1. Number Internal
Tutorial
Mr Ardern Pakuranga College

2. Internal (3 from 5) Percentage discounts Percentage of a number
Decreasing a number by a fraction
Finding the fraction of a number
Decreasing by a decimal

3. For Merit (2 from 3) Removing GST
Converting from NZ$ to over seas currency and vise-versa
Ratios

4. For Excellence Valid recommendation with justification
1 minor error allowed in calculations

5. Percentage
Decimal
Fraction
Sketch
50%
2/3
60%
0.1
5/7
37%
6/6
5/4 3%
0.025

6. Which fraction is bigger?
17/18 or 18/19 First try without a calculator. Explain your answer.

7. Finding the decimal of a number
E.g. Find 0.8 of $ Multiply the decimal by the number e.g. 0.8 x 110 = $88

8. Percentage of a number
E.g. Find 30% of $ Convert the percentage to a decimal e.g. 30 / 100 = Multiply the decimal by the number e.g. 0.3 x 200 = $60

9. Percentage Discounts
E.g. 15% off $ Convert the percentage to a decimal e.g. 15 / 100 = Multiply the decimal by the number e.g x 250 = $ Subtract answer from original number e.g. 250 – 37.5 = $212.5

10. The difference between ‘of’ and ‘off’
‘Off’ is removing the ‘of’ number. Both follow steps 1 and 2. “off” has a third subtraction step.

11. Finding the fraction of a number
E.g. Find 3/4 of $80 1. Convert the fraction to a decimal e.g. 3 / 4 = Multiply the decimal by the number e.g x 80 = $60

12. Finding the fraction off a number
E.g. Find 3/8 off $ Convert the fraction to a decimal e.g. 3 / 8 = Multiply the decimal by the number e.g x 120 = $45 3. Subtract answer from original number e.g. 120 – 45 = $75

13. Find the complete cost of the bathroom:
Items:
Shower $800
Vanity $540
Vanity tap $230
Mirror $115
Paint $80
Discounts:
25% OFF the shower
OFF the vanity
  Vanity tap Reduced by 0.18 of the price  
82% of the mirror 
6 7 th’s of the cost of the paint

14. Who’s got this?…
Items:
Shower $800
Vanity $540
Vanity tap $230
Mirror $115
Paint $80
Discounts:
25% OFF any one item
OFF any one item
  Reduced by 0.18 of the price  
Pay 82% of any one item 
Pay th’s of the cost of any one item
Apply the discounts on the right to the items on the left to work out the best total price.

15. Find the total cost of these items:
iphone $800
iphone case $40
Car charger $30
Selfie stick $15
Face plate $10
Discounts:
30% OFF any one item
OFF any one item
  Reduced by 0.20 of the price  
Pay 85% of any one item 
Pay th’s of the cost of any one item
Match the biggest price with the biggest discount.
Work as a group – not an individual

16. Alice and wonderland takes a red potion to make her 10% shorter
She then takes a blue potion to make her 10% taller.
If she repeats steps 1 and 2 many times what incredible thing begins to happen?

17. Removing a Percentage
Explain to your group why Alice gets smaller after a process of increasing and decreasing by the same percentage.

18. Removing a percentage (GST 15%)
E.g. Remove GST from $600
1. Divide number by 1.15
e.g. $600 / 1.15 = $521.74
2. Check your answer!!!!!!!!!!!!
e.g x 0.15 = 78.26
= 600

19. Splitting numbers into ratios
E.g. Split $55 into a 4:1 Ratio
1. Divide amount into the total number of parts.
E.g. 55 ÷ 5 = 11
2. Multiply the answer from above by the numbers in the ratio
E.g. 11 X 4 = 44 and 11 X 1 = 11
55 split into a 4:1 ratio is 44 parts to 11 parts.

20. Splitting numbers into ratios
E.g. Split $48 into a 5:3 ratio
1. Divide amount into the total number of parts.
E.g. 48 ÷ 8 = 6
2. Multiply the answer from above by the numbers in the ratio
E.g. 6 X 5 = 30 and 6 X 3 = 18
48 split into a 5:3 ratio is 30 parts to 18 parts.

21. Writing one number as a percentage of another
E.g. If in a test your scored 32 out of 36 what percentage have you scored?
1. Write the number as a fraction.
e.g. 32 / 36
2. Convert the fraction to a percentage
e.g. 32 ÷ 36 and then x 100 = 88.9%

22. Exchange Rates
E.g. One NZ dollar is worth US Dollars. What is 400 US$ in NZ$?