Solved Questions on Rational Numbers
1. Simplify the expression p − (q − r) using the values p = 5/11, q = 3/7 and r = − 7/11.
a) − (37/77)
b) − (47/77)
c) − (57/77)
d) − (67/77)
Answer: b) − (47/77)
Explanation:
2. The product of the two numbers is − 27/23. If one of the numbers is 235⁄23, what is the other number?
a) − (1/3)
b) − (2/3)
c) 1/3
d) 2/3
Answer: a) − (1/3)
Explanation:
3. What will be the result when the difference of -13⁄5 and 7/13 divides the sum of 11/13 and −3/5?
a) -711⁄16
b) 711⁄16
c) -811⁄16
d) 811⁄16
Answer: c) -811⁄16
Explanation:
4. Which of the following rational numbers is the result of adding the sum of the rational numbers represented by letters B, D, and E to the difference between the rational numbers represented by letters A and C?
a) -15⁄8
b) -17⁄8
c) -25⁄8
d) -27⁄8
Answer: d) -27⁄8
Explanation: The rational numbers for each point labelled with a letter are as follows:
Sum of the rational numbers represented by letters B, D and E = B + D + E
Difference between the rational numbers represented by letters A and C = A − C
Sum of the rational numbers represented by letters B, D and E and the difference between the rational numbers represented by letters A and C
5. Which of the following is five rational numbers between 2 and 3?
a) 1⁄5, 23⁄10, 3⁄2, 13⁄5, 29⁄10
b)
1⁄5,
23⁄10,
5⁄2,
13⁄5,
29⁄10
c)11⁄5,
23⁄10,
3⁄2,
13⁄5,
29⁄10
d) 11⁄5,
23⁄10,
5⁄2,
13⁄5,
29⁄10
Answer: d)11⁄5,
23⁄10,
5⁄2,
13⁄5,
29⁄10
Explanation: 2/1 and 3/1 are two rational numbers with the same denominator 7.
Follow these steps:
Step 1: First compare the numerators.
2 < 3 (2 is less than 3)
Step 2: Since there is no difference between the numerators 2 and 3.
Step 3: If you need more numbers in between, you can multiply both the original rational numbers by 10.
Step 4: Now there is a very large difference between the numerators 20 and 30. There are 10 numbers between the numerators 20 and 30. So, you can pick any 5 rational numbers in between.
Rational numbers between 
In the simplest form: 
Any five rational numbers lying between 2 and 3: 
Note: There are 10 numbers between the numerators 20 and 30. So, you may also choose the other 5 rational numbers in between.
