Page 199 - Ganit Kaushal

Some mixed fractions are shown below on the number line.

1  9 3  27 3  38 3  35
2  =  3  =  7  =  8  = 
4  4  8  8  5  5  4  4 

0 1 2 3 4 5 6 7 8 9 10

Algorithm to Convert a Mixed Fraction into an Improper Fraction

Step 1: Multiply the whole number part by the denominator and add it to the numerator.

Step 2: Write the improper fraction with the numerator as the number obtained above, keeping the denominator
unchanged.
The above two steps can be remembered by a single formula given below.

(Whole Number × Denominator) + Numerator
Improper fraction =
no
De minator
+
3 27×+ 3 14 3 17
For example: (i) 2 = = = , which is an improper fraction.
7 7 7 7
×+
1 39 1 28
(ii) 3 = = , which is an improper fraction.
9 9 9
Algorithm to Convert an Improper Fraction into a Mixed Fraction

Step 1: Divide the numerator by the denominator, and obtain the quotient and remainder.
Step 2: Write the mixed fraction with the quotient as the whole number, remainder as the numerator and keep
the denominator the same.
The above two steps can be remembered by a single formula given below.

Remainder
Mixed fraction = Quotient De minator
no

For example: (i) 17 = 3 2 [ Quotient = 3 and remainder = 2, when 17 is divided by 5]
5 5
48 6 113 3
(ii) = 6 and = 11 , etc.
7 7 10 10
| To display improper fractions on the number line, it is always preferable to convert them to mixed
form first. Some improper fractions are shown below on the number line

0 1 2 3 4 5 6 7 8 9 10
14 4 27 3
= 2 = 6
5 5 4 4
Lowest (Simplest) Form of a Fraction

The lowest or simplest form of a fraction is the one in which the numerator and the denominator have no
common factor other than 1. In other words, the numerator and denominator are co-prime, i.e., the HCF of the
numerator and denominator is 1.

Fractions 197