Ratio and Proportion

• Ratio


  The comparison between two numbers or quantities with the same units or the same category
• Ways to express a ratio

  • Column form (:)
  • Division form (%)
  • Phrase form (a is to b)
  • Fraction form (a/b)
• Simplifying a ratio

  Divide the numerator and denominator by the greatest common factor
• Proportion


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

  1. Check if the product of the means equals the product of the extremes

  2. Check if the ratios can be simplified to the same ratio
• If the product of the means equals the product of the extremes, the ratios form a proportion
• Extremes


  The two outer terms in a proportion
• Means


  The two inner terms in a proportion
• Multiplying the extremes and the means

  They must be equal for the proportion to be true
• Solving proportions

  Use cross multiplication to find missing values
• Proportions can be written in fraction or ratio form
• If the ratio of two numbers is 5 : 6, find their product.
• If the ratio of two numbers is 5 : 7, find their product.
• A rectangle has an area of 18 square units, with a perimeter of 20 units.
• Direct proportion can be represented by the equation y = kx, where k is the constant of proportionality.
• The ratio of the length to width is 3 : 2.
• In indirect proportion, as one variable increases, the other variable decreases at a constant rate.
• In direct proportion, as one variable increases, the other variable also increases at a constant rate.
• A rectangle has an area of 18 square units, with a perimeter of 20 units.
• Ratio

  A comparison of two or more quantities by division
• Proportion

  A relationship where two ratios are equal
• The dimensions are not proportional