Page 27 - ICSE Math 7

2 Fractions

Key Concepts

• Fractions • Reciprocal of a Fraction
• Classification of Fractions • Fraction as an Operator
• Reducing a Fraction to Its Simplest Form • Continued Fraction
• Like and Unlike Fractions • Simplification of Complex Fractions
• Comparison of Fractions • Simplification of an Expression
• Inserting a Fraction between Two Fractions • Word Problems
• Fundamental Operations on Fractions

Fractions
m
A fraction represents a part of a whole. It is represented by , where m and n are
n
m
whole numbers and n ≠ 0. The fraction represents m parts out of n equal parts.
n
m
In a fraction , m is called the numerator and n is called the denominator. For
n
example, if a circle is divided into 4 equal parts, then each part is one-fourth of
1
the whole circle and each part is represented by the fraction .
4
Classification of fractions
Proper fraction
A fraction whose numerator is less than its denominator is known as a proper fraction. For example,

1 17 and 35 are proper fractions.
,
2 19 36
Improper fraction

A fraction whose numerator is greater than or equal to its denominator is known as an improper
8
fraction. For example, , 11 and 17 are improper fractions.
7 10 14
Mixed fraction

A fraction which consists of a whole number and a proper fraction is known as a mixed fraction.
1
7
For example, 2 , 3 and 2 11 are mixed fractions.
4 8 17
Any mixed fraction can be converted into improper fraction by using the formula:

Numerator (Whole part × Denominator) + Numerator
Mixed fraction = Whole part + =
Denominator Denominator

Also, an improper fraction can be converted into a mixed fraction by using the formula:
Remainder
Improper fraction = Quotient Denominator

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