Fractions and Percentages — NSW Year 8 Maths
Fractions with negatives, mixed numerals and pronumerals, then percentages for discounts, GST, profit and loss. Twelve subtopics and 240 practice questions, each with a fully worked solution, aligned to NESA outcome MA4-FRC-C-01.
Fractions and Percentages in NSW Year 8
Year 8 takes the fraction and percentage skills from Year 7 and pushes them further. Students add, subtract, multiply and divide fractions that include negatives and mixed numerals, such as \(-\frac{3}{4} - \frac{5}{6}\), and simple fractions with pronumerals, then move freely between fractions, decimals and percentages and use percentages to solve real money problems.
The twelve subtopics below begin with fraction operations and fraction problems, then convert between the three forms, find fractions and percentages of quantities, express one amount as a percentage of another, and work through percentage increase and decrease, mental methods, the unitary method, profit, loss and GST, and mixed percentage problems. Fractions and Percentages is one of the 14 topics in NSW Year 8 Maths and sits in the Number and Algebra strand (NESA outcome MA4‑FRC‑C‑01). These skills lead straight into ratios and rates, and into financial mathematics in Stage 5.
Subtopics
Fractions and Percentages: common questions
What fractions and percentages are taught in Year 8 maths?
Year 8 extends Year 7 to fractions with negative signs and pronumerals, fraction problems with several steps, and percentages used for increases, decreases, discounts, GST, profit and loss. All 12 subtopics come with worked solutions.
How do you increase or decrease an amount by a percentage?
Multiply by a decimal multiplier. A 15% increase multiplies by 1.15 and a 15% decrease multiplies by 0.85, so $60 reduced by 15% is \(60 \times 0.85 = \$51\).
How do you add GST to a price or take it off?
GST in Australia is 10% of the price before tax. Multiply by 1.1 to add it, so $120 becomes \(120 \times 1.1 = \$132\). To find the price before GST from a GST-inclusive total, divide by 1.1, so \(\$330 \div 1.1 = \$300\).
Which NESA outcome covers fractions and percentages?
Fractions, decimals and percentages sit in Stage 4 of the NSW Mathematics K–10 Syllabus (2022) under outcome MA4‑FRC‑C‑01, taught across Year 7 and Year 8.
What is the unitary method?
The unitary method finds one unit first, then scales up. If a jacket costs $96 after a 20% discount, then $96 is 80% of the original price, so 1% is \(96 \div 80 = \$1.20\) and the original price is \(100 \times \$1.20 = \$120\).