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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

Proportion and its properties

Proportion and its properties

  1. A proportion is an equality of two ratios. If a/b = c/d we say that a
  2. b
  3. c and d are in proportion
  4. and we write a : b = c : d.
Comparison aspectMain ideaKeywords
•The extremes are a and d. The means are b and cextremesmeans
In every proportion
  • the product of the extremes = the product of the means
  • that is a × d = b × c
productextremesmeans
If a
  • b = b : c
  • then b is called a mean proportional between a and c. In this case b² = a × c
  • so b = √(a × c) for positive numbers
thencalledmeanproportional
In a
  • b = c : d
  • the number d is called the fourth proportional
numbercalledfourthproportional
•
  • We use the rule of extremes and means to check whether four numbers are in proportion
  • and to find an unknown in a proportion
ruleextremesmeanscheck
Statement Check
The numbers 4, 6, 10, 15 are in proportion
  • 4 × 15 = 60 and 6 × 10 = 60
  • so they are in proportion
The numbers 2, 3, 5, 7 are not in proportion
  • 2 × 7 = 14 and 3 × 5 = 15
  • so they are not in proportion
Ratio and Proportion · 2 / 6