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

Ratio and Proportion

Mathematics — First Preparatory

Ratio and Proportion

Worked examples

Worked examples

Comparison aspect	Main idea	Keywords
Example 1	Simplify the ratio 36 : 48	Simplifyratio
Solution	The greatest common factor of 36 and 48 is 12. Divide both terms by 12: 36 ÷ 12 = 3 and 48 ÷ 12 = 4. The simplest form is 3 : 4	greatestcommonfactorDivide
Example 2	Find x if 3 : 4 = 9 : x	Find
Solution	Product of extremes = product of means so 3 × x = 4 × 9 which gives 3x = 36 and x = 12. Check: 3/4 = 9/12 which is true	Productextremesmeansgives
Example 3	Are 4 10 and 15 in proportion in the order 4 : 6 = 10 : 15?	proportionorder
Solution	The product of the extremes is 4 × 15 = 60 and the product of the means is 6 × 10 = 60. They are equal so the numbers are in proportion. Also 4/6 = 2/3 and 10/15 = 2/3	productextremesmeansequal
Example 4	Find the mean proportional between 4 and 9	Findmeanproportionalbetween

Comparison aspect	Main idea	Keywords
Solution	Let the mean proportional be b. Then b² = 4 × 9 = 36 so b = 6 because the numbers are positive. Check: 4/6 = 6/9 = 2/3	meanproportionalThenbecause
Example 5 (the hardest)	Two numbers are in the ratio 5 : 7 and their sum is 96. Find the two numbers	numbersratioFind
Solution	Let the numbers be 5k and 7k. Their sum is 12k = 96 so k = 8. The numbers are 5 × 8 = 40 and 7 × 8 = 56. Check: 40 + 56 = 96 and 40 : 56 = 5 : 7	numbersCheck

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