Rates (harder)
This subtopic is about changing a rate into new units, one unit at a time, such as litres per minute into litres per hour. It is a key skill in NSW Year 7 maths for comparing speeds, prices and flow rates (NESA outcome MA4‑RAT‑C‑01).
You will use unit facts to decide whether to multiply or divide, convert rates where both units change, switch between m/s and km/h with the 3.6 shortcut, write hours and minutes as decimal hours, and round only at the end. Comparing a cheetah’s top speed with a greyhound’s is one example. This subtopic is part of Year 7 Ratios, Rates and Time.
Every question with a fully worked solution.
- Rates (harder) - Video - Converting Rates Watch
Theory
To convert a rate to new units, write the unit fact first, then change one unit at a time. \(12\) L/min is \(12 \times 60 = 720\) L/h. This Year 7 maths page shows how to change the time unit, the amount unit or both, and the shortcut between m/s and km/h.
Change the time unit. \(12\) L/min means \(12\) L every minute. An hour has \(60\) minutes, so multiply: \(12 \times 60 = 720\) L/h. A longer time gives a bigger amount; a shorter time gives a smaller amount, so divide.
Change the amount unit. Only the amount changes; the time stays the same: \(0.8\) m/h is \(0.8 \times 100 = 80\) cm/h.
Two units change? Change one unit, write the new rate, then change the other. Sometimes both change the same way: \(8\) km/L is \(8000\) m per \(1000\) mL, which is \(8\) m/mL.
Rounding. Round only at the end, to the places asked: \(1000\) kg/h \(= 1000 \div 3600 \approx 0.28\) kg/s (\(2\) decimal places).
m/s and km/h. Multiplying by \(3600\) and then dividing by \(1000\) is the same as multiplying by \(3.6\). So m/s \(\times 3.6 =\) km/h, and km/h \(\div 3.6 =\) m/s.
Hours and minutes. Change the minutes to hours: \(45\) min \(= \dfrac{45}{60}\) h \(= 0.75\) h, so \(1\) h \(45\) min \(= 1.75\) h.
Unit facts:
| Time | Length, volume, mass |
|---|---|
| \(1\) min \(= 60\) s | \(1\) km \(= 1000\) m |
| \(1\) h \(= 60\) min \(= 3600\) s | \(1\) m \(= 100\) cm |
| \(1\) day \(= 24\) h | \(1\) L \(= 1000\) mL |
| \(1\) kg \(= 1000\) g |
How to convert a rate
- Write the unit fact for the unit you are changing.
- Decide: should the number get bigger or smaller? Multiply or divide.
- Change one unit per line and write the new rate each time.
- Round only at the end, and check with a shortcut if there is one.
(i) What is the cost rate?
(ii) What is the cost of \(14\) LED bulbs?
| \(12.50 \div 5\) | \(=\) | \(2.50\) |
| \(14 \times 2.50\) | \(=\) | \(35\) |
(i) \(\$2.50\) per bulb
(ii) \(\$35.00\)
(ii) Change \(540\) mL/min to mL/s.
| \(18 \times 60\) | \(=\) | \(1080\) |
| \(540 \div 60\) | \(=\) | \(9\) |
(i) \(1080\) L/h (an hour is longer, so multiply)
(ii) \(9\) mL/s (a second is shorter, so divide)
| \(750 \times 60\) | \(=\) | \(45\,000\) |
| \(45\,000 \div 1000\) | \(=\) | \(45\) |
Step 1: \(45\,000\) g/h. Step 2: \(45\) kg/h.
| \(12 \times 3600\) | \(=\) | \(43\,200\) |
| \(43\,200 \div 1000\) | \(=\) | \(43.2\) |
\(43.2\) km/h. Check with the shortcut: \(12 \times 3.6 = 43.2\).
(i) Find her average speed in km/h.
(ii) Change this speed to m/s.
| \(1 + 0.5\) | \(=\) | \(1.5\) |
| \(54 \div 1.5\) | \(=\) | \(36\) |
| \(36\,000 \div 3600\) | \(=\) | \(10\) |
(i) \(36\) km/h
(ii) \(10\) m/s (check: \(36 \div 3.6 = 10\))
| \(4200 \div 3600\) | \(=\) | \(1.1666\ldots\) |
\(\approx 1.17\) kg/s
Common pitfalls
Frequently asked questions
How do you change L/min to L/h?
Multiply by \(60\), because an hour has \(60\) minutes. \(18\) L/min is \(1080\) L/h.
How do you change m/s to km/h?
Multiply by \(3.6\). \(25\) m/s is \(90\) km/h.
How do you change km/h to m/s?
Divide by \(3.6\). \(36\) km/h is \(10\) m/s.
How do you convert a rate when both units change?
Change one unit at a time. \(750\) g/min \(= 45\,000\) g/h \(= 45\) kg/h.
How do you write 1 hour 45 minutes in hours?
\(45\) min is \(\dfrac{45}{60} = 0.75\) h, so it is \(1.75\) h.