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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
Which of the following is the product of (-7/8) and 4/21?
- a)-1/6
- b)12
- c)-63/16
- d)-16/147
Correct answer is option 'A'. Can you explain this answer?
Which of the following is the product of (-7/8) and 4/21?
a)
-1/6
b)
12
c)
-63/16
d)
-16/147
|
Mishti Gupta answered |
-7 / 8 x 4 / 21 = - 1 / 6 - To find the product of two fractions, multiply the numerators together and the denominators together.
- (-7/8) * (4/21) = (-7 * 4) / (8 * 21) = -28 / 168
- Simplifying the fraction by dividing both the numerator and denominator by 4, we get -7 / 42
- Further simplifying by dividing both the numerator and denominator by 7, we get -1 / 6
- Therefore, the correct answer is A: -1/6.
- (-7/8) * (4/21) = (-7 * 4) / (8 * 21) = -28 / 168
- Simplifying the fraction by dividing both the numerator and denominator by 4, we get -7 / 42
- Further simplifying by dividing both the numerator and denominator by 7, we get -1 / 6
- Therefore, the correct answer is A: -1/6.
So option A is the correct answer.
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.
Subtract -5/9 from -3/7.
- a)62/63
- b)-8/63
- c)8/63
- d)-62/63
Correct answer is option 'C'. Can you explain this answer?
Subtract -5/9 from -3/7.
a)
62/63
b)
-8/63
c)
8/63
d)
-62/63
|
|
Anita Menon answered |
-3/7-(-5/9)
-3/7+5/9
(-3*9 + 5*7 )/63
(-27 + 35 )/63
8/63
-3/7+5/9
(-3*9 + 5*7 )/63
(-27 + 35 )/63
8/63
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.
Compare 
- a)
- b)
- c)
- d)
Correct answer is option 'D'. Can you explain this answer?
Compare
a)
b)
c)
d)
|
Shubham Sharma answered |
Expressing in standard form, we get 
Express each rational number with L.C.M as denominator. L.C.M of 9 and 5 is 9 × 5 = 45.
Express each rational number with L.C.M as denominator. L.C.M of 9 and 5 is 9 × 5 = 45.
∴ 
Comparing the numerators, we have −40<−36 .
∴ 
for -ve number the lesser number is actually bigger
for -ve number the lesser number is actually bigger
_______ 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
What is the sum of the additive inverse and multiplicative inverse of 2?- a)3/2
- b)-3/2
- c)1/2
- d)-1/2
Correct answer is option 'B'. Can you explain this answer?
What is the sum of the additive inverse and multiplicative inverse of 2?
a)
3/2
b)
-3/2
c)
1/2
d)
-1/2
|
Rohit Sharma answered |
Additive inverse of 2 is −2
Multiplicative inverse of 2 is 1/2
∴ The sum of multiplicative inverse and additive inverse =
Answer :
Multiplicative inverse of 2 is 1/2
∴ The sum of multiplicative inverse and additive inverse =
Answer :
Which number is in the middle if -1/6, 4/9, 6/-7, 2/5 and -3/4 arranged in descending order?- a)2/5
- b)4/9
- c)-1/6
- d)-6/7
Correct answer is option 'C'. Can you explain this answer?
Which number is in the middle if -1/6, 4/9, 6/-7, 2/5 and -3/4 arranged in descending order?
a)
2/5
b)
4/9
c)
-1/6
d)
-6/7
|
Anushka Basu answered |
The descending order is 
∴ The middle number is -1/6
Subtract 2/3 from 7/8- a)-5/24
- b)5/24
- c)7/16
- d)5/16
Correct answer is option 'B'. Can you explain this answer?
Subtract 2/3 from 7/8
a)
-5/24
b)
5/24
c)
7/16
d)
5/16
|
|
Ananya Das answered |
ANSWER :- b
Solution :- 7/8 - 2/3
= {(21-16)/24}
= 5/24
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.
________ 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.
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.
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.
Simplify 
- a)37/15
- b)-37/15
- c)-36/5
- d)-38/3
Correct answer is option 'A'. Can you explain this answer?
Simplify
a)
37/15
b)
-37/15
c)
-36/5
d)
-38/3
|
|
Shubham Sharma answered |
LCM of 5,3 and 15 is 15
The sum of two rational numbers is −3. If one of them is -11/5, find the other.- a)-4/5
- b)-8/5
- c)4/5
- d)8/5
Correct answer is option 'A'. Can you explain this answer?
The sum of two rational numbers is −3. If one of them is -11/5, find the other.
a)
-4/5
b)
-8/5
c)
4/5
d)
8/5
|
|
Ananya Das answered |
The correct answer is a.
Let the other number be x
x+(-11/5)= -3
x= -3+11/5
x=-15+11/5
x= -4/5
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.
What number should be added to -4/7 to get 5/9 ?- a)-71/63
- b)71/63
- c)1/63
- d)-1/63
Correct answer is option 'B'. Can you explain this answer?
What number should be added to -4/7 to get 5/9 ?
a)
-71/63
b)
71/63
c)
1/63
d)
-1/63
|
|
Ananya Das answered |
The correct answer is b
Let the number be x
Then,
X+(-4/7)=5/9
X=5/9+4/7
X= 35+36/63
X=71/63
The value of (5/4) – (8/3) is:- a)17/12
- b)-17/12
- c)12/17
- d)-12/17
Correct answer is option 'B'. Can you explain this answer?
The value of (5/4) – (8/3) is:
a)
17/12
b)
-17/12
c)
12/17
d)
-12/17
|
|
Ananya Das answered |
5/4 – 8/3
Making the denominator equal:
[(5/4) x (3/3)] – [(8/3) x (4/4)]
= (15/12) – (32/12)
= (15 – 32)/12
= -17/12
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 (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.
How is -28/84 expressed as a rational number with numerator -4?
- a)4/7
- b)-4/12
- c)4/12
- d)4/-7
Correct answer is option 'B'. Can you explain this answer?
How is -28/84 expressed as a rational number with numerator -4?
a)
4/7
b)
-4/12
c)
4/12
d)
4/-7
|
Madhurima Nair answered |
To express the fraction -28/84 as a rational number with a numerator of -4, you need to find a common factor to simplify the fraction. Both -28 and 84 are divisible by 4:
-28 ÷ 4 = -7 84 ÷ 4 = 21
So, -28/84 simplifies to -7/21. To express it with a numerator of -4, you can further simplify:
-7/21 = (-7 ÷ 7) / (21 ÷ 7) = -1/3
Now, to have a numerator of -4:
-1/3 * 4/4 = -4/12
Therefore, -28/84 expressed as a rational number with a numerator of -4 is -4/12.
What should be subtracted from -7/11 to get −2?- a)15/11
- b)-15/11
- c)29/11
- d)-29/11
Correct answer is option 'A'. Can you explain this answer?
What should be subtracted from -7/11 to get −2?
a)
15/11
b)
-15/11
c)
29/11
d)
-29/11
|
|
Amit Kumar answered |
Let x be subtracted from -7/11
then -7/11 - x= -2
-x= -2 + (7/11)
-x= -2 + 7/11
-x= -15/11
x= 15/11
then -7/11 - x= -2
-x= -2 + (7/11)
-x= -2 + 7/11
-x= -15/11
x= 15/11
Which of the following statements is false?- a)
- b)
- c)
- d)Both (b) & (c)
Correct answer is option 'D'. Can you explain this answer?
Which of the following statements is false?
a)
b)
c)
d)
Both (b) & (c)
|
Priya Nair answered |
So,
Hence, both (b) and (c) are false.By what rational number should -3/5 be multiplied to obtain 21?- a)507/4
- b)35
- c)-35
- d)507
Correct answer is option 'C'. Can you explain this answer?
By what rational number should -3/5 be multiplied to obtain 21?
a)
507/4
b)
35
c)
-35
d)
507
|
|
Geetika Shah answered |
Let the rational no be x
-3/5 X x = 21
x = (21 X5 )/ -3
x = -35
-3/5 X x = 21
x = (21 X5 )/ -3
x = -35
Which among the following is a rational number equivalent to -5/-3 ?- a)-25/15
- b)25/-15
- c)25/15
- d)-25/30
Correct answer is option 'C'. Can you explain this answer?
Which among the following is a rational number equivalent to -5/-3 ?
a)
-25/15
b)
25/-15
c)
25/15
d)
-25/30
|
Malavika Ahuja answered |
Hence the correct answer is 5/3.
Which of the following is the correct arrangement of 
in descending order?- a)
- b)
- c)
- d)
Correct answer is option 'B'. Can you explain this answer?
Which of the following is the correct arrangement of in descending order?
in descending order?a)
b)
c)
d)
|
|
Geetika Shah answered |
LCM of 5,10,15 and 20 which is 60. Now making the denominator same, we have 
. So descending order is 
that is 
. So descending order is that is ________ 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.
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
|
Ujwal Mukherjee answered |
Definition of a Rational Number
A rational number is a fundamental concept in mathematics, particularly in number theory. Here’s a detailed explanation of the correct definition.
Correct Definition
- The correct answer is option B: A number that can be written as p/q, where p and q are integers and q ≠ 0.
Key Features of Rational Numbers
- Fraction Representation: Rational numbers can be expressed as fractions where:
- p: Represents the numerator (an integer).
- q: Represents the denominator (an integer that cannot be zero).
- Integers: Since both p and q are integers, this means that rational numbers can include whole numbers (like 1, 2, 3), negative numbers (-1, -2), and proper or improper fractions (like 1/2, 3/4, 5/3).
Misconceptions in Other Options
- Option A states that a rational number cannot be written as a fraction, which is incorrect.
- Option C claims that a rational number can only be a fraction with positive integers, ignoring negative fractions and zero.
- Option D suggests that rational numbers are not whole numbers or fractions, which is false since whole numbers are also rational (e.g., 3 can be expressed as 3/1).
Conclusion
In summary, the definition of rational numbers is expansive and includes a wide range of numbers that can be expressed in fractional form. Understanding this concept is crucial for further studies in mathematics.
A rational number is a fundamental concept in mathematics, particularly in number theory. Here’s a detailed explanation of the correct definition.
Correct Definition
- The correct answer is option B: A number that can be written as p/q, where p and q are integers and q ≠ 0.
Key Features of Rational Numbers
- Fraction Representation: Rational numbers can be expressed as fractions where:
- p: Represents the numerator (an integer).
- q: Represents the denominator (an integer that cannot be zero).
- Integers: Since both p and q are integers, this means that rational numbers can include whole numbers (like 1, 2, 3), negative numbers (-1, -2), and proper or improper fractions (like 1/2, 3/4, 5/3).
Misconceptions in Other Options
- Option A states that a rational number cannot be written as a fraction, which is incorrect.
- Option C claims that a rational number can only be a fraction with positive integers, ignoring negative fractions and zero.
- Option D suggests that rational numbers are not whole numbers or fractions, which is false since whole numbers are also rational (e.g., 3 can be expressed as 3/1).
Conclusion
In summary, the definition of rational numbers is expansive and includes a wide range of numbers that can be expressed in fractional form. Understanding this concept is crucial for further studies in mathematics.
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
|
|
EduRev Class 8 answered |
The sum of two rational numbers is always a rational number because the sum of two fractions (where the denominator is not zero) always results in another fraction, which remains rational.
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
|
|
EduRev Class 8 answered |
The property used here is the Associative Property of Multiplication. This property states that the grouping of numbers in multiplication does not affect the product. In other words, for any numbers a, b, and c, we have:
a × (b × c) = (a × b) × c
In this case:
1/3 × (6 × 4/3) = (1/3 × 6) × 4/3
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.
What is the average of the two middle rational numbers when 
and 1/9 are arranged in ascending order?- a)1/8
- b)2/7
- c)-3/7
- d)-1/6
Correct answer is option 'D'. Can you explain this answer?
What is the average of the two middle rational numbers when and 1/9 are arranged in ascending order?
and 1/9 are arranged in ascending order?a)
1/8
b)
2/7
c)
-3/7
d)
-1/6
|
|
Arpita Rane answered |
Arranging the given rational numbers in ascending order, we get 
The two middle rational numbers
Their average is 
The two middle rational numbers
Their average is 
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
|
Ipsita Bose answered |
Understanding the Problem
To find the sum of the fractions 3/7, -6/11, -8/21, and 5/22, we need to follow these steps:
Step 1: Find the Least Common Denominator (LCD)
- The denominators are 7, 11, 21, and 22.
- The LCD is the smallest number that all denominators can divide into evenly.
- The prime factorization gives us:
- 7 = 7
- 11 = 11
- 21 = 3 × 7
- 22 = 2 × 11
- The LCD is 462.
Step 2: Convert Each Fraction to the Common Denominator
- Convert each fraction:
- 3/7 = (3 * 66) / 462 = 198/462
- -6/11 = (-6 * 42) / 462 = -252/462
- -8/21 = (-8 * 22) / 462 = -176/462
- 5/22 = (5 * 21) / 462 = 105/462
Step 3: Add the Converted Fractions
- Now, sum the fractions:
- 198/462 + (-252/462) + (-176/462) + 105/462
- Combine the numerators:
- 198 - 252 - 176 + 105 = -125
Step 4: Write the Final Answer
- The sum is -125/462.
Thus, the final result is -125/462, confirming that option 'A' is correct.
To find the sum of the fractions 3/7, -6/11, -8/21, and 5/22, we need to follow these steps:
Step 1: Find the Least Common Denominator (LCD)
- The denominators are 7, 11, 21, and 22.
- The LCD is the smallest number that all denominators can divide into evenly.
- The prime factorization gives us:
- 7 = 7
- 11 = 11
- 21 = 3 × 7
- 22 = 2 × 11
- The LCD is 462.
Step 2: Convert Each Fraction to the Common Denominator
- Convert each fraction:
- 3/7 = (3 * 66) / 462 = 198/462
- -6/11 = (-6 * 42) / 462 = -252/462
- -8/21 = (-8 * 22) / 462 = -176/462
- 5/22 = (5 * 21) / 462 = 105/462
Step 3: Add the Converted Fractions
- Now, sum the fractions:
- 198/462 + (-252/462) + (-176/462) + 105/462
- Combine the numerators:
- 198 - 252 - 176 + 105 = -125
Step 4: Write the Final Answer
- The sum is -125/462.
Thus, the final result is -125/462, confirming that option 'A' is correct.
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).
|
|
Poulomi Yadav answered |
Understanding Rational Numbers and Fractions
To determine which statements are true, we need to clarify the definitions of rational numbers and fractions.
What is a Fraction?
- A fraction is a way of representing a part of a whole. It is expressed as a/b, where "a" is the numerator and "b" is the denominator (b ≠ 0).
- Every fraction can be expressed as a division of two integers.
What is a Rational Number?
- A rational number is any number that can be expressed as a fraction (a/b) where both "a" and "b" are integers and "b" is not zero.
- This means that all fractions are rational numbers.
Analyzing the Statements
- Statement (a): Every fraction is a rational number.
- True! Since every fraction can be expressed in the form a/b, it falls under the definition of a rational number.
- Statement (b): Every rational number is a fraction.
- False! While many rational numbers can be expressed as fractions, some rational numbers can also be whole numbers (e.g., 5 can be expressed as 5/1).
- Statement (c): Every integer is a rational number.
- True! Any integer can be expressed as a fraction by writing it over 1 (e.g., 4 can be written as 4/1).
Conclusion
- Since both statements (a) and (c) are true, the correct answer is option 'D': Both (a) and (c).
- This understanding highlights the relationship between fractions, rational numbers, and integers, providing clarity on their definitions and interconnections.
To determine which statements are true, we need to clarify the definitions of rational numbers and fractions.
What is a Fraction?
- A fraction is a way of representing a part of a whole. It is expressed as a/b, where "a" is the numerator and "b" is the denominator (b ≠ 0).
- Every fraction can be expressed as a division of two integers.
What is a Rational Number?
- A rational number is any number that can be expressed as a fraction (a/b) where both "a" and "b" are integers and "b" is not zero.
- This means that all fractions are rational numbers.
Analyzing the Statements
- Statement (a): Every fraction is a rational number.
- True! Since every fraction can be expressed in the form a/b, it falls under the definition of a rational number.
- Statement (b): Every rational number is a fraction.
- False! While many rational numbers can be expressed as fractions, some rational numbers can also be whole numbers (e.g., 5 can be expressed as 5/1).
- Statement (c): Every integer is a rational number.
- True! Any integer can be expressed as a fraction by writing it over 1 (e.g., 4 can be written as 4/1).
Conclusion
- Since both statements (a) and (c) are true, the correct answer is option 'D': Both (a) and (c).
- This understanding highlights the relationship between fractions, rational numbers, and integers, providing clarity on their definitions and interconnections.
Chapter doubts & questions for Rational Numbers - Online MCQ Tests for Class 8 2025 is part of Class 8 exam preparation. The chapters have been prepared according to the Class 8 exam syllabus. The Chapter doubts & questions, notes, tests & MCQs are made for Class 8 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.
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