AnswersAPSB 2025 Math Essentials-ALPGraphing Two-Variable Linear Inequalities

Real Numbers Answers

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1
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Choose all true statements.

A
All real numbers are rational numbers.
B
Some rational numbers are natural numbers.
C
No real numbers are irrational numbers.
D
All whole numbers are integers.
E
Some integers are natural numbers.
F
No rational numbers are integers.
2
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Choose all the sets containing the number –1.576.

A
natural numbers
B
whole numbers
C
integers
D
rational numbers
E
irrational numbers
F
real numbers
3

Choose all the sets containing the number

Question illustration
A
natural numbers
B
whole numbers
C
integers
D
rational numbers
E
irrational numbers
F
real numbers
4

Which expression illustrates the associative property of addition?

A
(3 + 19) – 12 = (3 + 12) – 19
B
3 + (19 – 12) = 3 + (19 + 12)
C
(3 + 19) – 12 = 3 + (19 – 12)
D
3 + (19 –12) = 3 – (19 + 12)
5

Complete the statement below.The expression ✔ 11 × w x 3 = 11 × 3 × w11 × w x 3= 11 × w × 3(11 × w) × 3 = 11 × (w × 3)11 × (w × 3) = (11 × w ) + (11 × 3) illustrates the commutative property of multiplication.

A
✔ 11 × w x 3 = 11 × 3 × w
B
11 × w x 3= 11 × w × 3
C
(11 × w) × 3 = 11 × (w × 3)
D
11 × (w × 3) = (11 × w ) + (11 × 3)
6

Complete the statement below.The property can be used to remove the parentheses in the expression 1.7(x + 9).

Answer:

distributive

7

Write the expression 3x + 4 using words. Choose the correct phrase below.

A
the sum of three times a number and four
B
the product of four times a number and three
C
the quotient of three times a number and four
D
the sum of three and four times a number
8

Write the expression “the sum of seven times a number and five, divided by the sum of negative two times the number and eleven” using algebra. Choose the correct phrase below.

A
(–2x + 11) ÷ (7x + 5)
B
(–2x + 11) + (7x ÷ 5)
C
(7x + 5) + (–2x ÷ 11)
D
(7x + 5) ÷ (–2x + 11)
9

Under what operations are the set of integers closed? Explain your answer.

Answer:

The integers are closed under addition, subtraction, and multiplication because these operations on integers always produce another integer. They are not closed under division; for example, 1 ÷ 3 = 1/3, which is not an integer.

10

Which of the following facts did your answer include?

A
The set of integers is closed under addition, subtraction, and multiplication.
B
The set of integers is not closed under division.
C
Give a counterexample to show that the integers are not closed under division. For example, 1 divided by 3 is not an integer.

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