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


In everyday life, we often encounter percentages. Whether you're looking at shopping discounts, reading statistics in the news, or calculating your grades in school, percentages are everywhere. In this guide, we'll explore what percentages mean, how they relate to ratios and proportions, and how you can easily calculate them. By the end of this guide, you'll have a good understanding of percentages and be able to solve a variety of problems involving them.

What is the percentage?

A percentage is a way of expressing a number as a fraction of 100. It is represented by the "%" sign. For example, 50% means 50 out of 100, or simply 50/100. The word "percent" comes from the Latin percentum, meaning "from a hundred". This makes it a very useful tool for comparing different quantities, especially when working with hundred units.

Converting fractions to percentages

To convert a fraction to a percentage, you need to multiply the fraction by 100, and then add the percent sign "%". Let's look at an example:

Fraction: 3/4

To convert 3/4 to a percentage:

Percentage = (3/4) * 100 = 75%

This means that 3/4 is equal to 75%.

Converting decimals to percentages

Similarly, converting a decimal to a percentage involves multiplying the decimal value by 100 and then adding the "%" sign. Let's take an example of a decimal:

Decimal: 0.85

To convert 0.85 to a percentage:

Percentage = 0.85 * 100 = 85%

So 0.85 as a percentage is 85%.

Visual representation of percentages

Visual aids can help make percentages easier to understand. Consider a pie chart that shows a full circle divided into 100 equal parts. Each part represents 1% of the whole. For example, if we shade 30 of those parts, it represents 30% of the whole circle.

30%

Understanding ratio and proportion with percentages

Ratios compare two values, showing how much there is of one thing compared to another. For example, if you say the ratio of cats to dogs is 3:4, that means that for every 3 cats, there are 4 dogs. Percentages can also represent this ratio. To find the percentage that equals the part of the whole represented by the ratio, write the ratio as a fraction, and then convert the fraction to a percent.

Example:

Let the ratio of apples to total fruits be 3:8.

Fraction of apples = 3/8 Percentage of apples = (3/8) * 100 = 37.5%

This shows that the share of apples in total fruits is 37.5%.

Ratio and percentage

Ratios are statements that say that two ratios or fractions are equal. For example, if we have the ratio 1/2 = x/100, this means that 1 out of 2 is equal to x out of 100, or x percent. Solving for x gives us the equivalent percentage.

1/2 = x/100 => x = (1/2) * 100 => x = 50

So 1/2 = 50%.

Uses of percentages in real life

Percentages are often used to calculate discounts. If a $60 sweater is on sale for 25% off, you can determine the discount amount by calculating 25% of 60, then subtracting it from the original price.

Discount = 25% of $60 = (25/100) * $60 = $15 Selling price = $60 - $15 = $45

Thus, the price of the sweater after the discount will be $45.

Example problems

Let us work on some more examples to further strengthen our understanding.

Problem 1: Percentage of a number

Find 20% of 150.

20% of 150 = (20/100) * 150 = 30

So, 20% of 150 = 30.

Problem 2: Calculating percentages in reverse

If a student scores 84 marks out of a possible 120, what is his percentage mark?

Percentage = (84/120) * 100 = 70%

The student scored 70% marks.

Problem 3: Comparing percentages

Which is greater: 40% of 200 or 50% of 150?

40% of 200 = (40/100) * 200 = 80 50% of 150 = (50/100) * 150 = 75

40% (80) of 200 is greater than 50% (75) of 150.

Conclusion

Understanding percentages and their relationship to ratios and proportions is an essential skill that helps in a variety of everyday calculations. From calculating discounts to understanding statistics and comparing quantities, percentages make it easier to visualize and understand numerical relationships. We hope this guide has given you a clear understanding of percentages and equipped you with the skills to confidently handle complex percentage-based problems.


Grade 6 → 3.3


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Direct and Inverse Proportions
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Converting Ratios to Percentages

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Percentages

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