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

Introduction to Fractions and Decimals in Class 7

Fractions and decimals are two ways to represent numbers that are not whole. In Class 7 NCERT Mathematics, you learn how to work with these numbers to solve various problems.

• Fraction: A number expressed as $\frac{a}{b}$, where $a$ is the numerator and $b$ is the denominator (non-zero).
• Decimal: A number expressed with digits after a decimal point, representing parts of ten.

These concepts help you understand parts of objects, measurements, and quantities in daily life and exams.

Understanding Fractions: Definition and Types

A fraction represents a part of a whole or a collection. It consists of two parts:

• Numerator: The number of parts considered.
• Denominator: The total number of equal parts the whole is divided into.

Types of Fractions

Worked Example: Simplify $\frac{6}{8}$.

Divide numerator and denominator by 2:

$$\frac{6 \div 2}{8 \div 2} = \frac{3}{4}$$

So, $\frac{6}{8}$ simplifies to $\frac{3}{4}$.

Decimals: Place Value and Representation

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

• The place value to the right of the decimal point represents tenths, hundredths, thousandths, etc.

For example, in 12.345:

Decimals make it easier to perform arithmetic operations and understand precise measurements.

Worked Example: Write $\frac{7}{10}$ as a decimal.

Since denominator is 10, write 7 in the tenths place:

$$\frac{7}{10} = 0.7$$

Converting Between Fractions and Decimals

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

• To convert a fraction to a decimal, divide the numerator by the denominator.
• To convert a decimal to a fraction, write the decimal digits over the corresponding power of 10 and simplify.

Example 1: Convert $\frac{3}{4}$ to decimal.

$$3 \div 4 = 0.75$$

Example 2: Convert 0.6 to fraction.

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

Arithmetic Operations with Fractions and Decimals

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

Fractions

• Addition/Subtraction: Find LCM of denominators, convert fractions, then add/subtract numerators.
• Multiplication: Multiply numerators and denominators directly.
• Division: Multiply by the reciprocal of the divisor.

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

LCM of 3 and 4 is 12.

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

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

Decimals

• Align decimal points for addition and subtraction.
• Multiply as whole numbers, then place decimal point in the product.
• Divide by shifting decimal points to make divisor a whole number.

Example: Multiply 0.6 × 0.3

$$0.6 \times 0.3 = 0.18$$

Real-Life Applications of Fractions and Decimals

Fractions and decimals are used daily in many situations:

• Money: Rupees and paise use decimals for accurate transactions.
• Measurements: Length, weight, and volume often require fractional or decimal values.
• Cooking: Recipes use fractions to measure ingredients.
• Time: Hours and minutes can be expressed in decimals.

Understanding these concepts helps students solve practical problems and perform well in exams.