## Rates, Ratio and Proportion Exercise

1. Write these ratios as fractions in their simplest form:

(a) 8 : 10
(b) 12 : 20
(c) 11 : 4
(d) 3 : 1

2. Write these percentages as ratios in their simplest form:

(a) 30%
(b) 75%
(c) 120%
(d) 100%

3. Express the following ratios as simply as possible:

(a) 9 cm : 12 cm
(b) 14 : 28
(c) \$35 : \$40
(d) 10 kg : 30 kg : 25 kg

4. Make the units of the following ratios the same and then simplify:

(a) 300 g : 2 kg
(b) \$3.20 : 40c
(c) 400 m : 1 km
(d) 20 minutes : 1.5 hours

5. (a) If 2 : 6 = x : 30, find the value of x.

(b) If d : 12 = 6 : 9, find the value of d.

(c) If 5x = 159, find x.

(d) Find x if 2x8 = 916

6. (a) Divide 110 into two parts in the ratio 2 : 3

(b) Two people share \$85 in the ratio 3 : 7.

How much does each person receive?

 (c) A piece of wood, of length 1.2 m, is cut into three smaller pieces in the ratio 1 : 2 : 3. How long is each piece, in centimetres?

(d) Two people buy a house for \$250, 000. Pero puts in \$100, 000 and Alama puts in \$150, 000. If they sell the house a year later for \$300, 000, how much should each person get?

7. (a) A car travels from Christchurch to Dunedin, a distance of 420 km, in 6 hours. What is its average speed?

(b) The car uses 30 litres of fuel. What was its fuel consumption in km/litre?

(c) If the car is rented and costs \$120 and there are 5 people, how much does the rental cost per person?

(d) The petrol costs \$45. What is the total cost (rental plus petrol) per person?

8. Express each rate in its simplest form in the units given:

(a) 600 km in 5 hours in m/minute

(b) 2000 revolutions in 1 hour in revs/min

(c) 30 g per 10 cmin g/cm3

(d) \$500 per week in \$/day