Chapter 2 - Fractions - R D Sharma Solutions for Class 7

Let us define some terms to understand the concept of fractions

Fraction: A fraction is a number indicating a part of a whole. A fraction is in the form of ab where ‘a’ is numerator and ‘b’ is denominator. For example: 23 is a fraction with numerator ‘2’ and denominator ‘3’.

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Types of fractions

(1) Proper fraction: Those fractions in which numerator is less than the denominator. For example: 45,57 etc.

(2) Improper fraction: Those fractions in which numerator is more than or equal to the denominator. For example: 73,197 etc.

(3) Mixed fraction: It is a combination of a whole number and a proper fraction. For example: 214, 523 etc. For conversion of mixed fraction into an improper fraction, we follow one formula:

Improper fraction = whole number×denominator+numeratordenominator

(4) Equivalent fraction: Those fractions which does not look similar but results in same number after dividing or multiplying by the same non-zero number. For example: 510 and36 are the equivalent fractions. After simplification, both results in 12

If ab andcd are two equivalent fractions, then

ab=cd => a×d=c×b

(5) Like fraction: Those fraction which are having same denominators. For example: 17,37,57 etc.

(6) Unlike fraction: Those fractions which are having different denominators. For example: 117,419 etc.

(7) Fraction in lowest terms: Reduce the fraction in its lowest term until numerator and denominator have no common factor other than 1.

(8) Comparing fractions: There are some steps for comparing fractions

Step1: Find LCM of the denominators of the given fractions.

Step2: Convert each fraction to its equivalent fraction with denominator equal to the LCM obtained.

Step3: Arrange the fractions in ascending or descending order by arranging their numerators in ascending order.