Primary 5 maths · Ratio, rate & percentage · About 12 minutes
Solve discount GST and annual-interest problems
Label every amount in the story before choosing which one the percentage acts on.
Start the interactive lesson →Practise: Sale-day detectives
What you will learn
- Solve discount GST and annual-interest problems
Models used: number sentences, stories, tables.
Before you start
Percent is a share of one hundred
This grid is one whole. It has 100 equal squares.
The whole grid has 100 equal squares. One full row is 10 hundredths, or one tenth.
This grid is one whole. It has 100 equal squares.
One small square is one hundredth of the whole. Ten small squares make one tenth, so the same shaded amount can be described in more than one way.
0/100 = 0 = 0%
The whole grid has 100 equal squares. One full row is 10 hundredths, or one tenth.
Shade 25 squares. We have shaded one quarter of the whole.
25 out of 100 = 25%
One small square is one hundredth of the whole. Ten small squares make one tenth, so the same shaded amount can be described in more than one way.
25/100 = 0.25 = 25%
The full bar represents $80, which is 100%. The shaded share is 25%.
Now the whole is $80. One quarter of $80 is $20.
25% of $80 = $20
25% of $80 = $20
The complete bar is the whole. Each labelled section is one part of it.
A 25% discount removes $20. The $60 left is the sale price.
$80 − $20 = $60
What did the picture help us see?
A 25% discount removes $20. The $60 left is the sale price.
Worked example: A new example, together
A pre-tax price is $800. Using the 5% GST rate stated for this question, what is the price including GST?
| Original amount ($) | Stated rate (%) |
|---|---|
| 800 | 5 |
First find the percentage amount. Then decide whether the question needs that part or a final balance. Read each value with the heading above its column.
Label every amount in the story before choosing which one the percentage acts on.
GST adds the stated percentage of the pre-tax price.
First find the percentage amount. Then decide whether the question needs that part or a final balance. Original amount ($) Stated rate (%) 800 5 First find the percentage amount. Then decide whether the question needs that part or a final balance. Read each value with the heading above its column.
The percentage is calculated from $800.
First find the percentage amount. Then decide whether the question needs that part or a final balance. Original amount ($) Stated rate (%) 800 5 A pre-tax price is $800. Using the 5% GST rate stated for this question, what is the price including GST?
840 dollars
First find the percentage amount. Then decide whether the question needs that part or a final balance. Read each value with the heading above its column.
5% × $800 = $40.
First find the percentage amount. Then decide whether the question needs that part or a final balance. Original amount ($) Stated rate (%) 800 5 First find the percentage amount. Then decide whether the question needs that part or a final balance. Read each value with the heading above its column.
Add the GST: $800 + $40 = $840.
First find the percentage amount. Then decide whether the question needs that part or a final balance. Original amount ($) Stated rate (%) 800 5 First find the percentage amount. Then decide whether the question needs that part or a final balance. Read each value with the heading above its column.
Check the result against the question we started with.
The percentage amount is 5 parts out of every 100 of $800.
We found 840 dollars. GST adds the stated percentage of the pre-tax price.
First find the percentage amount. Then decide whether the question needs that part or a final balance. Original amount ($) Stated rate (%) 800 5
Common mistakes to discuss
- Using the wrong whole. Each percentage applies to a stated amount: a discount to the usual price, GST to the price before tax, interest to the amount at the start of the year.
Check your understanding
- Solve discount GST and annual-interest problems
- apply a percentage to the amount it refers to
- check the answer against the original quantities and units
Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.
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