Solved Questions on Rational Numbers
1. What is the decimal form of 1/3?
a) 0.36
b) 0.3
c) 0.33333….
d) 0.66666….
Answer: c) 0.33333….
Explanation: To express 1/3 as a decimal, we divide 1 by 3.
1 ÷ 3 = 0.33333333...
So, 1/3 expressed as a decimal is 0.33333333... (infinite repeating decimal)
2. Find the sum of 2/3 and 1/6.
a) 8/3
b) 7/3
c) 5/6
d) 13/6
Answer: c) 5/6
Explanation: To find the sum of 2/3 and 1/6, we first find a common denominator. In this case, the least common multiple of 3 and 6 is 6.
So, we convert both 2/3 and 1/6 to have a common denominator of 6.
2/3 = 4/6
1/6 = 1/6
Now, we add 4/6 and 1/6:
4/6 + 1/6 = 5/6
So, the sum of 2/3 and 1/6 is 5/6.
3. What is the simplest form of 54/81?
a) 2/3
b) 9/11
c) 6/9
d) 18/27
Answer: a) 2/3
Explanation: To simplify the fraction 54/81, we find the greatest common factor of the numerator and denominator and divide both by it. In this case, the greatest common factor of 54 and 81 is 27.
54/81 = 54/81
= 2/3
So, 54/81 simplified is 2/3.
4. Find the rational numbers in the following options.
a) √5/2
b) √4
c) π
d) 1.41421356237309504.......
Answer: (b) √4
Explanation: The rational numbers among the following are:
√5/2 is not a rational number.
√4 = 2 which is a rational number.
π is not a rational number.
1.41421356237309504....... is not a rational number.
5. Find two rational numbers between 2/5 and 3/5.
a) 3/7 and 4/7
b) 1/2 and 3/4
c) 1/3 and 2/3
d) 7/15 and 8/15
Answer: d) 7/15 and 8/15
Explanation: To find two rational numbers between 2/5 and 3/5, we need to know that how many rational numbers we have to find, let’s consider m is the number of rational numbers that we need to find, m = 2, now just find m + 1,
m +1 = 2 + 1 = 3
To find 2 rational numbers we need to multiply by m + 1 in both the rational number,
2/5 x 3/3 = 6/15
3/5 x 3/3 = 9/15
Therefore, a number between 2/5 and 3/5 is 7/15 and 8/15.
Worksheet for Rational Numbers
1. Which of the following is a rational number?
a) 0.453267663...
b) -√3
c) 5/6
d) ∞
Answer: c) 5/6
2. Which of the following is equivalent to 2/3 + (3/4 x 5/6)?
a) 3/4
b) 17/15
c) 31/24
d) 29/36
Answer: c) 31/24
3. Which of the following is not a rational number?
a) 2/5
b) -3/4
c) π
d) 0.8
Answer: c) π
4. What is the multiplicative inverse of 3/5?
a) 5/3
b) 2/5
c) 3/2
d) 1/3
Answer: a) 5/3
5. Which of the following operations between two rational numbers always results in a rational number?
a) Addition
b) Subtraction
c) Multiplication
d) Division
Answer: c) Multiplication
6. What is the reciprocal of 3/5?
a) 5/3
b) 2/5
c) 3/2
d) 1/3
Answer: a) 5/3
7. Which of the following is the smallest positive rational number?
a) 1
b) 0.5
c) 0.25
d) 0.1
Answer: d) 0.1
8. Which of the following statements is true for a rational number a/b where a and b are integers and b ≠ 0?
a) If a is odd and b is even, then a/b is irrational.
b) If a and b are both even, then a/b is irrational.
c) If a and b have a common factor other than 1, then a/b is irrational.
d) If a and b have a common factor other than 1, then a/b is rational.
Answer: d) If a and b have a common factor other than 1, then a/b is rational.
9. Which of the following fractions is in the simplest form?
a) 6/12
b) 3/5
c) 10/15
d) 4/8
Answer: b) 3/5
10. Which of the following is equivalent to (3/5) ÷ (1/2) + (2/3) x (4/5)?
a) 2/5
b) 1/2
c) 17/30
d) 26/15
Answer: d) 26/15
