Mathematics - Rational Numbers
Exam Duration: 45 Mins Total Questions : 30
Which of the following is not a rational number(s)?
- (a)
\(\frac { -2 }{ 9 } \)
- (b)
\(\frac { 4 }{ -7 } \)
- (c)
\(\frac { -3 }{ -17 } \)
- (d)
\(\frac { \sqrt { 2 } }{ 3 } \)
What type of a number is\(\frac { -3 }{ 0 } \) ?
- (a)
A positive rational number
- (b)
A negative rational number.
- (c)
Either a positive or a negative rational number
- (d)
Neither a positive nor a negative rational number.
What type of a numerator does \(\frac { 0 }{ 7 } \) have?
- (a)
Positive
- (b)
Negative
- (c)
Either positive or negative
- (d)
Neither positive nor negative
If \(\frac { -4 }{ 7 } =\frac { -32 }{ x } \) what is the value of x?
- (a)
-56
- (b)
56
- (c)
46
- (d)
-46
What is the percentage of the least number in the greatest number of \(\frac { 3 }{ 5 } ,\frac { 9 }{ 5 } ,\frac { 1 }{ 5 } \) and\(\frac { 7 }{ 5 } \)?
- (a)
11\(\frac { 1 }{ 9 } \)%
- (b)
10%
- (c)
20%
- (d)
25%
P: The quotient of two integers is always a rational number.
Q:\(\frac { 1 }{ 0 } \) is not rational.Which of the following statements is true?
- (a)
P is true and Q is the correct explanation of P.
- (b)
P is false and Q is the correct explanation of P.
- (c)
P is true and Q is false.
- (d)
Both P and Q are false.
Of which property is \(\frac { -7 }{ 5 } +\left( \frac { 2 }{ -11 } +\frac { -13 }{ 25 } \right) =\left( \frac { -7 }{ 5 } +\frac { 2 }{ -11 } \right) +\frac { -13 }{ 25 } \) an example?
- (a)
Closure property
- (b)
Commutative property
- (c)
Associative property
- (d)
Identity property
What number should be added to\(\frac { -5 }{ 6 } \) to get\(\frac { 3 }{ 2 } \) ?
- (a)
\(\frac { -7 }{ 3 } \)
- (b)
2\(\frac { 1 }{ 3 } \)
- (c)
\(\frac { 8 }{ 3 } \)
- (d)
\(\frac { -8 }{ 3 } \)
Which of the following statements is true?
- (a)
The reciprocals of 1 and -1 are themselves.
- (b)
Zero has no reciprocal
- (c)
The product of two rational numbers is a rational number
- (d)
All the above
The product of two rational numbers is .If one of the numbers is ,what is the other number?
- (a)
\(\frac { 36 }{ 48 } \)
- (b)
\(\frac { 25 }{ 64 } \)
- (c)
\(\frac { 27 }{ 49 } \)
- (d)
\(\frac { 27 }{ 64 } \)
Evaluate p + q given p = \(\left( -2\frac { 1 }{ 5 } \right) \)and q =\(\left( -1\frac { 1 }{ 3 } \right) \)
- (a)
1\(\frac { 8 }{ 15 } \)
- (b)
\(\left( -3\frac { 8 }{ 15 } \right) \)
- (c)
\(\left( -2\frac { 8 }{ 15 } \right) \)
- (d)
\(3\frac { 8 }{ 15 } \)
For what value of 'x' is\(\frac { 7 }{ 8 } -\left( -\frac { 11 }{ 4 } \right) +x=3\frac { 7 }{ 24 } \) ?
- (a)
\(\frac { -1 }{ 3 } \)
- (b)
\(\frac { 1 }{ 3 } \)
- (c)
\(\frac { 2 }{ 3 } \)
- (d)
-3
Determine 'y' so that y-2\(\frac { 1 }{ 3 } \)=\(\left( -3\frac { 7 }{ 12 } \right) \)
- (a)
-1\(\frac { 1 }{ 4 } \)
- (b)
1\(\frac { 1 }{ 4 } \)
- (c)
-1\(\frac { 1 }{ 12 } \)
- (d)
1\(\frac { 1 }{ 12 } \)
Find the simplest form of \(\left( -\frac { 1 }{ 2 } +\frac { 1 }{ 3 } +\frac { 1 }{ 6 } \right) \left( \frac { -2 }{ 5 } \right) \)
- (a)
\(\frac { -2 }{ 5 } \)
- (b)
0
- (c)
1
- (d)
\(\frac { 2 }{ 5 } \)
Rohit, Peter and Santosh walk around a circular park. They take\(\frac { 1 }{ 3 } \) h, \(\frac { 2 }{ 5 } \)h and \(\frac { 5 }{ 12 } \) h to complete one round. What is the total time taken by them to complete a round in minutes?
- (a)
79 minutes
- (b)
50 minutes
- (c)
60 minutes
- (d)
69 minutes
What should be subtracted from \(\frac { -2 }{ 3 } \)to get\(\frac { 5 }{ 6 } \) ?
- (a)
\(\frac { 3 }{ 2 } \)
- (b)
\(\frac { -3 }{ 2 } \)
- (c)
\(\frac { 2 }{ 3 } \)
- (d)
\(\frac { -2 }{ 3 } \)
By what number should be divided to get ?
- (a)
\(\frac { -4 }{ 3 } \)
- (b)
\(\frac { 4 }{ 3 } \)
- (c)
\(\frac { 3 }{ 4 } \)
- (d)
\(\frac { -3 }{ 4 } \)
Express\(\left[ \frac { -1 }{ 4 } -\left( \frac { -1 }{ 6 } \right) \right] \div \left[ \frac { 1 }{ 3 } +\left( \frac { -1 }{ 2 } \right) \right] \) in the simplest form
- (a)
\(\frac { -2 }{ 3 } \)
- (b)
\(\frac { 1 }{ 2 } \)
- (c)
\(\frac { 2 }{ 3 } \)
- (d)
\(\frac { -1 }{ 2 } \)
Given a =1\(\frac { 5 }{ 7 } \) ,b =\(\frac { 1 }{ 4 } \) .c =\(\frac { 1 }{ 9 } \) and d=\(\left( -1\frac { 1 }{ 4 } \right) \) evaluate a(b-c) ÷ d.
- (a)
\(\frac { -4 }{ 21 } \)
- (b)
\(\frac { -6 }{ 23 } \)
- (c)
\(\frac { -5 }{ 27 } \)
- (d)
\(\frac { 4 }{ 21 } \)
The average of the two middle rational numbers if \({4\over 7},{1\over3},{2\over3},{5\over9}\) are arranged in ascending order is_____________.
- (a)
\(4\over9\)
- (b)
\(71\over63\)
- (c)
\(2\over9\)
- (d)
\(71\over126\)
The product of two rational numbers is \(-9\over16\) . If one of the numbers is \({- 4\over 3}\) , then the other number is___________.
- (a)
\({36\over 48}\)
- (b)
\(25\over64\)
- (c)
\(27\over 49\)
- (d)
\({27\over64}\)
If P: every fraction is a rational number and q: every rational number is a fraction, then which of the following options hold?
- (a)
p is true and q is false.
- (b)
p is false and q is true
- (c)
Both p and q are true.
- (d)
Both p and q are false
Simplify :\(\left( \frac { \left( -18\frac { 1 }{ 3 } \times 2\frac { 8 }{ 11 } \right) -\left( 4\frac { 5 }{ 7 } \times 2\frac { 1 }{ 3 } \right) }{ \left| \frac { 3 }{ 5 } +\left( \frac { -9 }{ 10 } \right) \right| +\left| -\left( \frac { -3 }{ 5 } \right) \right| } \right) \)
- (a)
\(63{4\over81}\)
- (b)
\(-23{7\over9}\)
- (c)
\(-67{7\over9}\)
- (d)
\(12{6\over17}\)
Which of the following options are equivalent rational numbers?
- (a)
\({1\over4}and{-4\over-16}\)
- (b)
\({-2\over 3}and{8\over12}\)
- (c)
\({12\over15}and{10\over18}\)
- (d)
\({27\over54} and {3\over2}\)
Divide the sum of \({5\over12}and {-17\over24}\) by the product \({2\over5}and {7\over4}\) of What is the result?
- (a)
\({-8\over37}\)
- (b)
\(-5\over 12\)
- (c)
\(6\over31\)
- (d)
\(3\over12\)
A farmer grows vegetables in his field. In \({2\over3}\) of the field, he grows potatoes, in \(1\over4\) of the field, he grows onions and in the rest of the field, he grows tomatoes. In what part of the field does he grow tomatoes?
- (a)
\(1\over12\)
- (b)
\(11\over12\)
- (c)
\(3\over4\)
- (d)
\(1\over6\)
\(3\over20\)of a delegation are from India, \(1\over4\) are from Britain,\(3\over10\) are from Germany and the rest are Americans. If there are 1200 members in the delegation, then calculate how many Americans are there?
- (a)
460
- (b)
400
- (c)
360
- (d)
300
From his home, Rahul walks \(6\over7\) km towards school and then returns\(5\over6\) km on the same way towards his home to reach a landmark. At what distance will he be now from his home?
- (a)
\({1\over42}km\)
- (b)
\({1\over43}km\)
- (c)
\({30\over42}km\)
- (d)
\({11\over42}km\)
Match the following.
Column-I | Column-II |
(i) Divide the sum of \(12\over5\) and \({13\over7}\) by the product of \({-4\over7} and {-1\over2}\) . The result obtained is | (p)\(7\over10\) |
(ii) Niharika spent \({3\over4}\) her pocket money. She spent \({1\over2}\) of it on a book,\({1\over6}\) on a movie and rest for a dress__________part of her pocket money she spend on the dress. | (q) \(3{19\over28}\) |
(iii) If 35 shirts of equal size can be stitched from \(49\over2\) metres of cloth. The length (in m) of cloth required for each shirt is | (r) 14\(9\over10\) |
(iv) Two packets of chocolates weigh \({9\over4}kg \ and \ {10\over7} \ kg\) respectively. The total weight (in kg) of the chocolates is | (s) \(1\over4\) |
- (a)
(i) (ii) (iii) (iv) P Q R S - (b)
(i) (ii) (iii) (iv) R S P Q - (c)
(i) (ii) (iii) (iv) P R S Q - (d)
(i) (ii) (iii) (iv) R P S Q
Which of the following options hold?
(1) Every integer is a rational number and every fraction is a rational number.
(2) A rational number \(p\over q\) is positive if p and q are either both positive or both negative.
(3) A rational number \(p\over q\) is negative if one of p and q is positive and other is negative.
(4) If there are two rational numbers with common denominator then the one with the larger numerator is larger than the other.
- (a)
Both 1 and 4 are correct
- (b)
Both 2 and 3 are incorrect
- (c)
Only 1 is correct
- (d)
All are correct