Fractions and Decimals: Breaking Down the Basics

Chapter 2 of the NCERT Grade 7 Maths textbook delves into the intricacies of fractions and decimals, enabling students to confidently navigate these fundamental mathematical concepts.

Introduction to Fractions

A fraction represents a part of a whole and is expressed as a ratio of two whole numbers.

• Numerator: The top part that denotes the number of parts considered.

• Denominator: The bottom part indicating the total number of equal parts into which the whole is divided.

Types of Fractions

1. Proper Fraction: The numerator is less than the denominator. (e.g., 3/4)

2. Improper Fraction: The numerator is greater than or equal to the denominator. (e.g., 7/3)

3. Mixed Fraction: A combination of a whole number and a proper fraction. (e.g., 2 1/3)

Introduction to Decimals

Decimals express numbers as fractions with denominators being powers of ten.

• Example: 0.75 is a decimal representation of the fraction 3/4.

Converting Fractions to Decimals

1. Divide the numerator by the denominator.

2. The quotient obtained will be the decimal representation.

Converting Decimals to Fractions

1. Write the decimal without the decimal point as the numerator.

2. The denominator will be a power of ten, depending on the number of decimal places.

Operations Involving Fractions and Decimals

Addition and Subtraction of Fractions

1. Like Fractions: Add or subtract the numerators and keep the denominator the same.

2. Unlike Fractions: First find a common denominator, then add or subtract the numerators.

Multiplication of Fractions

1. Multiply the numerators together for the new numerator.

2. Multiply the denominators together for the new denominator.

Division of Fractions

1. Flip (find the reciprocal of) the divisor fraction.

2. Multiply the dividend by the reciprocal of the divisor.

Addition and Subtraction of Decimals

1. Ensure the decimals are aligned.

2. Add or subtract as with whole numbers.

Multiplication of Decimals

1. Multiply as with whole numbers.

2. Count the total number of decimal places in both numbers and adjust in the product.

Division of Decimals

1. Move the decimal point in the divisor to make it a whole number.

2. Adjust the dividend accordingly and then divide.

Practical Applications of Fractions and Decimals

1. Budgeting: Allocating a fraction of your savings for various expenditures.

2. Cooking: Using fractional measurements for ingredients.

3. Shopping: Calculating discounts, which are often expressed as decimals.

4. Measurement: Lengths, weights, and heights often involve decimal numbers.

Mastering Fractions and Decimals with Practice

Engaging in regular exercises, solving word problems, and applying the concepts of fractions and decimals in day-to-day activities will enhance comprehension and retention. This chapter sets the stage for more complex mathematical constructs you’ll explore later.

Conclusion: Fraction and Decimals in the Mathematical Universe

Chapter 2 of the NCERT Grade 7 Maths textbook beautifully unravels the interplay between fractions and decimals. As foundational elements in the world of mathematics, understanding these concepts paves the way for advanced learning in later grades.

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