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How do you calculate ratio Grade 12?

Published in Ratios and Proportions 3 mins read

Calculating ratios in Grade 12 involves understanding what a ratio represents and applying different mathematical techniques depending on the context of the problem. Here's a breakdown of how to calculate ratios, including simplification and applications:

Understanding Ratios

A ratio compares two or more quantities. It can be expressed in several ways:

  • Using a colon: a:b
  • As a fraction: a/b
  • Using the word "to": a to b

All of these represent the same relationship between 'a' and 'b'.

Calculating and Simplifying Ratios

  1. Express the Ratio: Write the ratio based on the given information. For example, if there are 81 apples and 108 oranges, the ratio of apples to oranges is 81:108.

  2. Simplify the Ratio (if possible): Find the greatest common factor (GCF) of the numbers in the ratio and divide each part of the ratio by the GCF. This reduces the ratio to its simplest form.

    • Example:
      • Ratio: 81:108
      • GCF of 81 and 108: 27
      • Divide both numbers by 27: (81/27) : (108/27)
      • Simplified Ratio: 3:4

Applications of Ratios in Grade 12 Math

In Grade 12, you'll encounter ratios in various contexts:

  • Trigonometry: Trigonometric ratios (sine, cosine, tangent) relate the sides of a right-angled triangle. For example, sin(θ) = opposite/hypotenuse.
  • Calculus: Ratios are used in rates of change, derivatives, and related rates problems.
  • Probability: Ratios represent the likelihood of an event occurring.
  • Geometry: Ratios are used in similarity, scaling, and proportions. Similar figures have corresponding sides that are in proportion, meaning the ratio of corresponding sides is the same.

Examples

  • Trigonometry: In a right triangle, if the opposite side to angle θ is 3 and the hypotenuse is 5, then sin(θ) = 3/5. The ratio of the opposite side to the hypotenuse is 3:5.

  • Geometry: Two triangles are similar. The sides of the first triangle are 4, 6, and 8. The shortest side of the second triangle is 6. Find the length of the longest side of the second triangle.

    • Set up the proportion (ratio): 4/6 = 8/x (shortest side of triangle 1 / shortest side of triangle 2 = longest side of triangle 1 / longest side of triangle 2)
    • Solve for x: x = (8 * 6) / 4 = 12. The longest side of the second triangle is 12.

Key Takeaways

  • Ratios compare quantities.
  • Simplifying ratios makes them easier to understand and use.
  • Ratios are applied in various areas of Grade 12 mathematics, including trigonometry, calculus, probability, and geometry.

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