Curriculum

Course: Mathematics — First Preparatory

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Curriculum

Mathematics — First Preparatory

Unit 1: Numbers

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Unit 2: Algebra

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Unit 3: Statistics

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Unit 4: Geometry

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Text lesson

Applications of Ratio and Proportion

Mathematics — First Preparatory

Applications of Ratio and Proportion

Worked examples

Worked examples

Comparison aspect	Main idea	Keywords
Example 1	A map is drawn to a scale of 1 : 500000. The distance between two towns on the map is 6 cm. What is the real distance in kilometres?	drawnscale500000distance
Solution	The real distance = 6 × 500000 = 3000000 cm. Divide by 100 to get 30000 m then divide by 1000 to get 30 km	realdistance5000003000000
Example 2	A room is 8 m long. We want to draw it to a scale of 1 : 50. What is its length on the drawing?	roomlongwantdraw
Solution	Convert 8 m to 800 cm. The length on the drawing = 800 ÷ 50 = 16 cm	Convertlengthdrawing
Example 3	Divide 180 pounds among three people in the ratio 2 : 3 : 4	Dividepoundsamongthree
Solution	The total number of parts is 2 + 3 + 4 = 9. The value of one part is 180 ÷ 9 = 20. The shares are 2 × 20 = 40 3 × 20 = 60 and 4 × 20 = 80. Check: 40 + 60 + 80 = 180	totalnumberpartsvalue

Comparison aspect	Main idea	Keywords
Example 4	A shirt costs 400 pounds and has a 15% discount. Find the price after the discount	shirtcostspoundsdiscount
Solution	The discount = 400 × 15 ÷ 100 = 60 pounds. The price after the discount = 400 − 60 = 340 pounds	discountpoundspriceafter
Example 5	Two partners invested 3000 and 5000 pounds in a project. The project made a profit of 2400 pounds. What is each partner’s share?	partnersinvested30005000
Solution	The ratio 3000 : 5000 = 3 : 5 and the total number of parts is 8. The value of one part is 2400 ÷ 8 = 300. The first partner gets 3 × 300 = 900 pounds and the second gets 5 × 300 = 1500 pounds. Check: 900 + 1500 = 2400	ratio30005000total

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