Maths Literacy Matric Revision: Ratio and rate

Revision Notes: Ratio and Rate – CAPS Mathematical Literacy Grade 12

Introduction

Understanding ratios and rates is essential for solving various real-world problems in Mathematical Literacy. These concepts are foundational and are frequently used across different topics such as measurement, finance, and data analysis.

Key Points

Ratio:
1. A ratio is a way to compare two quantities of the same unit.
2. Ratios can be written with a colon (:) or as a fraction.
– Example: The ratio 4:6 can also be written as 4/6 or simplified to 2/3.
3. When expressing ratios, ensure that the units of both quantities are the same.
– Example: If comparing 5ml to 250ml, write it as 5:250.

Rate:
1. A rate compares two quantities of different units.
2. The word “per” is often used in rates, implying “for each” or “for every”.
– Examples: kilometres per hour (km/h), Rands per hour (R/h), metres per second (m/s).
3. Rates can sometimes be expressed as percentages.
– Example: 12% = 12/100.

Real-World Applications

Example 1: Cooking
Problem: A recipe uses a ratio of butter to flour as 30g:90g.
– Simplified Ratio: ( \frac{30}{90} = \frac{1}{3} )
– If you have 300g of flour, how much butter do you need?
Solution: Using the ratio 1:3, Butter ( = \frac{1}{3} \times 300g = 100g ).

Example 2: Travel
Problem: A car travels 150 kilometers in 3 hours. Find the rate in kilometers per hour (km/h).
Solution: Rate ( = \frac{150 \text{ km}}{3 \text{ h}} = 50 \text{ km/h} ).

Common Misconceptions and Errors

  1. Misunderstanding Units in Ratios:
  2. Error: Comparing quantities of different units directly.
  3. Strategy: Always convert to the same units before forming a ratio.

  4. Simplification Errors:

  5. Error: Not simplifying a ratio correctly.
  6. Strategy: Divide both terms of the ratio by their greatest common divisor.

  7. Incorrect Rate Formation:

  8. Error: Mixing up units when writing rates.
  9. Strategy: Be mindful to establish the correct relationship between the units (e.g., distance over time).

Practice and Review

Practice Questions:

  1. Simplify the ratio 45:60.
  2. Solution: ( \frac{45}{60} = \frac{3}{4} )

  3. Calculate the rate for the following: A worker is paid R200 for 5 hours of work.

  4. Solution: Rate ( = \frac{R200}{5 \text{ h}} = R40/\text{h} )

  5. Express 8 out of 20 as a percentage.

  6. Solution: ( \frac{8}{20} \times 100 = 40\% )

Examination Tips:

  1. Keywords: Look for terms like “per”, “ratio”, “fraction”, and “percentage”.
  2. Time Management: Allocate time to check calculations, particularly ensuring units match and simplifying ratios correctly.

Connections and Extensions

  • Percentages and Fractions: Both ratios and rates are closely related to percentages and fractions. Understanding one helps in understanding the others.
  • Finance: Ratios are often used in financial contexts, such as in calculating interest rates or investment returns.
  • Data Analysis: Ratios and rates are essential in interpreting data sets, making comparisons, and presenting findings effectively.

Summary and Quick Review

  • Key Points: Ratios compare quantities of the same unit; rates compare quantities of different units.
  • Common Errors: Be cautious of unit mismatches and incorrect simplifications.
  • Practice: Work through problems systematically to build confidence.

Additional Resources

  • Online Tutorials: Khan Academy, Google Classroom.
  • Videos: “Ratios and Rates in Real Life” on YouTube.
  • Interactive Tools: Mathway, Desmos.

Summary

Ratios and rates are crucial mathematical concepts that allow us to compare quantities and understand relationships between different units. Mastery of these topics is essential for success in mathematical literacy and its applications in various fields.

Quick-Reference:
– Ratios: Same units, written with :
– Rates: Different units, often using per.
– Simplify ratios; convert units if needed.
– Rate example: speed = distance/time.

By revising these concepts and practicing regularly, you’ll strengthen your ability to tackle various real-world mathematical problems accurately and efficiently.

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