Free Year 9 Operations with rational numbers Practice | Skillo

Question 1 — Easy

Priya is mixing a sports drink using water and cordial in the ratio 7:3. She wants to make 2.5 litres of sports drink in total. How many millilitres of cordial does she need? Justify your answer by identifying which proportion of the total mixture represents cordial.

Answer: Cordial makes up 3 parts out of a total of 10 parts (7 + 3 = 10), so the proportion of cordial is 3/10. Multiplying 3/10 by 2500 mL gives 750 mL. Option A (300 mL) incorrectly uses 2 litres instead of 2.5 litres. Option C (700 mL) calculates the water (7/10 × 2500 = 1750 mL) incorrectly applied, or confuses water proportion with cordial. Option D (175 mL) divides 2500 by 10 and then multiplies by 0.7, misapplying the ratio.

Question 2 — Medium

A wildlife sanctuary near Cairns recorded that 45% of its 360 native animals are reptiles. Of those reptiles, one third are saltwater crocodiles. How many saltwater crocodiles are at the sanctuary?

Answer: First, calculate 45% of 360: 0.45 × 360 = 162 reptiles. Then find one third of 162: 162 ÷ 3 = 54 saltwater crocodiles. Option A (162) stops after the first step, finding only the total number of reptiles. Option B (60) incorrectly calculates one third of 180 (perhaps rounding 45% to 50%). Option D (40) divides 360 by 9 (treating 45% as 1/9 of the total), which is incorrect.

Question 3 — Hard

Anika is buying native plants for a school garden project. She has a budget of $200. The plants she wants are originally priced at $8.50 each. The nursery is offering a 20% discount on all plants. What is the maximum number of plants Anika can buy with her budget?

Answer: First, calculate the discounted price: 20% of $8.50 = $1.70, so the sale price is $8.50 − $1.70 = $6.80 per plant. Then divide the budget: $200 ÷ $6.80 = 29.41..., so Anika can buy a maximum of 29 plants (rounding down because she cannot buy a fraction of a plant). Option B (23) results from dividing $200 by $8.50 (the original price, ignoring the discount). Option C (25) incorrectly calculates the discounted price as $8.00 (subtracting only $0.50). Option D (20) divides $200 by $10, treating the original price as $10.