Ratio And Proportion

• Ratio


  The comparison between two numbers or quantities with the same units or the same category
• Ratio of triangles to squares


  • 2 is to 3
  • 4 is to 6
• Ways to write a ratio

  1. Column form

  2. Division form

  3. Phrase form

  4. Fraction form
• Ratios expressed in simplest form

  • 1 hour to 40 minutes = 3 is to 2
  • 2 weeks to 4 days = 7 is to 2
  • 8 tourists to 22 other passengers = 4 is to 11
  • 14 red marbles to 28 green marbles = 1 is to 2
  • 21 men to 28 women = 3 is to 4
  • 28 women to 49 people = 4 is to 7
• Proportion


  An equation that shows two ratios are equal
• Writing a proportion


  1. a is to b as c is to d

  2. a/b = c/d
• Product of extremes


  Equal to product of means
• If ratios can be simplified to the same ratio, they are equal and form a proportion
• Determining if ratios form a proportion

  • 4 is to 6 = 8 is to 12 (proportional)
  • 5 is to 24 = 4 is to 30 (proportional)
• Extremes


  The highest and lowest values in a set of data
• Means


  The average or middle value in a set of data
• Multiplying the extremes and the means

  1. Multiplying the highest and lowest values with the average values

  2. Checking if the products are equal
• If the products of multiplying the extremes and the means are equal, then the ratios are proportional
• When the products of multiplying the extremes and the means are equal

  The ratios are proportional
• Cross multiplication is a method to solve proportions
• Solving proportions using cross multiplication

  1. Multiply the extremes

  2. Equate the product to the product of the means

  3. Solve for the missing value
• The properties of proportions include cross multiplication, alternation, inverse, addition, subtraction, and sum of the original proportion
• Applying the properties of proportions

  1. Cross multiplication

  2. Alternation

  3. Inverse

  4. Addition

  5. Subtraction

  6. Sum of the original proportion
• Proportions can be expressed in fraction form or Holland form
• Proportions can also involve polynomials
• Solving polynomial proportions


  1. Cross multiply the extremes and means

  2. Solve for the missing variable