Review for Arithmetic of Real Numbers Knowledge Check

Introduction

On the Arithmetic of Real Numbers Knowledge Check, you will be assessed on the following content learning outcomes for MATH 096:[br][list][*]Classify numbers as natural, integer, whole, irrational, rational, and real.[/*][*]Evaluate and simplify arithmetic expressions without the use of a calculator.[/*][*]Simplify algebraic expressions using the properties of real numbers.[/*][*]Evaluate algebraic expressions.[/*][/list][br]This was created for you to use as a review to help you prepare for the Arithmetic of Real Numbers Knowledge Check. This review is NOT counted toward your grade in MATH 096.

Section 1: Classifying Numbers

In this first section, you will practice classifying numbers as natural/counting, integers, whole, irrational, rational, and real numbers.

1.1

From the set of numbers below, list the ⓐ whole numbers, ⓑ integers, ⓒ rational numbers, ⓓ irrational numbers, ⓔ real numbers for each set of numbers.[br][br][center]-8, 0, 1.95286..., [math]\frac{12}{5}[/math], [math]\sqrt{36}[/math], 9[/center][br][center][/center]

1.2

From the set of numbers below, list the ⓐ whole numbers, ⓑ integers, ⓒ rational numbers, ⓓ irrational numbers, ⓔ real numbers for each set of numbers.[br][br][center]-9, [math]-3\frac{4}{9}[/math], [math]-\sqrt{9}[/math], [math]0.409409409...[/math], [math]\frac{11}{6}[/math], 0.77, 7, [math]\sqrt{3}[/math], [math]\pi[/math][/center][br][center][/center]

Section 2: Order of Operations

In this section section, the review questions will focus on simplifying expressions using the order of operations.

2.1

Simplify.[br][br][math]20\div4+6\left(5-1\right)[/math]

2.2

Simplify.[br][br][math]3\left(12\div4\cdot2\right)-4^2[/math]

2.3

Simplify.[br][br][math]8+2\left[7-2\left(5-3\right)\right]-3^2[/math]

2.4

Simplify.[br][br][math]\frac{7\cdot4-2\left(8-5\right)}{9\cdot3-3\cdot5}[/math]

Section 3

Section three will focus on simplify algebraic expressions by removing parentheses and combining like terms.

3.1

Simplify.[br][br][math]43m+\left(-12n\right)+\left(-16m\right)-\left(9n\right)[/math]

3.2

Simplify.[br][br][math]9\left(\frac{5}{9}y-\frac{1}{3}\right)[/math]

3.3

Simplify.[br][br][math]\left(5m-3\right)-\left(m+7\right)[/math]

3.4

Simplify.[br][br][math]11\left(n-7\right)-5\left(n-1\right)[/math]

3.5

Simplify.[br][br][math]\frac{1}{6}\left(24y-18x\right)-\frac{1}{3}\left(3y-27x\right)[/math]

Section 4: Evaluating Algebraic Expressions

In section 4, you will focus on reviewing how to evaluate algebraic expressions for the given value of the variable.

4.1

Evaluate [math]\left|9a-2b\right|-8[/math], when a= -6 and b= -3

4.2

Evaluate [math]\frac{x+y}{x-2y}[/math] when x=4 and y=2.