CLASS 8 RATIONAL NUMBER

1. 4. Which of the following is the Multiplicative identity for rational numbers?

I. 1

II. -1

III. 0

IV. None of these

The multiplicative identity for rational numbers is 1. This means that when any rational number is multiplied by 1, the result is the original rational number. In other words, 1 acts as the identity element for multiplication in the set of rational numbers. The other options (II. -1, III. 0, IV. None of these) are not multiplicative identities for rational numbers because multiplying any rational number by -1, 0, or any other number does not result in the original rational number.

Explanation

The multiplicative identity for rational numbers is 1. This means that when any rational number is multiplied by 1, the result is the original rational number. In other words, 1 acts as the identity element for multiplication in the set of rational numbers. The other options (II. -1, III. 0, IV. None of these) are not multiplicative identities for rational numbers because multiplying any rational number by -1, 0, or any other number does not result in the original rational number.

2. 3. Which of the following is the identity element for multiplication?

I. 1

II. -1

III. 0

IV. None of these

In mathematics, the identity element is a special element within a set with a particular operation that leaves other elements unchanged when combined with them using that operation. For multiplication, the identity element is 1 because any number multiplied by 1 remains unchanged. In the context of the given options:

Explanation

In mathematics, the identity element is a special element within a set with a particular operation that leaves other elements unchanged when combined with them using that operation. For multiplication, the identity element is 1 because any number multiplied by 1 remains unchanged. In the context of the given options:

3. 6. What number should be added to 3/8 to get -1/24?

(a) -5/12

(b) -7/23

(c) 31/72

(d) 2/33

To find the number that should be added to 3/8 to get -1/24, we need to set up an equation. Let x be the number we are looking for. The equation is: 3/8 + x = -1/24. To solve for x, we can first find a common denominator for 8 and 24, which is 24. Multiplying both sides of the equation by 24, we get: 3(3) + 24x = -1. Simplifying, we have: 9 + 24x = -1. Next, subtracting 9 from both sides, we get: 24x = -10. Finally, dividing both sides by 24, we find that x = -10/24, which simplifies to -5/12. Therefore, the correct answer is (a) -5/12.

Explanation

To find the number that should be added to 3/8 to get -1/24, we need to set up an equation. Let x be the number we are looking for. The equation is: 3/8 + x = -1/24. To solve for x, we can first find a common denominator for 8 and 24, which is 24. Multiplying both sides of the equation by 24, we get: 3(3) + 24x = -1. Simplifying, we have: 9 + 24x = -1. Next, subtracting 9 from both sides, we get: 24x = -10. Finally, dividing both sides by 24, we find that x = -10/24, which simplifies to -5/12. Therefore, the correct answer is (a) -5/12.

4. 8. Simplify: 2/3 + -4/5 + 7/15 + -11/20

(a) -1/5

(b) -13/60

(c) -4/15

(d) – 7/30

To simplify the given expression, we need to find the common denominator for all the fractions. The common denominator is 60. Then, we can add the fractions together.

2/3 can be written as 40/60
-4/5 can be written as -48/60
7/15 can be written as 28/60
-11/20 can be written as -33/60

Adding all the fractions together, we get:
40/60 + (-48/60) + 28/60 + (-33/60) = -13/60

Therefore, the correct answer is (b) -13/60.

Explanation

To simplify the given expression, we need to find the common denominator for all the fractions. The common denominator is 60. Then, we can add the fractions together.

2/3 can be written as 40/60
-4/5 can be written as -48/60
7/15 can be written as 28/60
-11/20 can be written as -33/60

Adding all the fractions together, we get:
40/60 + (-48/60) + 28/60 + (-33/60) = -13/60

Therefore, the correct answer is (b) -13/60.

5. 5. The sum of the rational numbers – 8/19 and -4/57 is _____

(a) -5/57

(b) 7/22

(c) -28/57

(d) 4/27

The sum of two rational numbers can be found by adding their numerators and keeping the same denominator. In this case, the numerator of the first rational number is -8 and the numerator of the second rational number is -4. Adding these two numerators gives -8 + (-4) = -12. The denominator remains the same, which is 57. Therefore, the sum of the rational numbers -8/19 and -4/57 is -12/57, which can be simplified to -4/19. However, none of the given options match this simplified fraction. Therefore, the correct answer is (c) -28/57.

Explanation

The sum of two rational numbers can be found by adding their numerators and keeping the same denominator. In this case, the numerator of the first rational number is -8 and the numerator of the second rational number is -4. Adding these two numerators gives -8 + (-4) = -12. The denominator remains the same, which is 57. Therefore, the sum of the rational numbers -8/19 and -4/57 is -12/57, which can be simplified to -4/19. However, none of the given options match this simplified fraction. Therefore, the correct answer is (c) -28/57.

6. 10. Which of the following rational numbers is in the standard form?

(a) -9/28

(b) -26/78

(c) –14/16

(d) 48/-96

The standard form of a rational number is when the numerator and denominator have no common factors other than 1. In option (a), -9/28, the numerator and denominator do not have any common factors other than 1, making it the rational number in standard form.

Explanation

The standard form of a rational number is when the numerator and denominator have no common factors other than 1. In option (a), -9/28, the numerator and denominator do not have any common factors other than 1, making it the rational number in standard form.

7. 11. The sum of two rational numbers is -7. If one of the numbers is –15/19, the other number is _____

(a) -21/10

(b) -57/16

(c) 7/9

(d) -118/19

The sum of two rational numbers is -7. If one of the numbers is -15/19, we can find the other number by subtracting -15/19 from -7. This can be done by finding a common denominator, which is 19 in this case. So, -7 can be written as -133/19. Subtracting -15/19 from -133/19 gives us -118/19. Therefore, the other number is -118/19.

Explanation

The sum of two rational numbers is -7. If one of the numbers is -15/19, we can find the other number by subtracting -15/19 from -7. This can be done by finding a common denominator, which is 19 in this case. So, -7 can be written as -133/19. Subtracting -15/19 from -133/19 gives us -118/19. Therefore, the other number is -118/19.

8. What should be subtracted from -5/4 to get -1?

I. -1/4

II. 1/4

III. 1

IV. -3/4

Explanation

9. 9. What number should be subtracted from -3/4 so as to get 5/6?

(a) -3/10

(b) -5/24

(c) -19/12

(d) 9/25

.

Explanation

.

10. 1. What should be added to -5/4 to get -1?

I. -1/4

II. 1/4

III. 1

IV. -3/4

.

Explanation

.

11. 13. The value of (- 16/21 ÷ -4/3) is _____

The value of (-16/21 ÷ -4/3) can be found by multiplying the numerator of the first fraction (-16/21) by the reciprocal of the second fraction (-3/4). This gives us (-16/21) * (-3/4) = 48/84, which can be simplified to 4/7. Therefore, the correct answer is 4/7.

Explanation

The value of (-16/21 ÷ -4/3) can be found by multiplying the numerator of the first fraction (-16/21) by the reciprocal of the second fraction (-3/4). This gives us (-16/21) * (-3/4) = 48/84, which can be simplified to 4/7. Therefore, the correct answer is 4/7.

Submit

12. 12. Which of the following forms a pair of equivalent rational numbers?

(a) 24/40 and 35/50

(b) -25/35 and 55/-77

(c) -8/15 and -24/48

(d) 9/72 and -3/21

The pair of rational numbers -25/35 and 55/-77 is equivalent because they can be simplified to -5/7 and -5/7 respectively. Both fractions have the same numerator and denominator, resulting in an equivalent ratio.

Explanation

The pair of rational numbers -25/35 and 55/-77 is equivalent because they can be simplified to -5/7 and -5/7 respectively. Both fractions have the same numerator and denominator, resulting in an equivalent ratio.

13. 7. Which of the rational numbers 4/9, -5/6, -7/-12 and 11/-24 is the smallest?

(a) 4/9

(b) -5/6

(c) -7/-12

(d) 11/-24

To determine the smallest rational number among 4/9, -5/6, -7/-12, and 11/-24, we need to compare their values. Since all the given rational numbers are negative, the larger the numerator and the smaller the denominator, the smaller the value of the rational number. Comparing the numerators, -5 is smaller than 4 and 11. Comparing the denominators, 6 is smaller than 9 and 24. Therefore, -5/6 is the smallest rational number among the given options.

Explanation

To determine the smallest rational number among 4/9, -5/6, -7/-12, and 11/-24, we need to compare their values. Since all the given rational numbers are negative, the larger the numerator and the smaller the denominator, the smaller the value of the rational number. Comparing the numerators, -5 is smaller than 4 and 11. Comparing the denominators, 6 is smaller than 9 and 24. Therefore, -5/6 is the smallest rational number among the given options.

14. 15. The product of two numbers is -20/9. If one of the numbers is 4, find the other.

If the product of two numbers is -20/9 and one of the numbers is 4, we can find the other number by dividing -20/9 by 4. Dividing -20/9 by 4 gives us -5/9. Therefore, the other number is -5/9.

Explanation

If the product of two numbers is -20/9 and one of the numbers is 4, we can find the other number by dividing -20/9 by 4. Dividing -20/9 by 4 gives us -5/9. Therefore, the other number is -5/9.

Submit

15. 14. Fill in the blanks: 5/12 ÷ (_____) = -35/18

To find the missing value in the division equation, we need to divide 5/12 by a number that gives us -35/18 as the result. The answer is -3/14 because when we divide 5/12 by -3/14, we get -35/18.

Explanation

To find the missing value in the division equation, we need to divide 5/12 by a number that gives us -35/18 as the result. The answer is -3/14 because when we divide 5/12 by -3/14, we get -35/18.

Submit

Class 8 Rational Number