Class 7 Maths Chapter 1 Question Answers - Rational Numbers

Q1. List three rational numbers between -2 and -1
Ans: Let us write -1 and -2 as rational numbers with denominator 5 (why?)
We have -1 = -5/5 = -2 = -10/5
So,
or
The three rational numbers  between -2 and -1 would be
(You can take any three of )

Q2. Which of the following numbers lies between −1 and −2?
Ans:
Mean =
Mean of two numbers always lies between the two numbers.
So, answer is option B.

Q3. Represent these numbers on the number line.
(i) 7/4
(ii) -5/6
Ans:

Q4. Find ten rational numbers between -2/5 and 1/2.
Ans:

∴ Ten rational numbers are

This question can have different multiple solutions too.

Q5. Write five rational numbers greater than −2.
Ans:
We can represent the given number −2 as -14/7.
Five rational numbers that are greater than  -14/7 , using the common denominator method, are:


Q6. Find ten rational numbers between 3/5 an 3/4.
Ans:
We can represent 3/5 as 36/60 and 3/4 as 45/60 respectively
Therefore;
10 rational numbers are

This question might have a different answer. Answer showed here is one of the several possibility.

Q7. Write down ten positive rational numbers such that the sum of the numerator and the denominator of each is 11. Write them in decreasing order
Ans:
Firstly, let us determine the numbers whose sum is 11 as follows:
10 + 1, 9 + 2, 8 + 3, 7 + 4, 6 + 5, 5 + 6, 4 + 7, 3 + 8, 2 + 9 and 1 + 10
Now, the ten positive rational numbers in which the sum of the numerator and denominator is 11 are:

Hence, the decreasing order of the numbers is


Q8. State whether the following statements are true or false. Give reasons for your answers.
(i) Every natural number is a whole number.
(ii) Every integer is a whole number.
(iii) Every rational number is a whole number.
Ans:
(i) True every natural is a whole number because natural number start from    1 and whole number start from 0, so every natural number is a whole number.
(ii) True because an integer is a whole number ( not a fractional number ) that can be positive or zero.
(iii) False a rational number is any number that can be expressed as the quotient of two integers.  

Q9. Write down ten positive rational numbers such that numerator - denominator for each of them is −2. Write them in increasing order.
Ans:
Firstly, let us determine the numbers whose difference is −2 as follows:
10−12, 9−11, 8−10, 7−9, 6−8, 5−7, 4−6, 3−5, 2−4 and 1−3
Now, the ten positive rational numbers in which the subtraction of the numerator and denominator is −2 are:

Hence, the increasing order of the numbers is


Q10. Find 12 rational number between −1 and 2.
Ans:


12 rational numbers between −1 and 2:


Q11. Find a rational number between 2/3 and 3/4.
Ans:
Step - 1 : Try to make denominators of both the numbers same
LCM of 3 and 4 =12
Multiply the numerator with the same factor

a = 8/12, b = 9/12
Step - 2 : Try to find a number between a and b
If we want  n rational number between 2 numbers we will multiply with n + 1
Here, n= 1 so we will multiply both a and b with n + 1 = 2 in both numerator and denominator

We know that, 16 < 17 < 18

⇒  17/24 lies between a and b
 ∴ One rational number between a and b is 17/24
Hence, the rational number between 2/3 and 3/4 is 17/24.

Q12. Find two rational numbers between -3/4 and 1/2.
Ans:
a = -3/4 and b = 1/2
Let q₁ and q₂  be two rational numbers.

The two rational numbers are -1/20 and -13/14

Q13. State if the following statement is true or false.7.4848.. is an irrational number.
A. True
B. False
Ans:
Given number is 7.4848...
We can see that the decimal expansion of the given number is non-terminating, repeating.
And we know that, any number having a decimal expansion that is non-terminating, repeating, is a rational number.
So, the given number is a rational number.
Hence, the given statement is false.

Q14. Find a rational number and also an irrational number lying between the numbers 0.401001000100001000001........ and 0.404004000400004000004...........
Ans: Rational numbers between given numbers will be 0.402 and 0.403.
A rational number between these numbers = 0.402 + 0.403 / 2 = 0.4205 and irrational numbers, given between the numbers are 0.402002000200002000002........ and 0.403003000300003000003..........

Q15. I am a number between 20 and 30. If you divide 47 and 92 by me, the remainders are 3 and 4 respectively what number am I?
Ans:
When we divide 47  by the required number then the remainder =  3
∴ 47 - 3 = 44
so the number divides 44 exactly
Between 20 & 30 only 22 divides the number 44 exactly
Similarly,
92 - 4 = 88
Between 20 & 30 only 22 divides the number 88 exactly
so the required number is 22