Ratios, rates and percentages
Try these fresh problems without your notes. Explain your method before opening a solution. This practice is not a graded school assessment.
Check 1
In a ratio red:green = 3:7, what percentage of the total is red?
Check 2
If 16 is 40% of a number, what is the number?
Challenge 1
A map uses 2 cm for 5 km. A route measures 7 cm on the map. Find its real length in kilometres and metres.
Show a hint
Find kilometres per centimetre, then convert the resulting distance.
Show the worked solution
17.5 km, or 17,500 m.
The rate is 5/2 = 2.5 km per map centimetre. Multiply by 7 to get 17.5 km, then by 1,000 for metres.
Challenge 2
A 750 g cereal pack costs $3 and a 1 kg pack costs $4.40. Compare prices per kilogram.
Show a hint
Convert 750 g to kilograms before dividing price by mass.
Show the worked solution
The 750 g pack is cheaper per kilogram: $4/kg versus $4.40/kg.
750 g = 0.75 kg. The first unit price is 3 ÷ 0.75 = 4 dollars per kg. The second is already quoted for one kg.
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If a method was difficult to explain, return to that lesson and schedule a recall check. Unit-review answers are not saved as a score.
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