Page 65 - classs 6 a_Neat

1 2 5 9
3 3 12 3 9 EXAMPLE 8: 2 ,3 ,4 ,5 , etc., are all mixed fractions.
Short Method of 12 = [ × ] = = 9. 3 5 7 11
4 4 1 1
1
5 TO CONVERT A MIXED FRACTION INTO AN IMPROPER FRACTION
EXAMPLE 3: Find 8 of 32.

5 5 32 4 20 A mixed fraction = A whole number + Afraction.
SOLUTION: of 32 = [ × ] = = 20.
8 8 1 1 3 3 (2 × 5) + 3 13 4 4 (3 × 7) + 4 25

1 EXAMPLE 9: (i) 2 = 2 + = = (ii) 3 = 3 + = =
5 5 5 5 7 7 7 7
RULE: Multiply the whole number with the denominator of the fraction and to this product add the numerator
EXAMPLE 4: What fractton of a day ts 8 hours? of the fraction. This gives the numerator of the required improper fraction. Its denominator is the same as the
SOLUTION: We know that 1 day = 24 hours. denominator of the fractional part.

8 TO CONVERT AN IMPROPER FRACTION INTO A MIXED FRACTION
the required fraction =
24

EXAMPLE 10: Convert 29 into a mixed fraction.
EXAMPLE 5: What fraction of an hour ts 40 minutes? 8
On dividing 29 by 8, we get quotient = 3 and remainder = 5.
SOLUTION: We know that 1 hour = 60 minutes. 29 5 5 3

8 = 3 + 8 = 3 8 = 3 8
40
the required fraction = .
60 38 2 2
Similarly, = 4 + = 4
1 9 9 9
EXAMPLE 6: In the givenfigure, if we say that the shaded region is of the whole, then what ts TO REPRESENT MIXED FRACTIONS ON NUMBER LINE
the error in it? 2
SOLUTION: In the given figure, the shaded region is not equal to the unshaded region. o C
EXAMPLE 11: Represent 2 2 on the number line. A B P
1 5 0 1 2 2 2 3
shaded region is not equal to of the whole. SOLUTION: Let OA = AB = BC = 1 unit. 5
2
Then, clearly, OB = 2 units and OC = 3 units.
Divide BC into 5 equal parts and take 2 parts out of them to reach the point P.
PROPER, IMPROPER AND MIXED FRACTIONS
2
Clearly, P represents the number 2 •
PROPER FRACTIONS A fraction whose numerator is less than its denominator is called a proper fraction. 5

2 5 7 0 8 SOLVED EXAMPLES
EXAMPLE 7: , , , , etc., are all proper fractions.
5 8 11 4 15
Note: Each proper fraction is less than 1. EXAMPLE 12: Write six improper fractions with denominator 7.

SOLUTION: Clearly, 8 9 10 11 12 13 are all improper fractions,
IMPROPER FRACTIONS A fraction whose numerator is greater than or equal to its denominator is called an each with denominator 7. 7 , 7 , 7 , 7 , 7 , 7
improper fraction.

5 7 8 10 11 25
Thus , , , , , etc., are all improper fractions. EXAMPLE 13: Write six improper fractions with numerator 11.
4 3 5 10 6 9 11 11 11 11 11 11 11
SOLUTION: Clearly, , , , , , , are all improper fractions
MIXED FRACTIONS A combination of a whole number and a proper fraction is called a mixed fraction. with numerator 11. 2 3 3 4 5 6 7