Page 105 - Maths Class 06

Changing an Improper Fractions into a Mixed Fractions
You can change an improper fraction into a mixed fraction by dividing the numerator by the
denominator. The result obtained is expressed as
Remainder Remainder
Quotient + or Quotient
Divisor Divisor
Following an example of conversion of an improper fraction into a mixed fraction.
23 5 5
= 3 + or 3
6 6 6
EX AM PLE 1. Express the fol low ing as mixed frac tion:
17 23
(a) (b)
4 5
4 4
17 1 23 3
SOLUTION : (a) = 4 4 17 (b) = 4 5 23
4 4 5 5
- 16 - 20
1 3

Changing a Mixed Fractions into an Improper Fractions
To convert a mixed fraction into an improper fraction, first you multiply the whole number with the
denominator. Then, to the result obtained, you add numerator. What you get is the numerator of the
improper fraction. The denominator will be the same as that of the mixed fraction. This conversion
procedure can be described as:
(Whole number Denominator´ ) + Numerator
Denominator
EX AM PLE 2. Ex press the fol low ing as im proper frac tions:
2 1
(a) 6 (b) 3
5 4
2 6 ´ +5 2 32 1 3 ´ +4 1 13
SO LU TION : (a) 6 = = (b) 3 = =
5 5 5 4 4 4

NOTE

Proper fractions lie to the left of 1 as they are less than 1.
remainder
An improper fraction can be expressed as a mixed fraction as quotient ————— .
divisor
whole × denominator + numerator
A mixed fraction can be expressed as an improper fraction as ———————————————— .
denominator

Equivalent Fractions

The equivalent fractions are the two fractions having the same value. Equivalent fraction is obtained on
multiplying the numerator and denominator of the given fraction by the same number, e g. ., Let us find
1
the fractions equal to .
2

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