Write all ratios in their simplest form. 1. There are three children in the Skosana family. Each week the eldest earns R270, the middle child earns R180 and the youngest earns R90. Express these amounts as a ratio. 2. To make a certain colour of household paint, you need to mix \( \frac{3}{4} \ell \) of white paint with 15 ml of red paint and 10 ml of yellow paint. Express the paint mixture as a ratio. If you need a total volume of 31 litres of this paint, how much of each colour must you mix? 3. On Wednesday evening Sonto spent \( \frac{1}{2} \) hour doing homework, 45 minutes doing housework, 1 hour visiting friends and \( 1 \frac{1}{2} \) hours watching television. Write this information as a ratio.

Below are the solutions worked out step‐by‐step: ───────────────────────────── Problem 1 ───────────────────────────── The amounts the children earn are:  Eldest = R270  Middle = R180  Youngest = R90 To express these as a ratio, write them as 270:180:90. Divide each number by the greatest common divisor (which is 90):  270 ÷ 90 = 3  180 ÷ 90 = 2  90 ÷ 90 = 1 Thus, the simplest form of the ratio is:  3 : 2 : 1 ───────────────────────────── Problem 2 ───────────────────────────── The paint recipe calls for:  White paint: ¾ litre (which is 0.75 L)  Red paint: 15 ml  Yellow paint: 10 ml Because the units are not the same, convert everything to millilitres (knowing 1 litre = 1000 ml):  White: 0.75 L = 750 ml  Red: 15 ml  Yellow: 10 ml So the ratio in ml is 750 : 15 : 10. To simplify, divide each term by 5:  750 ÷ 5 = 150  15 ÷ 5 = 3  10 ÷ 5 = 2 Thus, the simplest ratio is:  150 : 3 : 2 Now, if a total of 31 litres of paint is needed, it is best to work in litres. First, convert the original recipe components to litres:  White: 750 ml = 0.75 L  Red: 15 ml = 0.015 L  Yellow: 10 ml = 0.01 L The total volume of one batch of the mix is:  0.75 + 0.015 + 0.01 = 0.775 L Notice that the ratio 750:15:10 (or 150:3:2) represents the parts of each component. The sum of the parts in the simplified ratio is:  150 + 3 + 2 = 155 parts If 155 parts correspond to 0.775 L, then each part equals:  0.775 L ÷ 155 = 0.005 L However, when scaling up to a total of 31 L, determine the value of one part from the new total:  Total parts = 155, so each part = 31 L ÷ 155 = 0.2 L Now, compute the required amounts for each colour:  White: 150 parts × 0.2 L/part = 30 L  Red: 3 parts × 0.2 L/part = 0.6 L  Yellow: 2 parts × 0.2 L/part = 0.4 L A quick check shows: 30 + 0.6 + 0.4 = 31 L. So, to prepare 31 litres of paint, you must mix:  30 L of white paint, 0.6 L of red paint, and 0.4 L of yellow paint. ───────────────────────────── Problem 3 ───────────────────────────── Sonto’s activities and their durations are:  Homework: ½ hour = 30 minutes  Housework: 45 minutes  Visiting friends: 1 hour = 60 minutes  Watching television: 1½ hours = 90 minutes Write the ratio in minutes:  30 : 45 : 60 : 90 Now simplify by dividing each term by the greatest common factor (15):  30 ÷ 15 = 2  45 ÷ 15 = 3  60 ÷ 15 = 4  90 ÷ 15 = 6 Thus, the simplest form of the ratio is:  2 : 3 : 4 : 6 ───────────────────────────── Final Answers ───────────────────────────── 1. 3 : 2 : 1 2. a) The paint mixture ratio is 150 : 3 : 2.   b) To make 31 L of paint, mix 30 L white, 0.6 L red, and 0.4 L yellow. 3. 2 : 3 : 4 : 6