Rukasha Maths

GCSE maths Beta

Rates, units and best buys · Revision guide

Foundation · Ratio · 1 page in the PDF

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Learning objectives

  • Calculate speed and density using consistent units.
  • Convert area units and compare unit costs.

Key ideas

A compound unit combines the units of both quantities.

speed=distancetime,density=massvolume\text{speed}=\frac{\text{distance}}{\text{time}},\qquad\text{density}=\frac{\text{mass}}{\text{volume}}

Convert minutes to hours before finding speed in kilometres per hour.

hours=minutes60\text{hours}=\frac{\text{minutes}}{60}

Area units square the length conversion.

1 m=100 cm,1 m2=10 000 cm21\text{ m}=100\text{ cm},\qquad1\text{ m}^2=10\,000\text{ cm}^2

For best buys, compare costs for one item or one common unit.

unit cost=total costquantity\text{unit cost}=\frac{\text{total cost}}{\text{quantity}}

Worked examples

Example 1

A cyclist covers thirty-six kilometres in one hour and thirty minutes. Find the average speed.

t=1+3060=1.5 ht=1+\frac{30}{60}=1.5\text{ h}
v=361.5=24 km/hv=\frac{36}{1.5}=24\text{ km/h}
24 km/h24\text{ km/h}

Example 2

Convert the area from square metres to square centimetres.

2.5 m2=2.5×10 000 cm2=25 000 cm22.5\text{ m}^2=2.5\times10\,000\text{ cm}^2=25\,000\text{ cm}^2
25 000 cm225\,000\text{ cm}^2

Watch out

Square the conversion factor for area. Thirty minutes is half an hour, not three tenths of an hour.