Quick questions on GST and percentage change for HSC Maths Standard 2

To add the $10\%$ GST you can find $10\%$ and add it on. It is faster and safer, though, to multiply the pre-GST price by $1.1$ in a single step. This works because $100\%$ of the price plus another $10\%$ is $110\% = 1.1$. A plumber who quotes $680 excluding GST adds $0.10 \times 680 = 68$, i.e.

The trap that catches the most students is going backwards from a price that already includes GST. Suppose a receipt total is $88.00, GST included. The GST is not $10\%$ of $88; that would give $8.80, which is too much. The $88 is $110\%$ of the pre-GST price, so the pre-GST price is $88 \div 1.1 = 80$, i.e.

A percentage increase or decrease is the same idea as adding GST, just with a different rate. To change an amount by $r$ (the rate as a decimal), multiply by $(1 + r)$ to increase or $(1 - r)$ to decrease. The number you multiply by is the multiplier. A $1450 laptop discounted by $30\%$ keeps $100\% - 30\% = 70\%$ of its price, so the sale price is $1450 \times 0.70 = 1015$, i.e.

When two or more percentage changes happen one after another, you apply each to the result of the previous one, never to the original. The clean way is to multiply the multipliers together. This is where students lose marks by adding percentages, which is always wrong. You see this stacking everywhere.