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grade8_rate_quiz1 draws its questions at random from a bank of 10 questions, with full worked solutions for every one.
A few of the question types, with full solutions, so you know what to expect.
Six exercise books cost R90. What is the cost of one book?
Answer: R15
\( \text{Unit price} = \dfrac{\text{Total cost}}{\text{Number of items}} \)
\( = \dfrac{\text{R}90}{6} \)
Simplify the rate: 180 km in 3 hours.
Answer: 60 km/h
\( \dfrac{180 \text{ km}}{3 \text{ h}} \)
\( 180 \div 3 = 60 \)
\( 3 \div 3 = 1 \)
A household uses 420 litres of water in 7 days. What is the daily usage?
Answer: 60 L/day
\( \text{Daily rate} = \dfrac{420 \text{ L}}{7 \text{ days}} \)
\( 420 \div 7 = 60 \)
*Divide both quantities by 7 to get the unit rate.
A runner covers 600 m in 2 minutes. What is the speed in m/s?
\( \text{Convert 2 minutes to seconds: } 2 \times 60 = 120 \text{ s} \)
\( \text{Speed} = \dfrac{600 \text{ m}}{120 \text{ s}} \)
\( 600 \div 120 = 5 \)
*Always convert to compatible units before calculating.
A bus travels 270 km in 3 hours. What is its average speed?
Answer: 90 km/h
\( \text{Speed} = \dfrac{\text{Distance}}{\text{Time}} \)
\( = \dfrac{270 \text{ km}}{3 \text{ h}} \)
\( 270 \div 3 = 90 \)