Working with Numbers — NSW Year 9 Core Maths
Integers, decimals, fractions, percentages, money, simple interest, ratios and rates. Ten subtopics and 200 practice questions with worked solutions, aligned to MA4-INT-C-01, MA4-FRC-C-01, MA4-RAT-C-01 and MA5-FIN-C-01.
Working with Numbers in NSW Year 9
Working with Numbers brings together the number skills every later topic depends on: directed numbers, decimals, fractions, percentages, ratios and rates. In Year 9 Core these are revised from Stage 4 and pushed a little further, with longer calculations such as \((3 - 4)^2 - (7 - 1)^2\), significant figures, recurring decimals turned back into fractions, reverse percentages and rates that change both units at once.
The ten subtopics below move from integers, decimals and recurring decimals through fractions and percentages to money problems with profit, loss and GST, then simple interest, ratios and rates, and converting rates. Working with Numbers is one of the 13 topics in NSW Year 9 Core Maths and belongs to the Number and Algebra strand. It revises the Stage 4 outcomes MA4‑INT‑C‑01, MA4‑FRC‑C‑01 and MA4‑RAT‑C‑01, and simple interest is new Stage 5 content under MA5‑FIN‑C‑01. The same skills return in Earning Money, in equations and in compound interest in Year 10.
Subtopics
Working with Numbers: common questions
Why does Year 9 Core maths revise number skills?
Almost every Year 9 topic, from algebra to trigonometry, relies on accurate work with negatives, fractions, decimals and percentages. Revising them early, at a slightly harder level, means later topics can focus on new ideas instead of arithmetic slips.
How do you turn a recurring decimal into a fraction?
Call the decimal \(x\), multiply by \(10\) or \(100\) so the repeating part lines up, then subtract. For \(x = 0.\dot{2}\dot{7}\), \(100x - x = 27\), so \(99x = 27\) and \(x = \frac{27}{99} = \frac{3}{11}\).
How do you find the original price after a discount?
Divide the sale price by the multiplier for the discount. A jacket reduced by \(15\%\) costs \(85\%\) of its original price, so if it now costs \(\$306\) the original price was \(306 \div 0.85 = \$360\).
What is the simple interest formula?
\(I = Prn\), where \(P\) is the principal, \(r\) is the interest rate per time period as a decimal and \(n\) is the number of time periods. For \(\$5000\) at \(3.65\%\) p.a. for \(3\) years, \(I = 5000 \times 0.0365 \times 3 = \$547.50\).
Which NESA outcomes cover Working with Numbers?
Most of the topic revises Stage 4 outcomes: MA4‑INT‑C‑01 for integers, MA4‑FRC‑C‑01 for fractions, decimals and percentages, and MA4‑RAT‑C‑01 for ratios and rates. Simple interest is Stage 5 Core content under MA5‑FIN‑C‑01.