metre D.  0.007 metre A7.  C:  0.7 metre Seven tenths = 7/10 = 0.7 metre (1st digit after the decimal point = tenths)   Q8.  Right - you're home with the shopping.  But you didn't finishing cleaning your room did you?  Your 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? How much do you pick up? A8.  £21 three fifths = 3/5 METHOD 1: 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                           7 x 3 = 21 OR METHOD 2: USE TENTHS AS A SHORTCUT: 3/5 = 6/10 1/10 of £35 = 3.50          So, 6/10 = 6 x 3.50 = 21

Q9.  Your sister shows you her clothes shopping. She says she paid £12 for her TeenGear wool jumper - and it was 40% of the original price. What was the original price? A9.  £30 Clue: the original amount = £100% of the price: You know:  40% of original amount = £12 You want:  100% of the original amount = £ ? How do you go from 40% to 100%?  Here's one way:         (divide by 4)          ( x by 10) 40%      ------>      10%      ------>      100%  12                          3                          30   Q10.  She also says she bought her JBC all-weather trainers with airsoles in the ' 10% Off ' sale. If the trainers were £80 before the sale, how much did she pay? A.  £72 B.  £88 C.  £70 D.  £79.20 A10.  A: £72 £10% means 1/10 or 'divide by 10' So, 10% Off means 'find 1/10 and subtract it from £80' : Discount:  10% of 80 = 1/10 of 80 = 8    £8 Sale Price: 80 - 8 = 72   £72

How well did your shopping trip go? 

- Did you calculate your bargain prices correctly
- or
- Did you pay more than you bargained for?

Your Score

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 no time!

5 - 8 
An outstandingly brilliant score, indicating dazzling Year 9 success - well done!

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 exams.