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Explanation To find what should be added to -5/4 to get -1, we need to find the difference between -1 and -5/4. This can be done by subtracting -5/4 from -1. The result is 1/4, which means that 1/4 should be added to -5/4 to get -1. Therefore, option II. 1/4 is the correct answer.
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2.
2. What should be subtracted from -5/4 to get -1?
A.
I. -1/4
B.
II. 1/4
C.
III. 1
D.
IV. -3/4
Correct Answer A. I. -1/4
Explanation To find the value that should be subtracted from -5/4 to get -1, we need to find the difference between these two values. The difference between -5/4 and -1 can be found by subtracting -1 from -5/4. This can be done by adding the additive inverse of -1 to -5/4. The additive inverse of -1 is 1, so we add 1 to -5/4. This gives us -5/4 + 1 = -5/4 + 4/4 = -1/4. Therefore, the value that should be subtracted from -5/4 to get -1 is -1/4.
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3.
3. Which of the following is the identity element?
A.
I. 1
B.
II. -1
C.
III. 0
D.
IV. None of these
Correct Answer A. I. 1
Explanation The identity element in mathematics is an element that, when combined with another element using a specific operation, leaves that element unchanged. In this question, the options are 1, -1, 0, and None of these. Out of these options, only 1 satisfies the condition of being an identity element. When 1 is combined with any other element using addition or multiplication, the result is always the other element itself. Therefore, 1 is the identity element in this case.
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4.
4. Which of the following is the Multiplicative identity for rational numbers?
A.
I. 1
B.
II. -1
C.
III. 0
D.
IV. None of these
Correct Answer A. I. 1
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.
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5.
5. The sum of the rational numbers – 8/19 and -4/57 is _____
A.
(a) -5/57
B.
(b) 7/22
C.
(c) -28/57
D.
(d) 4/27
Correct Answer C. (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.
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6.
6. What number should be added to 3/8 to get -1/24?
A.
(a) -5/12
B.
(b) -7/23
C.
(c) 31/72
D.
(d) 2/33
Correct Answer A. (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.
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7.
7. Which of the rational numbers 4/9, -5/6, -7/-12 and 11/-24 is the smallest?
A.
(a) 4/9
B.
(b) -5/6
C.
(c) -7/-12
D.
(d) 11/-24
Correct Answer B. (b) -5/6
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.
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8.
8. Simplify: 2/3 + -4/5 + 7/15 + -11/20
A.
(a) -1/5
B.
(b) -13/60
C.
(c) -4/15
D.
(d) – 7/30
Correct Answer B. (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.
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9.
9. What number should be subtracted from -3/4 so as to get 5/6?
A.
(a) -3/10
B.
(b) -5/24
C.
(c) -19/12
D.
(d) 9/25
Correct Answer C. (c) -19/12
Explanation To find the number that should be subtracted from -3/4 to get 5/6, we need to subtract -3/4 from 5/6. This can be done by finding a common denominator for both fractions, which is 12. Converting -3/4 and 5/6 to have a denominator of 12, we get -9/12 and 10/12 respectively. Subtracting -9/12 from 10/12 gives us 19/12. Therefore, the number that should be subtracted from -3/4 to get 5/6 is -19/12.
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10.
10. Which of the following rational numbers is in the standard form?
A.
(a) -9/28
B.
(b) -26/78
C.
(c) –14/16
D.
(d) 48/-96
Correct Answer A. (a) -9/28
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.
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11.
11. The sum of two rational numbers is -7. If one of the numbers is –15/19, the other number is _____
A.
(a) -21/10
B.
(b) -57/16
C.
(c) 7/9
D.
(d) -118/19
Correct Answer D. (d) -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.
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12.
12. Which of the following forms a pair of equivalent rational numbers?
A.
(a) 24/40 and 35/50
B.
(b) -25/35 and 55/-77
C.
(c) -8/15 and -24/48
D.
(d) 9/72 and -3/21
Correct Answer B. (b) -25/35 and 55/-77
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.
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13.
13. The value of (- 16/21 ÷ -4/3) is _____
Correct Answer 4/7
Explanation The value of (-16/21 รท -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.
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14.
14. Fill in the blanks: 5/12 ÷ (_____) = -35/18
Correct Answer -3/14
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.
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15.
15. The product of two numbers is -20/9. If one of the numbers is 4, find the other.
Correct Answer -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.