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3
So, the quantity of apples used is in a mixed fraction that is 1 kg and can be converted into an
4 1 2

improper fraction, and the quantities of maida, sugar and baking powder that are kg, kg and
3
2
1
2 tablespoon, respectively are proper fractions.
We can convert a mixed fraction into an improper fraction as:
( Wholepart× Denominator+ Numerator
)
Mixed fraction = = Improper fraction
Denominator
3 ( 47) + 3 28 3 31
×
+
For example, 4 = = =
7 7 7 7
Also, we can convert an improper fraction into a mixed fraction, by dividing the numerator of the
fraction with its denominator to get the quotient and the remainder. The quotient becomes the
whole part and the remainder becomes the numerator of desired mixed fraction with the same
denominator as given in the improper fraction.
Remainder
i.e., Mixed fraction = Quotient Divisor 5
17
For example, 17 3 –15
3 2
\ Quotient = 5 and remainder = 2
2
Thus, the required mixed fraction = 5
3
Example 1: Express the following mixed fractions as improper fractions or improper fractions
as mixed fractions.
2 12 25 2
(a) 4 (b) (c) (d) 14
3 5 3 9
2 432 12 2 14
×+
+
Solution: (a) 4 = = =
3 3 3 3 2
12 2
(b) = 2 5 12 i.e., Quotient = 2 and Remainder = 2
5 5 –10
2
25 1 8
(c) = 8 25 i.e., Quotient = 8 and Remainder = 1
3 3 3 –24
2 14 92 126 2 128 1
×+
+
(d) 14 = = =
9 9 9 9
Knowledge Desk

In sulba-sutra fractions were written in the same way as we do now, the numerator above the denominator,
but without the line between them. Both the numerator and the denominator were expressed in the decimal
place value system. When several fractions occured in the same problem, they were separated from each
other by a vertical and a horizontal line. When a mixed number has to be written the integer was given
2
3
above the fraction. So, 2 was written as 3 .
5
5

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