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 → Number System → Fractions ↓


Equivalent Fractions


Understanding equivalent fractions may seem a bit tricky at first glance, but with simple analysis and examples you will find that they are easy to understand. Basically, equivalent fractions represent the same part of a whole, even though they look different.

What are the fractions?

Before we learn about equivalent fractions, let's briefly look at what fractions are. Fractions are a way of representing a part of a whole. Fractions have two numbers: the numerator and the denominator. The numerator is the top number, which shows how many parts we have. The denominator is the bottom number, which shows how many parts the whole is divided into.

Fraction = Numerator / Denominator

For example, the fraction 1/2 has a numerator of 1 and a denominator of 2. This fraction means a part of something that is divided into two equal parts.

Understanding equivalent fractions

Equivalent fractions are fractions that represent the same quantity. For example, 1/2, 2/4, and 4/8 are equivalent fractions. They all represent the same part of a whole.

Visual example

1/2 2/4 4/8

In the above figures, each fraction represents the same shaded area of a rectangle. 1/2 of the first rectangle is shaded, which is equal to 2/4 of the second rectangle and 4/8 of the third rectangle.

How to find equivalent fractions

You can find equivalent fractions by multiplying or dividing both the numerator and denominator by the same number. This process does not change the value of the fraction, it only changes its form.

Multiplying to get equivalent fractions

Suppose you have a fraction such as 1/3. You can multiply the numerator and denominator by the same number to find an equivalent fraction.

1/3 multiplied by 2:

New Numerator = 1 * 2 = 2 
New Denominator = 3 * 2 = 6 
New Fraction = 2/6

Thus, 2/6 is an equivalent fraction to 1/3.

Multiplying 1/3 by 3:

New Numerator = 1 * 3 = 3 
New Denominator = 3 * 3 = 9 
New Fraction = 3/9

Thus, 3/9 is another fraction similar to 1/3.

Dividing to get equivalent fractions

Sometimes, a given fraction is not in its simplest form, and you can find an equivalent fraction by dividing the numerator and denominator by the same number. Consider the fraction 6/9.

Dividing the fraction by 3:

New Numerator = 6 / 3 = 2 
New Denominator = 9 / 3 = 3 
New Fraction = 2/3

Thus, 2/3 is equal to 6/9.

Why do we need equivalent fractions?

Understanding equivalent fractions is essential because it helps us simplify numerical problems and equations involving fractions. This allows us to work better with fractions when adding, subtracting, multiplying, and dividing. Simplification makes numbers easier to handle and understand, ensuring accurate calculations and reasoning.

Applications in real life

Equivalent fractions are often used in everyday life. For example, cooking often requires equivalent fractions when adjusting recipes. If a recipe calls for 1/2 cup of sugar, but you only have a one-quarter measuring cup, you will need two 1/4 cups to make 1/2 cup.

Another example of dividing time can be found, like converting 1 hour into minutes. Knowing that 30/60 means 1/2 helps in managing time calculations better.

Practice problems

Let's reinforce what we've learned with some practice problems.

Problem 1

Are the fractions 3/9 and 1/3 the same? Show your work.

Solution: Divide the numerator and the denominator of 3/9 by 3. 
New Numerator = 3 / 3 = 1 
New Denominator = 9 / 3 = 3 
New Fraction = 1/3 
Therefore, 3/9 and 1/3 are equivalent fractions.

Problem 2

Find the equivalent fraction of 2/5 by multiplying both the numerator and denominator by 4.

Solution: Multiply the numerator and denominator by 4. 
New Numerator = 2 * 4 = 8 
New Denominator = 5 * 4 = 20 
New Fraction = 8/20 
Therefore, 8/20 is equivalent to 2/5.

Conclusion

Equivalent fractions are a fundamental concept that helps make many aspects of math much simpler. Understanding how to find and use equivalent fractions is not only useful for academics, but is also a practical skill applicable to various aspects of daily life. Practice constantly to get comfortable converting fractions into equivalent forms, and you will find that many mathematical operations are more intuitive and straightforward.


Grade 6 → 1.3.2


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Types of Fractions
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Equivalent Fractions

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