The Real Number System

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| By Harrisritac

Harrisritac

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Quizzes Created: 2 | Total Attempts: 340

Questions: 10 | Attempts: 108 | Updated: Feb 13, 2024

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Bell Work for Algebra I Monday September 16, 2013

Questions and Answers

1.

What is the sum of 25 and its opposite?
- A.
  
  -50
- B.
  
  0
- C.
  
  25
- D.
  
  50
Correct Answer
B. 0

Explanation
Additive Inverse Property states that the sum of a number and its additive inverse (opposite) will always equal zero (0).

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2.

Which of the following is NOT a rational number?
- A.
  
  -(30/6)
- B.
  
  63/5
- C.
  
  9.8
- D.
  
  3.456789120
Correct Answer
D. 3.456789120

Explanation
Irrational numbers cannot be written as fractions, are not repeating or terminating decimals.

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3.

Simplify:
- A.
  
  10
- B.
  
  23
- C.
  
  50
- D.
  
  54
Correct Answer
B. 23

Explanation
According to the Order of Operations, perform the operations with the parenthesis first, next evaluate the power (exponents), multiply and divide from left to right (direction in which reading is done). Last add and/or subtract from left to right.

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4.

Name the property that is applied in this problem: (72 + 5) + 16 = 72 + ( 5 + 16)
- A.
  
  Commutative Property
- B.
  
  Associative Property
- C.
  
  Distributive Property
- D.
  
  Additive Identity
Correct Answer
B. Associative Property

Explanation
The Commutative Property deals with the order in which numbers are added or multiplied. The Associative Property deals with the grouping of numbers when adding or multiplying. The Distributive Property involves 2 operations, one of which must be multiplication the other operation can be addition or subtraction. The Additive identity states that when zero (0) is added to a number, the results is the original number.

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5.

What property is shown in this problem: 5(2 + 15) = (5)(2) + (5)(15)?
- A.
  
  Commutative Property
- B.
  
  Associative Property
- C.
  
  Distributive Property
- D.
  
  Multiplicative identity
Correct Answer
C. Distributive Property

Explanation
The two operations present are multiplication and addition. The Distributive Property is the only property of real numbers that involves two mathematical operations.

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6.

What property is illustrated by: (35)(45) = 1575 (45)(35) = 1575
- A.
  
  Commutative Property
- B.
  
  Associative Property
- C.
  
  Distributive Property
- D.
  
  Additive Identity
Correct Answer
A. Commutative Property

Explanation
The order in which the two numbers is different, therefore the commutative property is illustrated.

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7.

Simplify:
- A.
  
  468
- B.
  
  234
- C.
  
  0
- D.
  
  -234
Correct Answer
B. 234

Explanation
The absolute value is the distance that a number is from zero (0) on the number line. Distance is always thought of as positive, therefore the absolute value of a number is always positive.

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8.

Simplify: -
- A.
  
  45
- B.
  
  -45
- C.
  
  0
- D.
  
  90
Correct Answer
B. -45

Explanation
Read as the opposite of the absolute value of 45, the answer is -45. Remember that the opposite of any positive number is negative.

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9.

What is the reciprocal of -3/2?
- A.
  
  3/2
- B.
  
  2/3
- C.
  
  -2/3
- D.
  
  6
Correct Answer
C. -2/3

Explanation
Turn the fraction upside down and keep the sign.

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10.

The product of a number and its reciprocal always equals one
- A.
  
  True
- B.
  
  False
Correct Answer
A. True

Explanation
The product of a number and its reciprocal always equals one because the reciprocal of a number is the number that, when multiplied by the original number, gives a product of 1. This is a fundamental property of reciprocals, where any non-zero number multiplied by its reciprocal will result in the multiplicative identity, which is 1. Therefore, the statement is true.

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