Ratios

Understanding Ratios

  • A ratio is a way of comparing quantities. It shows the relative sizes of two or more values.
  • Ratios can be represented in different ways: a to b, a:b, or a/b.
  • In a ratio A:B, A is termed the first term or antecedent and B is the second term or consequent.
  • Ratios can be simplified by dividing both sides by their greatest common divisor.

Types of Ratios

Direct Proportion

  • Direct proportion happens when increasing one quantity leads to an increase in the other quantity.
  • When two quantities are in direct proportion, their ratio remains constant.

Inverse Proportion

  • Inverse proportion, or indirect proportion, happens when an increase in one quantity leads to a decrease in the other.
  • When two quantities are in inverse proportion, the product of their values is always constant.

Part-to-Part and Part-to-Whole Ratios

  • A part-to-part ratio compares different parts of a group to each other. For example, the ratio of boys to girls in a class.
  • A part-to-whole ratio compares one part of a group to the whole group. For instance, the ratio of boys to the whole class.

Solving Ratio Problems

  • To solve ratio problems, start by understanding the relationship between the quantities, simplify the ratio if possible, and then express the ratio as a fraction or a decimal if required.
  • Use the principles of direct or inverse proportion to solve problems involving different quantities.
  • Keep ratios in the simplest form for easy calculation and comparison.

Practice Problems

  • Problem: The ratio of boys to girls in a class is 3:2. If there are 10 boys, how many girls are there in the class?
    • Solution: You know that for every 3 boys there are 2 girls. Set up a proportion and solve for the unknown. So, the number of girls = 2/3 * 10 = 20/3 = 6.67 So, it implies approximately 7 girls.
  • Problem: A mixture contains sugar and flour in the ratio 5:2. If the total mixture weighs 14kg, how much of each is in the mixture?
    • Solution: The total ratio is 5 + 2 = 7. Each part of the ratio therefore represents 14/7=2kg. So, there are 52 = 10 kg of sugar and 22 = 4 kg of flour.

Key Points to Remember

  • Understand and differentiate between direct and inverse proportion.
  • Differentiate between part-to-part and part-to-whole ratios.
  • Practice solving ratio problems, and remember to simplify ratios where possible.
  • Get comfortable setting up proportions and solving for unknowns using ratios.