Complete Guide For Class 7 Math Chapter 2 Fractions and Decimals

Welcome to iPrep, your Learning Super App. Our learning resources for the chapter, Fractions, and Decimals in Mathematics for Class 7th are designed to ensure you grasp this concept with clarity and perfection. Whether you’re studying for an upcoming exam or strengthening your concepts, our engaging animated videos, practice questions and notes offer you the best of integrated learning with interesting explanations and examples. 

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

1. Multiplication of a Fraction by a Whole Number 
2. 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

1. Division of a Whole Number by a Fraction 
2. Division of a Fraction by a Whole Number
3. 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

1. Multiplication of Decimal Numbers by another Decimal Number
2. 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

1. Division of a Decimal by a Whole Number
2. Division of a Decimal Number by another Decimal Number
3. 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