What is Fractions and Decimals Class 7: Complete Guide for Students

Understanding Fractions: Definition and Types

Fractions represent parts of a whole or a collection. A fraction has two parts:

• Numerator: The top number, showing how many parts are considered.
• Denominator: The bottom number, showing the total equal parts.

For example, in the fraction $\frac{3}{5}$, 3 is the numerator and 5 is the denominator.

Types of Fractions:

• Proper Fraction: Numerator < Denominator (e.g., $\frac{3}{4}$)
• Improper Fraction: Numerator ≥ Denominator (e.g., $\frac{7}{4}$)
• Mixed Fraction: Combination of a whole number and a proper fraction (e.g., $1 \frac{3}{4}$)
• Equivalent Fractions: Different fractions representing the same value (e.g., $\frac{1}{2} = \frac{2}{4}$)

Fractions are fundamental in expressing parts of quantities and are widely used in everyday life and mathematics.

Decimals Explained: What Are They and How Do They Work?

Decimals are another way to represent fractions, especially those with denominators as powers of 10 (like 10, 100, 1000).

A decimal number has two parts separated by a decimal point:

• Whole number part: Left of the decimal point.
• Decimal part: Right of the decimal point, representing fractional parts.

For example, 3.75 means 3 whole units and 75 hundredths.

Place Value in Decimals:

Decimals make calculations easier, especially with money, measurements, and scientific data.

Converting Between Fractions and Decimals

Converting fractions to decimals and vice versa is an important skill in Class 7 Maths.

Fraction to Decimal:

Divide the numerator by the denominator.

Example: Convert $\frac{3}{4}$ to decimal.

$$ 3 \div 4 = 0.75 $$

Decimal to Fraction:

Write the decimal as a fraction with denominator as a power of 10, then simplify.

Example: Convert 0.6 to fraction.

$$ 0.6 = \frac{6}{10} = \frac{3}{5} $$

These conversions help in comparing, adding, or subtracting numbers in different forms.

Performing Operations on Fractions and Decimals

Class 7 NCERT teaches how to add, subtract, multiply, and divide fractions and decimals.

Operations on Fractions:

• Addition/Subtraction: Find a common denominator first.
• Multiplication: Multiply numerators and denominators directly.
• Division: Multiply by the reciprocal of the divisor.

Example: Add $\frac{2}{3}$ and $\frac{1}{4}$

Find LCM of 3 and 4 = 12

$$ \frac{2}{3} = \frac{8}{12}, \quad \frac{1}{4} = \frac{3}{12} $$

$$ \frac{8}{12} + \frac{3}{12} = \frac{11}{12} $$

Operations on Decimals:

• Align decimal points.
• Add or subtract as whole numbers.
• Multiply normally; count decimal places in the result.
• Divide by moving decimal points to make divisor whole.

Example: Multiply 1.2 by 0.5

$$ 1.2 \times 0.5 = 0.6 $$

Mastering these operations is vital for solving real-life problems.

Comparing Fractions and Decimals: Which is Greater?

To compare fractions and decimals, convert them into the same form.

Tips for Comparison:

• Convert fractions to decimals by division.
• Or convert decimals to fractions and simplify.
• Compare decimals place by place.

Example: Compare $\frac{3}{5}$ and 0.6

$$ \frac{3}{5} = 0.6 $$

Both are equal.

This skill helps in ordering numbers and solving inequalities.

Real-Life Applications of Fractions and Decimals

Fractions and decimals appear in daily life and various subjects:

• Money: ₹1.25 means 1 rupee and 25 paise (decimal).
• Measurements: Lengths like 2.5 meters or $\frac{3}{4}$ kg.
• Cooking: Recipes use fractions for ingredients.
• Science: Data readings often require decimals.

Understanding these concepts helps you solve practical problems and prepares you for higher studies in mathematics.