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Converting an Improper Fraction Into a Mixed Fraction

To convert an improper fraction into a mixed fraction, we follow the following steps:
Step 1: Divide the numerator with the denominator to get the quotient and the remainder.

Step 2: Retain the denominator.

Step 3: The quotient becomes the whole number part and the remainder becomes the numerator
of the fractional part of the mixed fraction.
Numerator Remainder
Improper fraction = = Quotient = Mixed frraction
Denominator Denominator
4 Quotient
17 1 Denominator 4 17 Numerator
For example, = 4 . (Divisor) 16 (Dividend)
4 4 1 Remainder

Example 4: Express the following into mixed fractions:
29 78
(a) (b) 7
4 5 29
Solution: (a) On dividing 29 by 4, we get 7 as a quotient and 1 as a remainder. ) 4 − 28

1 1
Thus, the required mixed fraction = 7 .
4
(b) On dividing 78 by 5, we get 15 as quotient and 3 as a remainder. 15
3 ) 578
Thus, the mixed fraction = 15 − 5
5 28
7 − 25
Example 5: Represent the fraction on the number line. 3
4
7 3
Solution: As = 1 , divide the distance between 1 and 2 into 4 equal parts and insert a dot on
4 4
the 3rd mark counting from 1.

0 1 2 3 4 5
7
4
3 7 7
This point represents the fraction 1 or , and the length of the line segment drawn above is
units. 4 4 4

Converting a Mixed Fraction Into an Improper Fraction

To convert a mixed fraction into an improper fraction we follow the following steps:
Step 1: Retain the denominator of the fraction.

Step 2: Multiply the integral part (natural number) with the denominator of the given fraction.
Step 3: Add the numerator to this product, as obtained in step 2.
Step 4: Take the sum as the numerator of the new fraction.

(Whole number × Denominator) + Numerator
Mixed fraction = = Impropper fraction
Denominator
3 ( 27 +) 3 14 3 17
×
+
For example, 2 = = =
7 7 7 7
211 Fractions