Class 7 Maths Fractions and Decimals Notes

Introduction:
The chapter “Fractions and Decimals” in Class 7 Maths focuses on understanding two important concepts in mathematics: fractions and decimals. Both of these represent parts of a whole, but in different ways. Understanding how to work with fractions and decimals is crucial for many real-life situations, such as shopping, measuring, and working with data. This chapter will teach you how to perform operations with fractions and decimals, convert between them, and apply these concepts in practical problems.

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Key Concepts Covered:

1. What is a Fraction?

• A fraction represents a part of a whole or a division of a quantity. It consists of two numbers:
  • Numerator: The number above the fraction bar, which indicates the number of parts we have.
  • Denominator: The number below the fraction bar, which indicates the total number of equal parts the whole is divided into.

Examples:

• $\frac{3}{4}$43​ (Three out of four parts)
• $\frac{5}{8}$85​ (Five out of eight parts)

2. Types of Fractions:

• Proper Fraction: A fraction where the numerator is smaller than the denominator (e.g., $\frac{3}{5}$53​).
• Improper Fraction: A fraction where the numerator is equal to or greater than the denominator (e.g., $\frac{7}{4}$47​).
• Mixed Fraction: A combination of a whole number and a proper fraction (e.g., $2 \frac{1}{4}$241​).

3. Fraction Operations:

• Addition of Fractions:
  • To add fractions with the same denominator, simply add the numerators and keep the denominator the same.
  • To add fractions with different denominators, find a common denominator, then add the numerators.
  Example: $$\frac{1}{4} + \frac{2}{4} = \frac{3}{4}$$41​+42​=43​ or $$\frac{1}{3} + \frac{1}{6} = \frac{2}{6} + \frac{1}{6} = \frac{3}{6} = \frac{1}{2}$$31​+61​=62​+61​=63​=21​
• Subtraction of Fractions:
  • Similar to addition, subtract the numerators while keeping the denominator the same for fractions with the same denominator.
  • For fractions with different denominators, find a common denominator before subtracting.
  Example: $$\frac{3}{4} – \frac{1}{4} = \frac{2}{4} = \frac{1}{2}$$43​−41​=42​=21​
• Multiplication of Fractions:
  • Multiply the numerators and the denominators separately.
  Example: $$\frac{2}{3} \times \frac{4}{5} = \frac{8}{15}$$32​×54​=158​
• Division of Fractions:
  • To divide by a fraction, multiply by its reciprocal (the fraction flipped upside down).
  Example: $$\frac{2}{3} \div \frac{4}{5} = \frac{2}{3} \times \frac{5}{4} = \frac{10}{12} = \frac{5}{6}$$32​÷54​=32​×45​=1210​=65​

4. What are Decimals?

• A decimal is another way of representing fractions, especially those with denominators that are powers of 10. Decimals are written with a decimal point, which separates the whole number part from the fractional part.

Example:

• $0.5$0.5 is equivalent to $\frac{5}{10}$105​.
• $0.75$0.75 is equivalent to $\frac{75}{100}$10075​.

5. Types of Decimals:

• Terminating Decimals: Decimals that have a finite number of digits after the decimal point. For example, $0.25$0.25 or $0.75$0.75.
• Non-Terminating Decimals: Decimals that have an infinite number of digits after the decimal point. Some non-terminating decimals are repeating, such as $0.3333…$0.3333…, which can be written as $\frac{1}{3}$31​.

6. Converting Between Fractions and Decimals:

• Converting a Fraction to a Decimal:
  • Divide the numerator by the denominator.
  Example: $$\frac{3}{4} = 3 \div 4 = 0.75$$43​=3÷4=0.75
• Converting a Decimal to a Fraction:
  • Write the decimal as a fraction with a denominator based on the number of decimal places.
  • Simplify the fraction if necessary.
  Example: $$0.6 = \frac{6}{10} = \frac{3}{5}$$0.6=106​=53​

7. Operations with Decimals:

• Addition and Subtraction of Decimals:
  • Line up the decimal points and then perform the addition or subtraction as with whole numbers.
  Example: $$1.2 + 3.45 = 4.65$$1.2+3.45=4.65
• Multiplication of Decimals:
  • Multiply the numbers as if they are whole numbers, then count the total number of decimal places in both factors and place the decimal point accordingly.
  Example: $$0.6 \times 0.5 = 0.30$$0.6×0.5=0.30
• Division of Decimals:
  • Move the decimal point to make the divisor a whole number, then divide as you would with whole numbers.
  Example: $$6.4 \div 2 = 3.2$$6.4÷2=3.2

8. Real-Life Applications of Fractions and Decimals:

• Fractions are often used in situations involving parts of a whole, such as recipes, sharing resources, and measuring distances or areas.
• Decimals are commonly used in money, measurements, and data analysis, where precision is required.

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Important Questions with Answers:

1. What is a fraction?
   • Answer: A fraction represents a part of a whole and consists of a numerator (top number) and a denominator (bottom number).
2. How do you convert a fraction to a decimal?
   • Answer: To convert a fraction to a decimal, divide the numerator by the denominator.
3. What is the difference between a terminating and a non-terminating decimal?
   • Answer: A terminating decimal has a finite number of digits after the decimal point (e.g., 0.25), while a non-terminating decimal has an infinite number of digits (e.g., 0.3333…).
4. How do you add fractions with different denominators?
   • Answer: To add fractions with different denominators, find the LCM (Least Common Multiple) of the denominators, convert the fractions to have the same denominator, and then add the numerators.
5. How do you multiply fractions?
   • Answer: To multiply fractions, multiply the numerators and the denominators separately.
6. How do you divide fractions?
   • Answer: To divide by a fraction, multiply by its reciprocal (flip the second fraction upside down).
7. How do you convert a decimal to a fraction?
   • Answer: Write the decimal as a fraction with a denominator based on the number of decimal places, then simplify the fraction.
8. What are the uses of fractions and decimals in daily life?
   • Answer: Fractions and decimals are used in daily life for tasks like cooking, shopping, measuring distances, and handling money.