Working with Numbers — NSW Year 9 Advanced Maths
Recurring decimals, percentages, simple interest, ratios and rates. Seven subtopics and 140 practice questions with fully worked solutions, aligned to NESA outcomes MA4-FRC-C-01, MA4-RAT-C-01, MA5-FIN-C-01 and MA5-IND-P-02.
Working with Numbers in NSW Year 9 Advanced
Working with Numbers sharpens the number skills that money, measurement and algebra rely on. In Year 9 Advanced, students explain why a fraction gives a terminating or recurring decimal, convert recurring decimals back to fractions, handle repeated and reverse percentage changes, calculate simple interest, and solve multi-step ratio and rate problems.
The seven subtopics below cover terminating and recurring decimals, converting recurring decimals to fractions, operations with percentages, percentages and money, simple interest, ratios and rates, and converting rates. Working with Numbers is one of the 14 topics in NSW Year 9 Advanced Maths and belongs to NESA's Number and Algebra strand. It revises the Stage 4 outcomes MA4‑FRC‑C‑01 and MA4‑RAT‑C‑01, and adds Stage 5 content from MA5‑FIN‑C‑01 (simple interest) and MA5‑IND‑P‑02 (recurring decimals). These skills lead on to earning money, compound interest and direct proportion.
Subtopics
Working with Numbers: common questions
How do you change a recurring decimal to a fraction?
Let \(x\) equal the decimal, multiply by 10, 100 or 1000 so the repeating parts line up, then subtract. For \(x = 0.686868\ldots\), \(100x - x = 68\), so \(x = \frac{68}{99}\).
Which fractions give terminating decimals?
A fraction in simplest form terminates only when its denominator has no prime factors other than 2 and 5. So \(\frac{9}{40}\) terminates because \(40 = 2^3 \times 5\), but \(\frac{5}{12}\) recurs because 12 has a factor of 3.
How do you find the original price after a percentage change?
Divide by the multiplier, not by the percentage. After a 12% increase a bill is $1904, so the original bill was \(1904 \div 1.12 = 1700\) dollars.
How is simple interest calculated?
Use \(I = Prn\), where \(P\) is the principal, \(r\) the interest rate per period and \(n\) the number of periods. For example, $2000 at 7.3% p.a. for 105 days earns \(2000 \times 0.073 \times \frac{105}{365} = 42\) dollars.
Which NESA outcomes cover Working with Numbers?
Decimals and percentages revise MA4‑FRC‑C‑01, and ratios and rates revise MA4‑RAT‑C‑01, from Stage 4. Simple interest is the Stage 5 Core outcome MA5‑FIN‑C‑01, and converting recurring decimals to fractions comes from the Path outcome MA5‑IND‑P‑02.