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Add GST to a price

Start a set of 8
Step 4 of 12

Use the price before tax

Let E be the price excluding GST, G the GST amount and I the price including GST. These purchases are fully taxable at 10%; not every real-world purchase is taxable

  1. 1Tax amount Take one tenth of the exclusive price \(\displaystyle G=0.10E\)
  2. 2Total including tax Add the tax to the exclusive price \(\displaystyle I=E+G=1.10E\)
  3. 3Rounding Use the stated invoice rounding rule. Do not round the starting price or percentage multiplier
Year 11, VCE Units 1 & 2, Chapter 1, 3 difficulty levels, Calculator allowedBuild a worksheet

Adding GST to an exclusive price

These examples assume the whole purchase is taxable at 10%. Find GST from the exclusive price, then add it. GST-free and mixed purchases need different treatment. Let E be the price excluding GST, G the tax and I the price including GST

\[\begin{gathered}G = E \div 10\\I = E + G\end{gathered}\]
  1. Identify the exclusive price The GST-exclusive price is the amount before GST is added, so it is the base for the calculation \(\displaystyle \text{GST base} = E\)
  2. Divide by ten GST is 10% of the exclusive price, and 10% is one tenth \(\displaystyle \begin{gathered}10\% = \frac{10}{100}\\= \frac{1}{10}\end{gathered}\)
  3. Add the tax The GST-inclusive price is the exclusive price plus the GST amount \(\displaystyle I = E + G\)
  4. Round at the stated stage Keep the working exact and round the GST amount to the nearest cent only when the question requires it \(\displaystyle \begin{gathered}\$240.07 \div 10 = \$24.007\\\approx \$24.01\end{gathered}\)

Worked example

A plumber's callout invoice is $347.80 before GST is added. Calculate the GST and the GST-inclusive total

\[E = \$347.80\]
  1. \(\displaystyle \begin{gathered}G = \$347.80 \div 10\\= \$34.78\end{gathered}\)The invoice excludes GST, so divide its amount by 10 to calculate the tax
  2. \(\displaystyle \begin{gathered}I = \$347.80 + \$34.78\\= \$382.58\end{gathered}\)Add the GST to the amount before GST to find the inclusive total
  3. \(\displaystyle \begin{gathered}\$382.58 - \$347.80\\= \$34.78\end{gathered}\)The difference between the total and the exclusive price is the GST amount

Common mistakes

Using the inclusive total as the base
✕\(\displaystyle \begin{gathered}G = \$220 \div 10\\= \$22\end{gathered}\)✓\(\displaystyle \begin{gathered}G = \$200 \div 10\\= \$20\end{gathered}\)
Here $200 is the price before GST and $220 is its GST-inclusive total. GST is 10% of the price before GST, so the inclusive total cannot be used as the base
Rounding before finding GST
✕\(\displaystyle \begin{gathered}\$240.07 \approx \$240\;\\\Rightarrow \;\$240 \div 10\\= \$24\end{gathered}\)✓\(\displaystyle \begin{gathered}\$240.07 \div 10 = \$24.007\\\approx \$24.01\end{gathered}\)
Rounding the exclusive price before dividing can change the GST, so keep the original amount until the stated rounding step
Subtracting GST from the exclusive price
✕\(\displaystyle \$240 - \$24 = \$216\)✓\(\displaystyle \$240 + \$24 = \$264\)
An exclusive price does not include GST, so the tax must be added to reach the inclusive total

Difficulty levels

introCalculate GST from a whole-dollar exclusive price, with the tax amount requested
standardCalculate the GST and inclusive total for an exact exclusive price with cents
challengeRound GST to the nearest cent and handle line items or a discounted price before applying GST

Questions about this topic

Why is GST found by dividing the exclusive price by 10?+

GST is 10% of the exclusive price, and 10% is one tenth, so dividing the exclusive price by 10 gives the GST

How is the GST-inclusive price found?+

Add the GST amount to the price before GST is added. The result contains both the original price and the tax

Why is an inclusive total not divided by 10 to find GST?+

An inclusive total already contains GST, so it is larger than the base used to calculate the tax. Dividing it by 10 gives too much GST

Does every purchase have GST?+

No. These questions assume the whole purchase is taxable at 10%. Real receipts may contain GST-free items or a mix, so do not apply 10% to every receipt automatically

When should I round an invoice?+

Follow the rule stated in the question. In these examples, keep the before-tax amounts exact and round the GST when requested. Real invoices can use different permitted rounding methods

Can I use a calculator?+

A calculator is allowed unless a question is marked no calculator

Which year level and chapter is this?+

Year 11, VCE Units 1 & 2, General Mathematics, chapter 1: Percentages and ratios

In this chapter

Convert between fractions, decimals and percentagesFind a percentage of a quantityExpress one quantity as a percentage of another1A Percentages: Find the original amount from a percentageIncrease or decrease a quantity by a percentageFind percentage changeAdd GST to a priceFind the GST and the pre-GST price from an inclusive priceExpress a ratio in simplest formComplete an equivalent ratioDivide a quantity in a given ratio1E Dividing in a ratio: Use one known part of a ratio to find the others1F Unitary method: Find the original amount from a percentage1F Unitary method: Use one known part of a ratio to find the othersScale a proportional quantity with the unitary methodDecide which option is the better value