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 ↓


Types of Fractions


Fractions are an essential concept in math, and they represent a part of a whole. Understanding fractions can be a bit challenging initially, but once you get the hang of it, you'll find them quite useful! In this article, we'll explore the different types of fractions and provide examples to make the concepts easier to understand.

First, a fraction has two parts: the numerator and the denominator. The numerator is the top number, and it shows how many parts we have. The denominator is the bottom number, and it shows how many equal parts the whole is divided into. A simple representation of a fraction is shown below:

a - b
a - b

Here a is the numerator and b is the denominator. Now, let us discuss the different types of fractions in detail.

Proper fractions

A proper fraction is a fraction in which the numerator is smaller than the denominator. These fractions are often less than a whole because you have fewer parts than the number of parts that make up a whole.

For example:

1
2

This is one-half. Since 1 is smaller than 2, this is a proper fraction.

Let's look at another example:

3
4

This is three-fourths. We can represent this on the number line. Imagine a number line between 0 and 1:

-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|----- 0 1/4 2/4 3/4 1
-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|----- 0 1/4 2/4 3/4 1

As you can see, 3/4 is three parts of four, which lie between 0 and 1 on the number line.

Improper fractions

An improper fraction is a fraction in which the numerator is greater than or equal to the denominator. This means that you have more parts (or the same number of parts) than you need to make a whole. These fractions are greater than or equal to one.

For example:

5
3

This is five-thirds. We can look at it on the number line like this:

-----|-----|-----|-----|-----|-----|-----|-----|-----|----- 0 1 2 3 4 5
-----|-----|-----|-----|-----|-----|-----|-----|-----|----- 0 1 2 3 4 5

Note that five-thirds is more than one integer but less than two integers. In terms of numbers, 5/3 can be written as 1 2/3. This brings us to the next type of fraction.

Mixed fractions

Mixed fractions or mixed numbers consist of a whole number and a proper fraction. They are used to express improper fractions in another form.

For example, let's convert the improper fraction we mentioned earlier:

5/3 can be written as:

1 2/3

This fraction has 1 whole number and 2/3 is a proper fraction. This means you have a whole number and two-thirds more.

Let's look at another example of converting 9/4 into a mixed number:

9/4 = 2 1/4

You have two whole and one-fourth more.

Equivalent fractions

Equivalent fractions have the same value, even though they look different. You can find equivalent fractions by multiplying or dividing both the numerator and denominator by the same number (not zero).

For example, the fractions 1/2 and 2/4 are equal because:

1 * 2 = 2 -- 2 * 2 = 4
1 * 2 = 2 -- 2 * 2 = 4

Similarly, multiply 1/2 by 3:

1 * 3 = 3 -- 2 * 3 = 6
1 * 3 = 3 -- 2 * 3 = 6

Therefore, 1/2 is also equal to 3/6. You can verify this by dividing 2/4 and 3/6 by their greatest common divisor, 1/2.

Like and unlike fractions

Fractions can be classified into equal or unequal fractions depending on their denominators:

Like fractions

Like fractions are fractions that have the same denominator. Like fractions are easy to add or subtract because you only need to focus on the numerators.

For example, consider these fractions:

3
8
,
5
8

Since the denominators are the same, you can add them as follows:

3/8 + 5/8 = (3 + 5)/8 = 8/8 = 1

Unlike fractions

Fractions are fractions that have different denominators. Before you can add or subtract these fractions, you must find a common denominator.

Consider unequal fractions:

1
3
,
1
6

Find a common denominator to add these, such as 6:

1/3 + 1/6 = (2/6) + (1/6) = (2 + 1)/6 = 3/6 = 1/2

Unit fraction

A unit fraction is a fraction in which the numerator is 1 and the denominator is a positive integer. These types of fractions represent a part of a whole.

For example:

1
4
,
1
7

In these examples, each fraction represents a part of a divided whole, such as cutting a cake into 4 or 7 pieces and taking a piece of it.

Summary

Understanding fractions and their types is essential to mastering math concepts. Whether you encounter proper, improper, mixed, equivalent, equal, unequal, or unit fractions, the main idea is to look at these numbers as parts of a whole. With practice, you can become comfortable working with any type of fraction.

We hope that this journey into the world of fractions has been revelatory for you and that you now feel more confident solving problems involving fractions in maths!


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Types of Fractions

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