Mark against the correct answer in each of the following:
Q1 ) A fraction equivalent to \(\frac{ 3 }{ 5 }\) is
(a) \(\frac{3 + 2}{5 + 2}\)
(b) \(\frac{3 -2}{5 – 2}\)
(c) \(\frac{3 \times 2}{5 \times 2}\)
(d) none of these
Ans. 1) (c) \(\frac{3 \times 2}{5 \times 2}\)
Q2) A fraction equivalent to \(\frac{ 8 }{ 2 }\) is
(a) \(\frac{ 8 + 4 }{ 12 + 4 }\)
(b) \(\frac{ 8 -4 }{ 12 – 4 }\)
(c) \(\frac{ 8 \div 4 }{ 12 \div 4 }\)
(d) none of these
Ans. 2) (c) \(\frac{ 8 \div 4 }{ 12 \div 4 }\)
Q3) A fraction equivalent to \(\frac{ 24 }{ 36 }\)
(a) \(\frac{ 3 }{ 4 }\)
(b) \(\frac{ 2 }{ 3 }\)
(c) \(\frac{ 8 }{ 9 }\)
(d) none of these
Ans. 3) (b) \(\frac{ 2 }{ 3 }\)
Factors of 24 are 1 , 2 , 3 , 4 , 6 , 8 , 12 , 24 .
Factors of 36 are 1 , 2 , 3, 4 , 6 , 9 , 12 , 18 , 36.
Common Factors of 24 and 36 are 1 , 2 , 3, 4 , 6 , 12.
H.C.F. = 12
Dividing both the numerator and the denominator by 12 :
\(\frac{ 24 }{ 36 }\)
= \(\frac{ 24 \div 12 }{ 36 \div 12 }\)
=\(\frac{ 2 }{ 3 }\)
Q4) If \(\frac{ 3 }{ 4 }\) is equivalent to \(\frac{ x }{ 20 }\) then the value of x is
(a) 15 (b) 18 (c) 12 (d) none of these
Ans. 4) (a) 15
Explanation:
\(\left (\frac{ 3 }{ 4 } = \frac{ x }{ 20 } \right )\)
We have:
20 = 4 x 5
So, we have to multiply the numerator by 5.
Therefore, x = 3 x 5 = 15
Q5) If \(\frac{ 45 }{ 60 }\) is equivalent to \(\frac{ 3 }{ x }\) then the value of x is
(a) 4 (b) 5 (c) 6 (d) 20
Ans. 5) (a) 4
Explanation:
\(\left (\frac{ 45 }{ 60 } = \frac{ 3 }{ x } \right )\)
Now, 3 = 45 / 15
So, we have to divide the denominator by 15.
Therefore, x = 60 / 15 = 4
Q6) Which of the following are like fractions?
(a) \(\frac{ 2 }{ 5 } , \frac{ 2 }{ 7 } , \frac{ 2 }{ 9 } , \frac{ 2 }{ 11 }\)
(b) \(\frac{ 2 }{ 3 } , \frac{ 3 }{ 4 } , \frac{ 4 }{ 5 } , \frac{ 5 }{ 6 }\)
(c) \(\frac{ 1 }{ 8 } , \frac{ 3 }{ 8 } , \frac{ 5 }{ 8 } , \frac{ 7 }{ 8 }\)
(d) none of these
Ans. 6) (c) \(\frac{ 1 }{ 8 } , \frac{ 3 }{ 8 } , \frac{ 5 }{ 8 } , \frac{ 7 }{ 8 }\)
( Fractions having the same denominator are called like fractions .)
Q7) Which of the following is a proper fraction?
(a) \(\frac{ 5 }{ 3 }\)
(b) 5
(c) \(1 \frac{ 2 }{ 5 }\)
(d) none of these
Ans. 7) (d) none of these
In a proper fraction , the numerator is less than the denominator.
Q8) Which of the following is a proper fraction?
(a) \(\frac{ 7 }{ 8 }\)
(b) \(1 \frac{ 7 }{ 8 }\)
(c)\(\frac{ 8 }{ 7 }\)
(d) none of these
Ans. 8) (a) \(\frac{ 7 }{ 8 }\)
In a proper fraction, the numerator is less than the denominator.
Q9) Which of the following statements are correct ?
(a) \(\frac{ 3 }{ 4 } > \frac{ 3 }{ 5 }\)
(b) \(\frac{ 3 }{ 4 } < \frac{ 3 }{ 5 }\)
(c) \(\frac{ 3 }{ 4 } and \frac{ 3 }{ 5 }\) cannot be compared
Ans. 9) (b) \(\frac{ 3 }{ 4 } < \frac{ 3 }{ 5 }\)
Between the two fractions with the same numerator, the one with smaller denominator is the greater.
Q10) The smallest of the fractions \(\frac{ 3 }{ 5 } , \frac{ 2 }{ 3 } , \frac{ 5 }{ 6 } , \frac{ 7 }{ 10 }\) is
(a) \(\frac{ 2 }{ 3 }\)
(b) \(\frac{ 7 }{ 10 }\)
(c) \(\frac{ 3 }{ 5 }\)
(d) \(\frac{ 5 }{ 6 }\)
Ans. 10) (c) \(\frac{ 3 }{ 5 }\)
L.C.M. of 5, 3, 6 and 10 = ( 2 x 3 x 5 ) = 30
Thus, we have:
\(\frac{ 3 }{ 5 } = \frac{ 3 \times 6 }{ 5 \times 6 } = \frac{ 18 }{ 30 }\)
\(\frac{ 2 }{ 3 } = \frac{ 2 \times 10 }{ 3 \times 10 } = \frac{ 20 }{ 30 }\)
\(\frac{ 5 }{ 6 } = \frac{ 5 \times 5 }{ 6 \times 5 } = \frac{ 25 }{ 30 }\)
\(\frac{ 7 }{ 10 } = \frac{ 7 \times 3 }{ 10 \times 3 } = \frac{ 21 }{ 30 }\)
Therefore, The smallest fraction = \(\frac{ 18 }{ 30 }\)
= \(\frac{ 3 }{ 5 }\)
Q11) The largest of the fractions \(\frac{ 4 }{ 5 } , \frac{ 4 }{ 7 } , \frac{ 4 }{ 9 } , \frac{ 4 }{ 11 }\) is
(a) \(\frac{ 4 }{ 11 }\)
(b) \(\frac{ 4 }{ 5 }\)
(c) \(\frac{ 4 }{ 7 }\)
(d) \(\frac{ 4 }{ 9 }\)
Ans. 11) (b) \(\frac{ 4 }{ 5 }\)
Among the given fractions with same numerator, the one with smallest denominator is the greatest .
Q12) The smallest of the fractions \(\frac{ 6 }{ 11 } , \frac{ 7 }{ 11 } , \frac{ 8 }{ 11 } , \frac{ 9 }{ 11 }\) is
(a) \(\frac{ 6 }{ 11 }\)
(b) \(\frac{ 7 }{ 11 }\)
(c) \(\frac{ 8 }{ 11 }\)
(d) \(\frac{ 9 }{ 11 }\)
Ans. 12) (a) \(\frac{ 6 }{ 11 }\)
Among like fractions, the fraction with the smallest numerator is the smallest.
Q13) The smallest of the fractions \(\frac{ 3 }{ 4 } , \frac{ 5 }{ 6 } , \frac{ 7 }{ 12 } , \frac{ 2 }{ 3 }\) is
(a) \(\frac{ 2 }{ 3 }\)
(b) \(\frac{ 3 }{ 4 }\)
(c) \(\frac{ 5 }{ 6 }\)
(d) \(\frac{ 7 }{ 12 }\)
Ans. 13) (d) \(\frac{ 7 }{ 12 }\)
Explanation:
L.C.M. of 4, 6, 12 and 3 = ( 2 x 2 x 3 ) = 12
Thus , we have:
\(\frac{ 3 }{ 5 } = \frac{ 3 \times 6 }{ 5 \times 6 } = \frac{ 18 }{ 30 }\)
\(\frac{ 2 }{ 3 } = \frac{ 2 \times 10 }{ 3 \times 10 } = \frac{ 20 }{ 30 }\)
\(\frac{ 5 }{ 6 } = \frac{ 5 \times 5 }{ 6 \times 5 } = \frac{ 25 }{ 30 }\)
\(\frac{ 7 }{ 12 }\)
Clearly, \(\frac{ 7 }{ 12 }\) is the smallest fraction.
Q14) \(4 \frac{ 3 }{ 5 }\) = ?
(a) \(\frac{ 17 }{ 5 }\)
(b) \(\frac{ 23 }{ 5 }\)
(c) \(\frac{ 17 }{ 3 }\)
(d) none of these
Ans. 14) (b) \(\frac{ 23 }{ 5 }\)
Q15) \(\frac{ 34 }{ 7 }\) = ?
(a) \(3 \frac{ 4 }{ 7 }\)
(b) \(7 \frac{ 3 }{ 4 }\)
(c) \(4 \frac{ 6 }{ 7 }\)
(d) none of these
Ans. 15) (c) \(4 \frac{ 6 }{ 7 }\)
On dividing 34 by 7:
Quotient = 4
Remainder = 6
\(\frac{ 34 }{ 7 } \; = \; 4 \; + \; \frac{ 6 }{ 7 } \; = \; 4 \frac{ 6 }{ 7 }\)
Q16) \(\frac{ 5 }{ 8 } + \frac{ 1 }{ 8 }\) = ?
(a) \(\frac{ 3 }{ 8 }\)
(b) \(\frac{ 3 }{ 4 }\)
(c) 6
(d) none of these
Ans. 16) (b) \(\frac{ 3 }{ 4 }\)
Explanation:
Addition of like fractions = Sum of the numerators / Common denominator
= \(\frac{ 5 }{ 8 } + \frac{ 1 }{ 8 }\)
= \(\frac{ ( 5 + 1 ) }{ 8 } \; = \; \frac{ 6 }{ 8 } \; = \; \frac{ 3 }{ 4 }\)
Q17 ) \(\frac{ 5 }{ 8 } – \frac{ 1 }{ 8 }\) = ?
(a) \(\frac{ 1 }{ 4 }\)
(b) \(\frac{ 1 }{ 2 }\)
(c) \(\frac{ 1 }{ 16 }\)
(d) none of these
Ans. 17) (b) \(\frac{ 1 }{ 2 }\)
Explanation:
\(\frac{ 5 }{ 8 } – \frac{ 1 }{ 8 }\)
= \(\frac{ ( 5 – 1 ) }{ 8 } \; = \; \frac{ 4 }{ 8 } \; = \; \frac{ 1 }{ 2 }\)
Q18) \(3 \frac{ 3 }{ 4 } – 2 \frac{ 1 }{ 4 }\) = ?
(a) \(1 \frac{ 1 }{ 2 }\)
(b) \(1 \frac{ 1 }{ 4 }\)
(c) \(\frac{ 1 }{ 4 }\)
(d) none of these
Ans. 18) (a) \(1 \frac{ 1 }{ 2 }\)
Explanation:
\(3 \frac{ 3 }{ 4 } – 2 \frac{ 1 }{ 4 }\)
\(3 \frac{ 3 }{ 4 } – 2 \frac{ 1 }{ 4 }\)
\(\frac{ ( 15 – 9 ) }{ 4 }\)
\(\frac{ 6 }{ 4 } = \frac{ 3 }{ 2 } = 1 \frac{ 1 }{ 2 }\)
Q19) \(\frac{ 5 }{ 6 } + \frac{ 2 }{ 3 } – \frac{ 4 }{ 9 }\) = ?
(a) \(1 \frac{ 1 }{ 3 }\)
(b) \(1 \frac{ 1 }{ 6 }\)
(c) \(1 \frac{ 1 }{ 9 }\)
(d) \(1 \frac{ 1 }{ 18 }\)
Ans. 19) (d) \(1 \frac{ 1 }{ 18 }\)
Explanation:
\(\frac{ 5 }{ 6 } + \frac{ 2 }{ 3 } – \frac{ 4 }{ 9 }\)
( L.C.M. of 3, 6 and 9 = ( 2 x 3 x 3 ) = 18 )
= \(\frac{ (15 + 12 – 8) }{ 18 }\)
[ 18 / 6 = 3 , 3 x 5 = 15 ] , [ 18 / 3 = 6 , 6 x 2 = 12 ] and [ 18 / 9 = 2 , 2 x 4 = 8 ]
= \(\frac{ (27 – 8) }{ 18 } = \frac{ 19 }{ 18 } = 1\frac{ 1 }{ 18 }\)
Q20) Which is greater: \(3\frac{ 1 }{ 3 } \; or \; \frac{ 33 }{ 10 }\) ?
(a) \(3 \frac{ 1 }{ 3 }\)
(b) \(\frac{ 33 }{ 10 }\)
(c) both are equal
Ans. 20) (a) \(3 \frac{ 1 }{ 3 }\)
Explanation:
Let us compare \(3 \frac{ 1 }{ 3 }\)and \(\frac{ 33 }{ 10 }\)
or \(\frac{ 10 }{ 3 }\) and \(\frac{ 33 }{ 10 }\) .
10 x 10 = 100 and 3 x 33 = 99
Clearly, 100 < 99
Therefore, \(\frac{ 10 }{ 3 } < \frac{ 33 }{ 10 }\) or
\(3 \frac{ 1 }{ 3 } < \frac{ 33 }{ 10 }\)
