Proportion If two things are proportional, it means that they are related to each other in a specifi c way.
Direct proportion Direct proportion relates to two things, whereby as one increases the other increases.
For example, if a babysitter is paid an hourly rate, then the more hours he works, the more pay he will get. In this case, the time worked is directly proportional to the money earned.
Worked example 2 A football coach is buying new footballs for his team. If 8 balls cost €96, how much will 10 balls cost?
Solution
The cost of the footballs is directly proportional to the number bought.
Practice questions 10.1 1. Write the ratios shown in the images below. Give your answers in the simplest form.
(i) Apples to pears (ii) Cats to dogs (iii) Spiders to ladybirds
(iv) Chocolate bars to ice creams
(v) Books to pens
(vi) Pumpkins to cabbages
2. Simplify the following ratios. (i) 6 : 3 (ii) 18 : 10
(iii) 16 : 36 (iv) 42 : 24
3. Divide each of the following quantities in the given ratio. (i) €50 in the ratio 2 : 3 (ii) 81 km in the ratio 5 : 4
(iii) 121 g in the ratio 9 : 2 (iv) 105 hrs in the ratio 8 : 7
(v) 5 : 25 (vi) 48 : 60
(v) 169 cm in the ratio 8 : 5 (vi) 28 cents in the ratio 3 : 4
4. A company off ers to give €50 to charity for every €200 raised by its employees. What is the ratio (in simplest form) of the money given by the company to the money given by the employees?