Module 1 Essential Mathematics

1
Module 1Essential Mathematics

• Percentages
• Decreasing and increasing by a percentage
• Finding a percentage change
• Working backwards
• Multiple percentages
• Exchange rates
• Ratios

Learning objectives covered1.2-1.4
2
Using percentages

• A percentage is a way of writing a fraction.
• ½ 0.5 50
• 30 of 34 30/100 34 10.20
• 12.5 of 80 12.5 / 100 80
• Decreasing by a percentage
• A television costs 2000. Henry Norval is
  offering 25 off (for a short time only). How
  much will the TV cost?
• 25 off 100 (100-25) 75
• So the quick way is to multiply by 75 ( 0.75)
• 2000 0.75 1500.
• You do it
• A fridge costs 1200. What will the price be with
  a discount of 15 ?
• 15 off 100 (100-15) 85
• 1200 0.85 1020

of means times
3
Increasing by a percentage

• All the prices at a petrol station are increasing
  by 3. What will a price of 4.80 become?
• A 3 increase is (100 3) 103 1.03
• The price increases to 4.80 1.03 4.94400
• This is sensibly given as 4.94.
• Casual workers have holiday pay of 8 added on to
  their pay. Leos pay-rate without holiday pay is
  12.25 per hour. What is his pay-rate with
  holiday pay?
• An 8 increase is (100 8) 108 1.08
• The pay-rate with holiday pay is 12.25 1.08
  13.23
• Clothing shops can have very high markups on
  their garments - as much as 200 or 300
• A dress shop usually puts a 250 markup on their
  stock. A skirt is bought for 32. What will it
  retail for?
• A 250 increase is (100 250) 350 3.5
• The skirt will retail for 32 3.5 112.00

4
Finding a percentage change

• The important thing is to make sure you put the
  right number on the bottom!
• Sales went from 3200 in January to 3500 in
  February. State this as a percentage change.
• Amanda saw a pair of shoes that cost 28 from the
  wholesaler. The shop was selling it for 70. What
  percentage mark-up is the shop using?

Calculator hint Use brackets around the top line
of the formula.
5
Working backwards

• The price for a phone is 259 including GST. What
  is the price before the GST (of 12.5) is added?
• The original price was multiplied by 1 12.5/100
  1.125 to get the price including GST.
• To find the original price, we divide the 259 by
  1.125 230.22.
• The price for a calculator is 89 including GST.
  What is the price before the GST is added?
• 89/1.12579.11

1.125
Without GST
With GST
1.125
6
Multiple percentages

• Nats pay-rate is 13 per hour, plus 8 holiday
  pay. He pays 18 income tax. What is his net
  hourly rate?
• 13 1.08 0.82 11.51
• Unless stated otherwise, you should multiply the
  effects, not add them.
• Example
• Price of 1000, a mark-up of 50, 12.5 GST
• ? You DO NOT add the 50 and the 12.5 to get
  62.5, then add it on, giving 1620. ?
• You DO multiply by (1 0.5) and by (10.125),
  giving 1667.50. ?
• Example
• Original price is 75, the markup is 120, and
  staff discount of 20 off retail. Price for staff
  member?
• 75 2.2 0.8 132. ?
• ? NOT markup less discount is 100, so price is
  150.

7
Exchange rates

• Example
• A DVD costs 13. The exchange rate is NZ1 buys
  0.35. How much will the DVD cost in NZ?
• (Think will it be more or less? )
• 13/0.35 37.14.
• A book costs US15, plus 7 postage and packing.
  The exchange rate is NZ1 buys US0.71. How much
  will the book cost, including postage and
  packing, in NZ?
• 15 1.07 / 0.71 22.61

0.35
NZ
UK
0.35
8
Ratios

• Three friends, Ann, Ben and Carrie put,
  respectively, 300, 200 and 400, into a small
  business venture. They agree to split the profit
  in the ratio 324.
• They get a profit of 1575. How much will Ann
  get?
• Step 1 Add the values in the ratio together
• 324 9
• Step 2 Divide the amount by the sum of the
  ratios.
• 1575/9175.
• Step 3 Multiply by the part you are interested
  in.
• 175 3 525.
• Ann will get 525.
• Exercise
• They decide that since Ann is doing more work,
  the ratio should change to ratio 424.
• How much profit will Ann get under the new ratio?
• 424 10
• 1575/10157.5
• 157.5 4 630.
• Ann will get 630.