GST Rules

In New Zealand, the current rate of GST is 12.5% after initially being 10%. For these 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:

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.)