# Complete Guide For Class 7 Math Chapter 2 Fractions and Decimals

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The chapter on Fractions and Decimals is designed to build a strong foundational understanding of fractions and decimals, including their properties and operations. This knowledge is not only crucial in mathematics but also plays a significant role in real-world applications, such as measurement, financial literacy, and understanding ratios and proportions. This chapter aims to provide students with a comprehensive understanding of fractions and decimals, their properties, representations, and operations, thereby equipping them with the necessary skills for more advanced mathematical topics.

**Fractions & Decimals**

**Let’s understand Fractions**:

**Basic Definitions**

**Proper Fractions:**A “proper fraction” represents a part of a whole, where the numerator is less than the denominator.**Improper Fractions:**An “improper fraction” is a combination of a whole number and a proper fraction. In an improper fraction, the numerator is equal to or greater than the denominator.

**Mixed Fractions**: A “mixed fraction” contains a whole number and a proper fraction. An improper fraction can be represented as a mixed fraction.

### Examples

- Proper Fraction: 3/4
- Improper Fraction: 5/4
- Mixed Fraction: 8¹/₇

**Let’s understand the Addition and Subtraction of Fractions**

**Addition of Fractions with the same denominators**

**Key Points**:

- Ensure the denominators are the same.
- Add the numerators and place the result over the common denominator.
- Simplify the fraction if needed.

Example: 2/5 + 3/8 = 2+⅗ = 5/5 = 1

**Subtraction of Fractions with the same denominators**

**Key Points**:

- Ensure the denominators are the same.
- Subtract the numerators and place the result over the common denominator.
- Simplify the fraction if needed.

Example: 3/4 – 1/4 = 3 – 1/4 = 2/4 = 1/2

**Addition of Fractions with different denominators**

**Key Points**:

- The bottom numbers are different. So we need to make them the same.
- Add the top numbers and put them over the same.
- Simplify the fraction.

Example: 2/5 + 3/25 = 10+3 /25 = 13/25

**Subtraction of Fractions with different denominators**

**Key Points**:

- The bottom numbers are different. So we need to make them the same.
- Subtract the top numbers and put them over the same denominator.
- Place the sign of the greater number.
- Simplify the fraction.

Example: 2/5 + 3/25 = 10+3 /25 = 13/25

**Now Let’s understand Multiplication and Division of Fractions**.

## **Multiplication of Fractions**

- Multiplication of a Fraction by a Whole Number
- Multiplication of a Fraction by a Fraction

**Basic Rules of Multiplication of Fractions**

- Multiply the numerators.
- Multiply the denominators.
- Simplify the result.

Examples:

- 2 x 1/4 = 2/4 = 1/2
- 2/3 x 3/4 = 6/12 =1/2

**Division of Fractions**

- Division of a Whole Number by a Fraction
- Division of a Fraction by a Whole Number
- Division of a Fraction by another Fraction

**Basic Rules of Division of Fractions**

- Invert (flip) the second fraction.
- Multiply the fractions.
- Simplify the result.

Examples:

- 1 ÷ 1/2 = 1 x 2/1 = 2
- 1/2 ÷ 2 = 1/2 x 2/1 = 1
- 1/2 ÷ 3/4 = 1/2 x 4/3 = 4/6 = 2/3

**Decimal Numbers**

Decimals represent numbers that are not whole, using a decimal point to separate the whole number part from the fractional part. Example: Whole number: 5, Decimal: 5.75

**Multiplication of Decimal Numbers**

- Multiplication of Decimal Numbers by another Decimal Number
- Multiplication of Decimal Numbers by 10,100,1000

**Key Points**:

- Ignore the decimal points and multiply the numbers as if they were whole numbers.
- Count the total number of decimal places in both numbers.
- Place the decimal point in the result so it has the same number of decimal places.

Examples:

- 0.6 × 0.7 = 0.42
- 0.5 x 10 = 5/10 x 10 = 5

**Division of Decimal Numbers**

- Division of a Decimal by a Whole Number
- Division of a Decimal Number by another Decimal Number
- Division by 10, 100 and 1000

**Key Points:**

- Move the decimal point in the divisor to the right until it is a whole number.
- Move the decimal point in the dividend the same number of places to the right.
- Divide the new numbers.

Examples:

- 0.5 ÷ 2 = 5/10 x 2 = 1
- 0.8 ÷ 0.2 = 4

**When dividing by 10, 100, or 1000, shift the decimal point to the left by the number of zeros in the divisor.**

Example:0.593 ÷ 100 = 0.00593

### Practice questions on Chapter 2 - Fractions and Decimals

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