Transcript Slide 1
A ratio is used to compare numbers or quantities. What are some examples??? Eg. In my hand I have a glass of fruit juice. It is one part fruit and four parts water. Therefore the ratio of fruit to water is 1 to 4. This is written as 1:4. All together there are five parts. Ratio is the number of parts to a mix. The paint mix is 4 parts, with 3 parts blue and 1 part white. The order in which a ratio is stated is important. Mixing paint in the ratio 3:1 (3 parts blue paint to 1 part white paint) means 3 + 1 = 4 parts in all. 3 parts blue paint to 1 part white paint = is ¾ blue paint to ¼ white paint. COMPLETE THE FOLLOWING AS RATIOS: Six parts fruit to 2 parts milk 6:2 Sixteen boys to thirteen girls 16:13 Nine kilograms to twelve kilograms 9:12 Four seconds to one minute 4:60 Four hundred meters to one kilometer 400:1000 Sixteen cm to one meter 16:100 Forty ml to one litre 40:1000 Four parts black paint to seven parts red paint 4:7 In the earlier example we learnt that the ratio of fruit to water in our fruit juice glass was 1:4. What happens if we need to make lots of fruit juice??? If I had six glasses in one jug, then the ratio of fruit to water is 6:24. The taste is the same because the ratio of fruit to water is in PROPORTION. To keep ratios equivalent, or in proportion, you need to multiply both the first and second number by the same number. Eg. 1:4 is the same as 2:8 or 4:16 or 8:32 and so on... KEEP THE RATIOS IN THE SAME PROPORTION: a) 3:2 = 12:__ b) 4:5 = __:50 c) 4:1 = __:10 d) 1:4 = 5:__ e) 10:3 = 20:__ f) 50:1 = 100:__ g) 7:9 = 21:__ h) 1:25 = __:100 i) 4:3 = __: 6 iMaths 7, pg. 81 Q.2 SERVES 8 SERVES 12 Coconut Coconut Marshmallows Marshmallows Unsalted peanuts Unsalted peanuts Red raspberries Red raspberries Milk Chocolate Milk Chocolate A rate is a ratio that compares quantities measured in different units. For example, the speed of a car is measured in km/h (kilometres per hour). The ‘per’ symbol (/) is also a form of division, so rates may be calculated by dividing the two quantities measured. For Example: What is the average speed of a car that travelled 360km in 4 hours? Average speed (km/h) = 360km / 4h = 360 divided by 4 = 90km/h What is the run rate of a one-day cricket team that scored 300 runs in 50 overs? Run rate (runs/over) = 300 runs / 50 overs = 300 divided by 50 = 6 runs/over 1. Solve these problems involving rates: a) What is the average speed of a train that travelled 600km in 3 hours? b) What is the cost per minute of an 8 minutes phone call costing $2.40? c) Mr James ran 26 kilometres in 2 and a half hours. How fast did he run per hour? How fast did he run per minute? 2. Solve these problems involving rates: a) What is the cost per metre of 7m of rope that costs $21? b) A driver takes 10 hours to travel from Sydney to Melbourne. What is the average speed for this 880km trip? c) The UAE needs 81 runs in the next 9 overs to win a one-day cricket match. What run rate is required per over? d) The 1400km plane ride from Sharjah to Egypt takes 3 hours. What is the average speed of the aircraft? e) A patient’s heart beats 360 times in 5 minutes. What is the patient’s heart rate in beats per minute? f) A 20 litre can of paint costs $80. What is the cost per litre? g) A taxi driver paid $90 for 60L of fuel. What is the cost per litre?