Grade 6
  1. Number System  1.1. Whole Numbers  1.1.1. Place Value and Face Value  1.1.2. Comparing and Ordering Numbers  1.1.3. Rounding Numbers  1.1.4. Properties of Whole Numbers (Associative, Commutative, Distributive)  1.2. Integers  1.2.1. Introduction to Integers  1.2.2. Addition and Subtraction of Integers  1.2.3. Multiplication and Division of Integers  1.2.4. Properties of Integer Operations  1.3. Fractions  1.3.1. Types of Fractions  1.3.2. Equivalent Fractions  1.3.3. Simplification of Fractions  1.3.4. Addition and Subtraction of Fractions  1.3.5. Multiplication and Division of Fractions  1.3.6. Comparing and Ordering Fractions  1.4. Decimals  1.4.1. Understanding Decimals  1.4.2. Conversion between Fractions and Decimals  1.4.3. Addition and Subtraction of Decimals  1.4.4. Multiplication and Division of Decimals  1.4.5. Comparing and Ordering Decimals
  2. Algebra  2.1. Basics of Algebra  2.1.1. Variables and Constants  2.1.2. Expressions and Equations  2.1.3. Algebraic Terms and Coefficients  2.2. Solving Simple Equations  2.2.1. Balancing Equations  2.2.2. Solving One-Step Equations  2.2.3. Solving Two-Step Equations  2.3. Patterns and Sequences  2.3.1. Identifying Patterns  2.3.2. Arithmetic Sequences
  3. Ratio and Proportion  3.1. Ratios  3.1.1. Understanding Ratios  3.1.2. Equivalent Ratios  3.1.3. Simplifying Ratios  3.2. Proportion  3.2.1. Introduction to Proportion  3.2.2. Direct and Inverse Proportions  3.3. Percentages  3.3.1. Converting Ratios to Percentages  3.3.2. Percentage Increase and Decrease  3.3.3. Discount and Profit Calculations  3.3.4. Simple Interest Calculations in Percentages in Ratio and Proportion
  4. Geometry  4.1. Basic Geometric Shapes  4.1.1. Points, Lines, and Angles  4.1.2. Types of Angles  4.1.3. Intersecting and Parallel Lines  4.2. Triangles  4.2.1. Types of Triangles  4.2.2. Properties of Triangles  4.2.3. Sum of Angles in a Triangle  4.2.4. Congruence of Triangles  4.3. Quadrilaterals  4.3.1. Types of Quadrilaterals  4.3.2. Properties of Quadrilaterals  4.4. Circles  4.4.1. Radius and Diameter  4.4.2. Circumference and Area  4.4.3. Arcs and Chords  4.4.4. Sector and Segment
  5. Mensuration  5.1. Perimeter  5.1.1. Perimeter of Simple Shapes  5.2. Area  5.2.1. Area of Rectangles and Squares  5.2.2. Area of Triangles and Parallelograms  5.2.3. Area of Composite Figures  5.2.4. Area of Trapezium  5.3. Volume  5.3.1. Volume of Cubes and Cuboids  5.3.2. Volume of Cylinders  5.3.3. Volume of Cones  5.3.4. Surface Area of Simple Solids
  6. Data Handling  6.1. Introduction to Data  6.1.1. Types of Data  6.1.2. Organizing Data  6.1.3. Frequency Distribution  6.2. Graphs and Charts  6.2.1. Bar Graphs  6.2.2. Line Graphs  6.2.3. Pictographs  6.2.4. Pie Charts  6.3. Mean, Median, and Mode  6.3.1. Calculating Mean  6.3.2. Finding Median  6.3.3. Identifying Mode  6.3.4. Range of Data in Mean, Median, and Mode
  7. Probability  7.1. Basics of Probability  7.1.1. Understanding Probability  7.1.2. Probability of Simple Events  7.1.3. Experimental and Theoretical Probability
  8. Practical Geometry  8.1. Construction of Shapes  8.1.1. Constructing Triangles  8.1.2. Constructing Quadrilaterals  8.1.3. Constructing Circles and Arcs  8.2. Symmetry  8.2.1. Line of Symmetry  8.2.2. Rotational Symmetry  8.2.3. Translational Symmetry

Grade 6 → Ratio and Proportion → Percentages ↓


Converting Ratios to Percentages


Understanding the relationship between ratios and percentages is an important concept in math. Ratios and percentages are two ways to express ratios. Ratios give the comparison of two quantities, while percentages express the ratio per 100. In this lesson, we will learn how to convert ratios to percentages through simple steps and examples. We will delve into detailed explanations by checking out various examples and exercises to ensure comprehensive understanding.

Understanding ratios

A ratio is a way of comparing two quantities. It tells us how much of one thing is compared to another. For example, if you have 2 apples and 3 oranges, you can express the ratio of apples and oranges like this:

2:3

This notation means that for every 3 oranges there are 2 apples.

Understanding percentages

A percentage is a fraction or ratio expressed as a fraction of 100. It is a way of expressing a number as part of a whole. For example, 50% means 50 out of 100 or half of the whole.

50% = 50/100 = 0.5

Now, let us learn how to convert a given ratio into a percentage.

Steps to convert ratio to percentage

  1. Write the ratio as a fraction: Start by writing the ratio as a fraction. For example, if we have a ratio of 3:4, we could write it as 3/4.
  2. Convert a fraction to a decimal: Find the decimal form of the fraction by dividing the numerator (top number) by the denominator (bottom number). For the fraction 3/4:
    3. 3 ÷ 4 = 0.75
  3. Convert a decimal to a percent: Multiply the decimal by 100 to get the percentage. For 3/4 (0.75) as a decimal:
    4. 0.75 × 100 = 75%

Detailed example 1

Convert the ratio 5:8 to a percentage.

  1. Write the ratio as a fraction: 5/8
  2. Convert fraction to decimal:
    3. 5 ÷ 8 = 0.625
  3. Convert decimal to percentage:
    4. 0.625 × 100 = 62.5%

The ratio 5:8 is equal to 62.5%.

Visual example

5/8 or 62.5% 8/8 or 100%

Detailed example 2

Now, let's convert the ratio 1:5 into a percentage.

  1. Write the ratio as a fraction: 1/5
  2. Convert fraction to decimal:
    3. 1 ÷ 5 = 0.2
  3. Convert decimal to percentage:
    4. 0.2 × 100 = 20%

The ratio 1:5 is equal to 20%.

How to interpret these calculations

Understanding how to convert ratios to percentages helps you understand data more effectively. For example, if a student scored 3 out of 5 on a quiz, you can express this as a percentage:

(3 ÷ 5) × 100 = 60%

This means that the student scored 60% on the quiz.

Conclusion

Converting ratios to percentages is a valuable skill that allows you to understand data comparisons more clearly. Whether dealing with scores, measurements or other ratios, knowing how to express them as percentages helps to understand their magnitude in terms of the whole. By practicing these conversions, you will become more confident in your mathematical abilities and be better prepared to tackle related problems in the future. Remember, the main steps are to convert the ratio to a fraction, divide to find the decimal and then multiply by 100 to find the percentage.

Practice these concepts with different ratios to get more comfortable with conversions and applications in real-world scenarios.


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Converting Ratios to Percentages

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