Class 3 Notes - Fractions

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Welcome to the chapter on Fractions. In this chapter, we will explore the concept of fractions, understand their types, and learn how to compare them. Let's begin our journey into the world of fractions!

What is a Fraction?

A fraction represents a part of a whole. It consists of two numbers separated by a horizontal line:

  • The number above the line is called the numerator.
  • The number below the line is called the denominator.

For example, in the fraction 1/2, 1 is the numerator, and 2 is the denominator. This fraction represents one part out of two equal parts of a whole.

Types of Fractions

Fractions can be categorized into three types:

1. Proper Fractions

A fraction where the numerator is less than the denominator is called a proper fraction. These fractions represent a part of a whole that is less than one.

Examples:

3/4, 2/5, 7/8

2. Improper Fractions

A fraction where the numerator is equal to or greater than the denominator is called an improper fraction. These fractions represent a value equal to or greater than one.

Examples:

5/4, 9/7, 6/6

3. Mixed Fractions

A mixed fraction combines a whole number and a proper fraction. It represents a value greater than one.

Examples:

1 1/2, 2 3/4, 3 2/5

Converting Mixed Fractions to Improper Fractions

To convert a mixed fraction to an improper fraction, follow these steps:

  1. Multiply the whole number by the denominator.
  2. Add the result to the numerator.
  3. Write the sum as the new numerator over the original denominator.

Example:

Convert 2 1/3 to an improper fraction.

Solution:

  1. Multiply the whole number by the denominator: 2 × 3 = 6
  2. Add the result to the numerator: 6 + 1 = 7
  3. Write the sum as the new numerator over the original denominator: 7/3

Converting Improper Fractions to Mixed Fractions

To convert an improper fraction to a mixed fraction, follow these steps:

  1. Divide the numerator by the denominator.
  2. The quotient becomes the whole number part.
  3. The remainder becomes the numerator of the proper fraction.
  4. The denominator remains the same.

Example:

Convert 7/3 to a mixed fraction.

Solution:

  1. Divide the numerator by the denominator: 7 ÷ 3 = 2 with a remainder of 1
  2. The quotient is 2 (whole number part).
  3. The remainder is 1 (numerator of the proper fraction).
  4. The denominator remains 3.

Thus, 7/3 = 2 1/3

Equivalent Fractions

Two fractions are said to be equivalent if they represent the same portion of a whole, even if they have different numerators and denominators.

Example:

1/2 is equivalent to 2/4 and 3/6 because they all represent the same portion of a whole.

Comparing Fractions

To compare fractions, we consider the denominators:

1. Like Fractions

Fractions with the same denominator are called like fractions. The fraction with the larger numerator is greater.

Example:

Compare 3/5 and 4/5

Since 4 > 3, 4/5 is greater.

2. Unlike Fractions

Fractions with different denominators are called unlike fractions. To compare them, we convert them to like fractions by finding a common denominator.

Example:

Compare 1/3 and 1/4.

Finding a common denominator (12), we get:

4/12 and 3/12.

Since 4 > 3, 1/3 is greater.

Adding and Subtracting Fractions

1. Like Fractions

When adding or subtracting like fractions, simply add or subtract the numerators while keeping the denominator the same.

Example:

2/7 + 3/7 = 5/7

2. Unlike Fractions

To add or subtract unlike fractions, first convert them to like fractions by finding a common denominator.

Example:

1/2 + 1/3

Common denominator = 6:

3/6 + 2/6 = 5/6

Fraction Word Problems

Example:

Riya ate 2/5 of a cake. Her friend ate 1/5. How much cake did they eat together?

Solution:

2/5 + 1/5 = 3/5

So, they ate 3/5 of the cake together.

Exercises

Practice Questions:

  1. Identify the numerator and denominator of 5/8.
  2. Convert 3 2/5 into an improper fraction.
  3. Find the equivalent fraction of 2/3 with denominator 9.
  4. Compare 4/7 and 3/7.
  5. Simplify: 7/10 - 3/10.
  6. Ravi has a chocolate bar and eats 3/8 of it. His sister eats 2/8. How much did they eat together?

Practice these problems to strengthen your understanding of fractions!