Fraction: RD Sharma Solutions - Ex-1.2 Integers, Class 7, Math

A fraction is a mathematical representation of a part of a whole. It is a way of expressing a division or ratio between two numbers. In a fraction, there are two parts: the numerator and the denominator. The numerator is the number on top of the fraction, and the denominator is the number below the fraction line.

Representation and Interpretation:
Fractions can be represented in various forms, such as:

1. Proper Fraction: A proper fraction is a fraction where the numerator is less than the denominator. For example, 2/5, 3/7, etc.

2. Improper Fraction: An improper fraction is a fraction where the numerator is greater than or equal to the denominator. For example, 7/4, 5/3, etc.

3. Mixed Fraction: A mixed fraction is a whole number combined with a proper fraction. For example, 2 1/3, 3 4/5, etc.

Equivalent Fractions:
Equivalent fractions are fractions that have the same value but are represented differently. To find equivalent fractions, you can multiply or divide both the numerator and denominator by the same non-zero number. For example, 2/4 and 1/2 are equivalent fractions.

Operations on Fractions:
There are several operations that can be performed on fractions, including:

1. Addition and Subtraction: To add or subtract fractions, you need to have a common denominator. If the denominators are different, you need to find the least common multiple (LCM) and convert the fractions to have the same denominator.

2. Multiplication: To multiply fractions, simply multiply the numerators together and the denominators together. The resulting fraction may need to be simplified.

3. Division: To divide fractions, multiply the first fraction by the reciprocal of the second fraction. The reciprocal is obtained by swapping the numerator and denominator of the second fraction.

Simplifying Fractions:
To simplify a fraction, you need to find the greatest common divisor (GCD) of the numerator and denominator and divide both by it. This will reduce the fraction to its simplest form. For example, 4/8 can be simplified to 1/2 by dividing both the numerator and denominator by 4.

Conclusion:
Fractions are an important concept in mathematics that represent a part of a whole. They can be represented in different forms and can be operated upon using various mathematical operations. Understanding fractions is crucial as they are used in many real-life situations, such as cooking, measurements, and financial calculations.

Fractions are numbers representing part of a whole. A fraction is a number of the form p/q, such that q is not equal to zero or one. A fraction has two parts. The number on the top is numerator and the number below is the denominator.