Question

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1. which of the following number sets does not include $-sqrt{25}$?

a. real numbers
b. integers
c. whole numbers
d. rational numbers

1. which of the following is a true statement?

a. all real numbers are rational numbers.
b. all whole numbers are natural numbers.
c. all integers are whole numbers.
d. all natural numbers are integers.

1. which equation illustrates the associative property of addition?

a. $(x + y) + 3 = x + (y + 3)$
b. $3(x + y) = 3x + 3y$
c. $x + y = y + x$
d. $x + 0 = x$

1. which equation illustrates the inverse property of multiplication?

a. $a cdot 1 = a$
b. $a cdot 0 = 0$
c. $a cdot \frac{1}{a} = 1$
d. $a - a = 0$

1. which property justifies the statement below?

\if $-4x = 28$, then $28 = -4x$\
a. commutative property
b. symmetric property
c. identity property
d. transitive property

1. simplify the numerical expression $2^3 cdot 21 + 15 div 3$

a. 47
b. 61
c. 96
d. 173

1. evaluate the expression if $x = -5$ and $y = -2$.

$3x^2 - |y|$
a. 73
b. 77
c. -73
d. -77

1. simplify the expression below:

$4(n - 3) - 2(-3 + n)$
a. $2n - 6$
b. $2n + 6$
c. $4n - 18$
d. $6n - 2$

Explanation:

Question 1

Step1: Simplify \(-\sqrt{25}\)

\(-\sqrt{25} = - 5\)

Step2: Analyze each number set

• Real Numbers: Include all rational and irrational numbers, \(-5\) is real.
• Integers: Include whole numbers and their negatives, \(-5\) is an integer.
• Whole Numbers: Start from \(0,1,2,\dots\), \(-5\) is not a whole number.
• Rational Numbers: Numbers that can be written as \(\frac{p}{q}\) (\(q

eq0\)), \(-5=\frac{-5}{1}\) is rational.

• Option A: Real numbers include irrational numbers (e.g., \(\sqrt{2}\)) which are not rational, so A is false.
• Option B: Whole numbers include \(0\), natural numbers start from \(1\), so \(0\) is a whole number but not a natural number, B is false.
• Option C: Integers include negative numbers (e.g., \(-1\)) which are not whole numbers, C is false.
• Option D: Natural numbers (\(1,2,3,\dots\)) are all integers, D is true.

• Associative property of addition: \((a + b)+c=a+(b + c)\).
• Option A: \((x + y)+3=x+(y + 3)\) follows associative property of addition.
• Option B: \(3(x + y)=3x + 3y\) is distributive property.
• Option C: \(x + y=y + x\) is commutative property of addition.
• Option D: \(x + 0=x\) is identity property of addition.

Answer:

C. Whole Numbers

Question 2