Estimate and find percentages of whole number and decimal amounts.
Number Framework Stage 8
Squared paper
In New Zealand, the current rate of GST is 15% after initially being 10% and then being increased to 12.5%. For the two earlier percentages (and only a few others), there are two simple whole number division rules, one to add on GST, and the other remove GST.
Using Materials
Problem: “When GST began in New Zealand, the rate was 10%. When a price includes tax, what fraction of it is tax?”
“What is 10% as a familiar fraction?” (Answer:1/10 .)
Draw a rectangle 20 centimetres by 2 centimetres to represent a number and divide it into 10 parts. Add a shaded tenth to represent GST.
“Look at the new diagram as a new whole. What fraction is shaded?” (Answer:1/11 .)
Discuss why adding 10% to a number is reversed by subtracting 1/11 from the answer. So 1/11 of the GST inclusive price is tax.
Examples: Find the fractions of GST inclusive prices that are tax for these rates of GST. Draw pictures: 12.5% 20% 25% 5%
Using Number Properties
Problem: “Herbie pays $98.55 for a new pair of trousers. The bill says this amount includes 12.5% GST of $10.95. Is this correct?”
(Answer: Yes 12.5% = 1/8. So a GST inclusive price has 1/9 tax. And 1/9 of $98.55 = $10.95.)
Examples: The following prices include GST for a given GST rate. Find the amount
of tax included in the prices: $495, GST 10% $900, GST 12.5% $120, GST 20%
$1,000, GST 25%
Understanding Number Properties:
Explain why the current rate of 15% GST does not work with these easy whole number division procedures.
For a GST rate of 50%, explain how to find the
tax included in a GST-inclusive price.
Understanding Number Properties:
For a GST rate of 100/n%, explain what
fraction of the GST-inclusive price is tax. (Answer: 1/n+1.)