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All questions of Rational Numbers for Class 8 Exam
Write the additive inverse of 4/5.- a)1
- b)-4/5
- c)4/5
- d)0
Correct answer is option 'B'. Can you explain this answer?
Write the additive inverse of 4/5.
a)
1
b)
-4/5
c)
4/5
d)
0
 | EduRev Class 8 answered |
additive inverse means adding what number will give you zero
so let that no be x
x + 4/5 = 0
x = -4/5
trick : just change the sign of number
so let that no be x
x + 4/5 = 0
x = -4/5
trick : just change the sign of number
Find the multiplicative inverse of -13.- a)13
- b)-13
- c)-1/13
- d)12
Correct answer is 'C'. Can you explain this answer?
Find the multiplicative inverse of -13.
a)
13
b)
-13
c)
-1/13
d)
12
 | Anita Menon answered |
In order to find the multiplicative inverse of the given number, find the reciprocal of that number.
Here the given number is -13
So the reciprocal of -13 will be -1/13
Here the given number is -13
So the reciprocal of -13 will be -1/13
Therefore, option C is the correct answer.
For any three rational numbers a, b and c, a + (b + c) = __________.- a)(a + b) + c
- b)(a + b) - c
- c)(a - b) + c
- d)(a - b) - c
Correct answer is 'A'. Can you explain this answer?
For any three rational numbers a, b and c, a + (b + c) = __________.
a)
(a + b) + c
b)
(a + b) - c
c)
(a - b) + c
d)
(a - b) - c
 | Geetika Shah answered |
It is the associative property and we know that the rational numbers are associative under addition.
For eg: 5/3 + (3/2 + 1/3) = 7/2;
(5/3 + 3/2) + 1/3 = 7/2
Here, Option 'a' is the correct answer.
For eg: 5/3 + (3/2 + 1/3) = 7/2;
(5/3 + 3/2) + 1/3 = 7/2
Here, Option 'a' is the correct answer.
Therefore, a+(b+c) = (a+b)+c
_____ is the only rational number that is equal to its reciprocal. - a)2
- b)1
- c)1/2
- d)0
Correct answer is option 'B'. Can you explain this answer?
_____ is the only rational number that is equal to its reciprocal.
a)
2
b)
1
c)
1/2
d)
0
 | Pooja Shah answered |
1 because the reciprocal of 1 is 1/1 which is equal to 1.
Which of the following (rational number) lies between 0 and -1?- a) 0
- b)-3
- c)-2/3
- d)4/3
Correct answer is option 'C'. Can you explain this answer?
Which of the following (rational number) lies between 0 and -1?
a)
0
b)
-3
c)
-2/3
d)
4/3
 | Trisha Vashisht answered |
Option C: -2/3, because -2/3 is a rational number that lies between 0 and -1. The number 0 is greater than -2/3, and -3 is less than -1, while 4/3 is greater than 1, making it outside the range.
_______ are closed under addition.- a)Irrational numbers
- b)Negative numbers
- c)Rational numbers
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
_______ are closed under addition.
a)
Irrational numbers
b)
Negative numbers
c)
Rational numbers
d)
none of these
| | Ananya Das answered |
Rational Numbers: This set is closed under addition, subtraction, multiplication, and division (with the exception of division by 0).
Find a rational number between 1/4 and 1/2.- a)2
- b)1/2
- c)3/8
- d)0
Correct answer is option 'C'. Can you explain this answer?
Find a rational number between 1/4 and 1/2.
a)
2
b)
1/2
c)
3/8
d)
0
| | Amit Sharma answered |
A rational number between a and b is (a + b)/2
clearly it is there half so it will be between them
where a and b are numbers
a = 1/4, b = 1/2
Therefore, rational no. between 1/4 and 1/2 is
= (1/4 + 1/2)/2
= [(1 + 2)/4]/2
= 3/8
clearly it is there half so it will be between them
where a and b are numbers
a = 1/4, b = 1/2
Therefore, rational no. between 1/4 and 1/2 is
= (1/4 + 1/2)/2
= [(1 + 2)/4]/2
= 3/8
Zero has ________ reciprocal.- a)1
- b)2
- c)no
- d)3
Correct answer is option 'C'. Can you explain this answer?
Zero has ________ reciprocal.
a)
1
b)
2
c)
no
d)
3
 | Akshay Mehra answered |
Zero has no reciprocal. Because 1/0 is not defined and also remember any number multiplied by zero gives 0. Therefore, if reciprocal was supposed to be there then that reciprocal when multiplied by 0 should give 1 which is not possible.
A number which can be written in the form, p/q where p and q are integers and _____ is called a rational number.- a)q = 0
- b)q ≠ 0
- c)q = 1
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
A number which can be written in the form, p/q where p and q are integers and _____ is called a rational number.
a)
q = 0
b)
q ≠ 0
c)
q = 1
d)
none of these
| | Pooja Shah answered |
Given, A rational number is defined as a number that can be expressed in the form p/q , where p and q are integers
We have to find the condition that satisfies the definition.
A number that can be expressed in the form p/q , where p and q are integers and q ≠ 0, is called a rational number.
Therefore, the condition that satisfies the definition is q ≠ 0
Find the multiplicative inverse of 1/4.- a)4
- b)-1/4
- c)-4
- d)1/4
Correct answer is option 'A'. Can you explain this answer?
Find the multiplicative inverse of 1/4.
a)
4
b)
-1/4
c)
-4
d)
1/4
 | Urvashi Sharma answered |
In multiplicative inverse we reciprocal the numbers by which we get the answer =1 that's why 1/4×4/1 which we consider as 4 so 4 is the multiplicative inverse of 1/4
Which of the following is the reciprocal of the reciprocal of a rational number?- a) -1
- b) 1
- c) 0
- d)The number itself
Correct answer is option 'D'. Can you explain this answer?
Which of the following is the reciprocal of the reciprocal of a rational number?
a)
-1
b)
1
c)
0
d)
The number itself
| | Pooja Shah answered |
1 is the Multiplicative identity for rational numbers.
________ are closed under subtraction.- a)Irrational numbers
- b)Negative numbers
- c)Rational number
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
________ are closed under subtraction.
a)
Irrational numbers
b)
Negative numbers
c)
Rational number
d)
none of these
| | Amit Sharma answered |
Rational numbers are closed under subtraction.Because if we subtract a rational number with another rational number we will get rational number. For example 45−35 = 10, which is also a rational number.
Correct option is C.
Correct option is C.
Find the multiplicative inverse of 2/9 .- a)-9/2
- b)9/2
- c)-2/9
- d)2/9
Correct answer is option 'B'. Can you explain this answer?
Find the multiplicative inverse of 2/9 .
a)
-9/2
b)
9/2
c)
-2/9
d)
2/9
 | Rohit Sharma answered |
Multiplicative inverse is nothing but a reciprocal of a number 2/9 which is 9/2.
1 is the __________ for rational numbers.- a)multiplicative identity
- b)Addition of zero
- c)additive identity
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
1 is the __________ for rational numbers.
a)
multiplicative identity
b)
Addition of zero
c)
additive identity
d)
none of these
| | Geetika Shah answered |
If you multiply any number with 1,the product will always be the same number which you multiply with 1. Therefore, 1 is the multiplicative identity.
Find the multiplicative inverse of -13.- a)13
- b)-13
- c)-1/13
- d)12
Correct answer is option 'C'. Can you explain this answer?
Find the multiplicative inverse of -13.
a)
13
b)
-13
c)
-1/13
d)
12
 | Kavya Saxena answered |
In order to find the multiplicative inverse of the given number, find the reciprocal of that number.
Here the given number is -13
So the reciprocal of -13 will be -1/13
Here the given number is -13
So the reciprocal of -13 will be -1/13
Therefore, option C is the correct answer.
The sum of two rational numbers is always:- a)A natural number
- b)A whole number
- c)A rational number
- d)An irrational number
Correct answer is option 'C'. Can you explain this answer?
The sum of two rational numbers is always:
a)
A natural number
b)
A whole number
c)
A rational number
d)
An irrational number
| | Ujwal Mukherjee answered |
Understanding Rational Numbers
Rational numbers are defined as numbers that can be expressed in the form of a fraction, where both the numerator and the denominator are integers, and the denominator is not zero. Examples include 1/2, -3/4, and 5.
Sum of Two Rational Numbers
When we add two rational numbers, the result is also a rational number. Here's why:
1. Definition of Addition
- When we add two fractions, we find a common denominator and then sum the numerators.
- For example, to add 1/2 and 3/4, we convert them to the same denominator:
- 1/2 = 2/4
- Now, add: 2/4 + 3/4 = 5/4.
2. Closure Property
- Rational numbers exhibit a closure property under addition. This means that if you take any two rational numbers and add them together, you will always get another rational number.
- For instance, if you take 2/3 and 4/5, their sum is (2*5 + 4*3) / (3*5) = 22/15, which is also rational.
3. Real-World Implications
- This property is essential in various fields, such as finance, physics, and engineering, where calculations involving rational numbers are common.
Conclusion
Thus, the correct answer to the question is option 'C': the sum of two rational numbers is always a rational number. Understanding this property helps in solving mathematical problems more effectively.
Rational numbers are defined as numbers that can be expressed in the form of a fraction, where both the numerator and the denominator are integers, and the denominator is not zero. Examples include 1/2, -3/4, and 5.
Sum of Two Rational Numbers
When we add two rational numbers, the result is also a rational number. Here's why:
1. Definition of Addition
- When we add two fractions, we find a common denominator and then sum the numerators.
- For example, to add 1/2 and 3/4, we convert them to the same denominator:
- 1/2 = 2/4
- Now, add: 2/4 + 3/4 = 5/4.
2. Closure Property
- Rational numbers exhibit a closure property under addition. This means that if you take any two rational numbers and add them together, you will always get another rational number.
- For instance, if you take 2/3 and 4/5, their sum is (2*5 + 4*3) / (3*5) = 22/15, which is also rational.
3. Real-World Implications
- This property is essential in various fields, such as finance, physics, and engineering, where calculations involving rational numbers are common.
Conclusion
Thus, the correct answer to the question is option 'C': the sum of two rational numbers is always a rational number. Understanding this property helps in solving mathematical problems more effectively.
________ is not associative for rational numbers.- a)Subtraction or Division
- b)Addition or Multiplication
- c)Addition or Division
- d)Multiplication or Division
Correct answer is option 'A'. Can you explain this answer?
________ is not associative for rational numbers.
a)
Subtraction or Division
b)
Addition or Multiplication
c)
Addition or Division
d)
Multiplication or Division
| | Amit Sharma answered |
This is how associative property works. It states that you can add or multiply numbers regardless of how they are grouped. Addition and multiplication are associative for rational numbers. Subtraction and division are not associative for rational numbers.
The product of two rational numbers is always a _______.- a)irrational number
- b)negative number
- c)rational number
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
The product of two rational numbers is always a _______.
a)
irrational number
b)
negative number
c)
rational number
d)
None of these
| | Kavya Saxena answered |
Product of two rational numbers is always a rational number.
For example, 1/2 + 1/2 = 1
For example, 1/2 + 1/2 = 1
Which of the following is the correct definition of a rational number?- a)A number that cannot be written as a fraction of two integers
- b)A number that can be written as p/q, where p and q are integers and q≠0
- c)A number that can only be written as a fraction with positive integers
- d)A number that is not a whole number or a fraction
Correct answer is option 'B'. Can you explain this answer?
Which of the following is the correct definition of a rational number?
a)
A number that cannot be written as a fraction of two integers
b)
A number that can be written as p/q, where p and q are integers and q≠0
c)
A number that can only be written as a fraction with positive integers
d)
A number that is not a whole number or a fraction
| | Trisha Vashisht answered |
Answer: B) A number that can be written as p/q, where p and q are integers and q ≠ 0.
A rational number is defined as any number that can be expressed as the ratio of two integers, where the denominator q is not equal to zero.
A rational number is defined as any number that can be expressed as the ratio of two integers, where the denominator q is not equal to zero.
What property allows you to compute 1/3 × (6 × 4/3) as (1/3 × 6) × 4/3?- a)Associative Property
- b)Distributive property
- c)Commutative property
- d)None of the above
Correct answer is option 'A'. Can you explain this answer?
What property allows you to compute 1/3 × (6 × 4/3) as (1/3 × 6) × 4/3?
a)
Associative Property
b)
Distributive property
c)
Commutative property
d)
None of the above
 | Dipika Saha answered |
Understanding the Associative Property
The Associative Property is a fundamental principle in arithmetic that allows you to group numbers in different ways without changing the result of the operation.
Key Features of the Associative Property:
- It applies to addition and multiplication.
- It states that the way in which numbers are grouped does not affect the sum or product.
Example in Context:
In the expression 1/3 × (6 × 4/3), the operation inside the parentheses (6 × 4/3) is computed first. According to the Associative Property, we can also group the numbers differently:
- (1/3 × 6) × 4/3
Both expressions yield the same final result due to the property of associativity in multiplication.
Why the Correct Answer is 'A':
- The operation you are performing with fractions—multiplying them—allows for regrouping.
- By using the Associative Property, you can rearrange the expression without altering the outcome.
Other Properties Explained:
- Distributive Property: This is used when you multiply a single term by terms in parentheses, but it does not apply here.
- Commutative Property: This property states that changing the order of numbers does not affect the sum or product, but it does not explain regrouping.
In conclusion, the ability to regroup numbers in multiplication is what identifies the Associative Property, making option 'A' the correct answer to the question.
The Associative Property is a fundamental principle in arithmetic that allows you to group numbers in different ways without changing the result of the operation.
Key Features of the Associative Property:
- It applies to addition and multiplication.
- It states that the way in which numbers are grouped does not affect the sum or product.
Example in Context:
In the expression 1/3 × (6 × 4/3), the operation inside the parentheses (6 × 4/3) is computed first. According to the Associative Property, we can also group the numbers differently:
- (1/3 × 6) × 4/3
Both expressions yield the same final result due to the property of associativity in multiplication.
Why the Correct Answer is 'A':
- The operation you are performing with fractions—multiplying them—allows for regrouping.
- By using the Associative Property, you can rearrange the expression without altering the outcome.
Other Properties Explained:
- Distributive Property: This is used when you multiply a single term by terms in parentheses, but it does not apply here.
- Commutative Property: This property states that changing the order of numbers does not affect the sum or product, but it does not explain regrouping.
In conclusion, the ability to regroup numbers in multiplication is what identifies the Associative Property, making option 'A' the correct answer to the question.
What is the sum of 3/7 + (-6/11) + (-8/21) + 5/22 ?- a)-125/462
- b)-125/446
- c)-100/462
- d)125/462
Correct answer is option 'A'. Can you explain this answer?
What is the sum of
3/7 + (-6/11) + (-8/21) + 5/22 ?
a)
-125/462
b)
-125/446
c)
-100/462
d)
125/462
| | Trisha Vashisht answered |
3/7 + (-6/11) + (-8/21) + 5/22
= [3/7 + (-8/21)] + [(-6/11) + 5/22]
(by using commutativity and associativity)
(by using commutativity and associativity)
= [9/21 + (-8/21)] + [-12/22 + 5/22]
LCM of 7 and 21 is 21; LCM of 11 and 22 is 22
= 1/21 + (-7/22)
= 22/462 + (-147/462)
= -125/462
= 22/462 + (-147/462)
= -125/462
Which of the following statements is true?- a)Every fraction is a rational number.
- b)Every rational number is a fraction.
- c)Every integer is a rational number.
- d)Both (a) and (c).
Correct answer is option 'D'. Can you explain this answer?
Which of the following statements is true?
a)
Every fraction is a rational number.
b)
Every rational number is a fraction.
c)
Every integer is a rational number.
d)
Both (a) and (c).
| | EduRev Class 8 answered |
- Rational Numbers: a rational number is defined as one that can be expressed in the form a/b, where a is an integer and b is a natural number. This means that every fraction is a rational number.
- But every rational number is not a fraction. For example, -4/9 is a rational number but not a fraction, as fractions include only whole numbers as numerators and natural numbers only as denominators.
- In addition, every integer can be expressed as a fraction (for example, as the integer divided by 1). Therefore, all three statements are true.
Which of the following sets contains five rational numbers greater than -2?- a)−3,−2.5,−1.5,0,2
- b)−3,−4,−1,1,3
- c)−1.9,−1,0,1,2
- d)−2,−3,−5,−6,−7
Correct answer is option 'C'. Can you explain this answer?
Which of the following sets contains five rational numbers greater than -2?
a)
−3,−2.5,−1.5,0,2
b)
−3,−4,−1,1,3
c)
−1.9,−1,0,1,2
d)
−2,−3,−5,−6,−7
| | Ujwal Mukherjee answered |
Understanding Rational Numbers
Rational numbers are numbers that can be expressed as the quotient of two integers, where the denominator is not zero. For this question, we need to find a set of five rational numbers that are greater than -2.
Evaluating Each Option
Let's analyze the provided options:
Option A: -3, -2.5, -1.5, 0, 2
- Numbers greater than -2: -1.5, 0, 2
- Only three numbers are greater than -2.
Option B: -3, -4, -1, 1, 3
- Numbers greater than -2: -1, 1, 3
- Only three numbers are greater than -2.
Option C: -1.9, -1, 0, 1, 2
- Numbers greater than -2: -1.9, -1, 0, 1, 2
- All five numbers are greater than -2.
Option D: -2, -3, -5, -6, -7
- Numbers greater than -2: None
- All numbers are less than or equal to -2.
Conclusion
After evaluating all the options, only Option C contains five rational numbers that are all greater than -2. The numbers included are:
- -1.9
- -1
- 0
- 1
- 2
Thus, the correct answer is indeed Option C.
Rational numbers are numbers that can be expressed as the quotient of two integers, where the denominator is not zero. For this question, we need to find a set of five rational numbers that are greater than -2.
Evaluating Each Option
Let's analyze the provided options:
Option A: -3, -2.5, -1.5, 0, 2
- Numbers greater than -2: -1.5, 0, 2
- Only three numbers are greater than -2.
Option B: -3, -4, -1, 1, 3
- Numbers greater than -2: -1, 1, 3
- Only three numbers are greater than -2.
Option C: -1.9, -1, 0, 1, 2
- Numbers greater than -2: -1.9, -1, 0, 1, 2
- All five numbers are greater than -2.
Option D: -2, -3, -5, -6, -7
- Numbers greater than -2: None
- All numbers are less than or equal to -2.
Conclusion
After evaluating all the options, only Option C contains five rational numbers that are all greater than -2. The numbers included are:
- -1.9
- -1
- 0
- 1
- 2
Thus, the correct answer is indeed Option C.
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