Number Internal Tutorial Mr Ardern Pakuranga College 2014

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

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

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

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

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

Finding the decimal of a number E.g. Find 0.8 of $110 1. Multiply the decimal by the number e.g. 0.8 x 110 = $88

Percentage of a number E.g. Find 30% of $200 1. Convert the percentage to a decimal e.g. 30 / 100 = 0.3 2. Multiply the decimal by the number e.g. 0.3 x 200 = $60

Percentage Discounts E.g. 15% off $250 1. Convert the percentage to a decimal e.g. 15 / 100 = 0.15 2. Multiply the decimal by the number e.g. 0.15 x 250 = $37.5 3. Subtract answer from original number e.g. 250 – 37.5 = $212.5

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

Finding the fraction of a number E.g. Find 3/4 of $80 1. Convert the fraction to a decimal e.g. 3 / 4 = 0.75 2. Multiply the decimal by the number e.g. 0.75 x 80 = $60

Finding the fraction off a number E.g. Find 3/8 off $120 1. Convert the fraction to a decimal e.g. 3 / 8 = 0.375 2. Multiply the decimal by the number e.g. 0.375 x 120 = $45 3. Subtract answer from original number e.g. 120 – 45 = $75

Find the complete cost of the bathroom: Items: Shower $800 Vanity $540 Vanity tap $230 Mirror $115 Paint $80 Discounts: 25% OFF the shower 2 8 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

Who’s got this?… Items: Shower $800 Vanity $540 Vanity tap $230 Mirror $115 Paint $80 Discounts: 25% OFF any one item 2 8 OFF any one item   Reduced by 0.18 of the price   Pay 82% of any one item  Pay 6 7 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.

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 2 6 OFF any one item   Reduced by 0.20 of the price   Pay 85% of any one item  Pay 6 8 th’s of the cost of any one item Match the biggest price with the biggest discount. Work as a group – not an individual

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?

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

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. 521.74 x 0.15 = 78.26 521.74 + 78.26 = 600

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.

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.

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%

Exchange Rates E.g. One NZ dollar is worth 0.780 US Dollars. What is 400 US$ in NZ$?