Class 7 Notes - Fractions and Decimals

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Fractions and Decimals

In this chapter, students will deepen their understanding of fractions and decimals, learn how to perform operations with them, and apply these concepts to real-life situations.

1. Introduction to Fractions

  • A fraction represents a part of a whole.
  • It is written as a/b, where a is the numerator and b is the denominator.
  • Examples: 1/2, 3/4, 7/8

2. Types of Fractions

  • Proper Fractions: Numerator is less than denominator (e.g., 3/5).
  • Improper Fractions: Numerator is greater than or equal to denominator (e.g., 7/4).
  • Mixed Fractions: Combination of a whole number and a proper fraction (e.g., 2 1/3).
  • Like Fractions: Fractions with the same denominator.
  • Unlike Fractions: Fractions with different denominators.
  • Equivalent Fractions: Fractions that represent the same value (e.g., 1/2 = 2/4).

3. Operations with Fractions

  • Addition and Subtraction: Like fractions can be added/subtracted directly. Unlike fractions need to be converted to like fractions first.
  • Multiplication: Multiply numerators and denominators.
  • Division: Invert the second fraction and multiply.
Example: 2/3 + 1/6 = 4/6 + 1/6 = 5/6

4. Introduction to Decimals

  • Decimals are another way to represent fractions, especially those with denominators of 10, 100, 1000, etc.
  • Decimal point separates the whole number part from the fractional part.
  • Examples: 0.5, 2.75, 3.06

5. Place Value in Decimals

  • Tenths (0.1), Hundredths (0.01), Thousandths (0.001), etc.
  • Example: In 3.47, 3 is the whole number, 4 is tenths, 7 is hundredths.

6. Operations with Decimals

  • Addition and Subtraction: Line up the decimal points before performing the operation.
  • Multiplication: Multiply as whole numbers, then place the decimal point in the product.
  • Division: Move the decimal point to make the divisor a whole number, then divide.
Example: 0.6 + 0.25 = 0.85

7. Converting Between Fractions and Decimals

  • To convert a fraction to a decimal, divide the numerator by the denominator.
  • To convert a decimal to a fraction, write it as a fraction with denominator 10, 100, etc., and simplify.
  • Example: 3/4 = 0.75; 0.2 = 2/10 = 1/5

8. Comparing and Ordering Fractions and Decimals

  • Convert to like fractions or decimals to compare.
  • Arrange in ascending or descending order as required.

9. Applications in Real Life

  • Money (₹2.50, ₹0.75)
  • Measurements (1.5 meters, 0.25 liters)
  • Shopping, recipes, and more

10. Common Mistakes

  • Not aligning decimal points in addition/subtraction.
  • Forgetting to convert unlike fractions before adding/subtracting.
  • Misplacing the decimal point in multiplication/division.

11. Practice Exercises

  1. Add: 3/8 + 1/8
  2. Subtract: 0.9 - 0.45
  3. Multiply: 2/5 × 3/4
  4. Convert 0.6 to a fraction.
  5. Arrange in ascending order: 0.7, 3/4, 0.65

12. Summary

  • Fractions and decimals are ways to represent parts of a whole.
  • Learn to convert, compare, and perform operations with them.
  • They are used in daily life for money, measurement, and more.