Fraction & Decimal Fraction
Question
Q1.
a/b + b/a = 1 a ≠ 0 , b ≠ 0, find a3 + b3
(a) 3 (b) 2 (c) 0
(d) 1
Solution.
a2 + b2 = ab
a2 + b2 - ab = 0
a3 + b3 =
(a + b)(a2 + b2 - ab) = 0
Solution
Q2.
A fraction becomes 4/7, when its denominator increased by 10% and numerator decreased by 10% respectively . find the original fraction.
(a) 61/78 (b) 1/3 (c) 44/81 (d) 4/9
Solution.
(90% of x)/(110% of y) = 4/7
90x/110y = 4/9
x/y = (4 x 110)/(9 x 90)
= 44/81
Solution
Q3.
Write 0.121212------- in the form of p/q.
(a) 4/33 (b) 2/33 (c) 1/33 (d) 2/99
Solution.
= 0.121212------
= 12/99
= 4/33
Solution
Q4.
Find the value of 0.123̅6̅
Solution.
(1236 - 12)/9900 = 102/825
Solution
Q5.
Which fraction is improper.
(a)12/7 (b)7/12 (c)3/5 (d)3/4
Solution.
Improper fraction is 12/7.
In improper fractions numerators are greater than or equal to denominator.
Solution
Q6.
(0.9 x 0.9 x 0.9 + 0.1 x 0.1 x 0.1) is equal to.
(a)0.73 (b)0.82 (c)0.91 (d)1.00
Solution.
(0.9)3 + (0.1)3
= 0.729 + 0.001
=0.73
Solution
Q7.
In the lowest form of a fraction, denominator and numerator are prime number to each other.
(a) Yes (b) No (c) Can't say
Solution.
(a) Yes
Solution
Q8.
Find the smallest fraction which when multiplied to 2/5 x 10/24 x 7/5 x 3/8 gives a whole number.
(a) 3/10 (b) 2/3
(c) 7/80 (d) 80/7
Solution.
(d) 80/7
Simplifying 2/5 x 10/24 x 7/5 x 3/8
= 2/12 x 21/40
= 7/(20 x 4) = 7/80
Solution
Q9.
The expression 34n - 52n has a factor
(a)60 (b)56 (c)18 (d)10
Solution.
Ans.56
As we known that xn - an is exactly divisible by x-a (when x is odd or even)
Solution
Q10.
The expresion 26n - 32n has a factor
(a)11 (b)9 (c)7 (d)6
Solution.
(23)2n - (3)2n = 82n - 32n
2n is an even integer {xn - an is
exactly divisible by x+a when n is even.}
Solution
