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

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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

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