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• Order of operations
• Evaluating expressions
• Simplifying algebraic expressions
• Multi-step equations
• Work word problems
• Distance-rate-time word problems
• Mixture word problems
• Absolute value equations
• Multi-step inequalities
• Compound inequalities
• Absolute value inequalities
• Discrete relations
• Continuous relations
• Evaluating and graphing functions
• Review of linear equations
• Graphing absolute value functions
• Graphing linear inequalities
• Direct and inverse variation
• Systems of two linear inequalities
• Systems of two equations
• Systems of two equations, word problems
• Points in three dimensions
• Systems of three equations, elimination
• Systems of three equations, substitution
• Basic matrix operations
• Matrix multiplication
• All matrix operations combined
• Matrix inverses
• Geometric transformations with matrices
• Operations with complex numbers
• Properties of complex numbers
• Rationalizing imaginary denominators
• Properties of parabolas
• Vertex form
• Graphing quadratic inequalities
• Factoring quadratic expressions
• Solving quadratic equations w/ square roots
• Solving quadratic equations by factoring
• Completing the square
• Solving equations by completing the square
• Solving equations with the quadratic formula
• The discriminant
• Naming and simple operations
• Factoring a sum/difference of cubes
• Factoring by grouping
• Factoring quadratic form
• Factoring using all techniques
• Factors and Zeros
• The Remainder Theorem
• Irrational and Imaginary Root Theorems
• Descartes' Rule of Signs
• More on factors, zeros, and dividing
• The Rational Root Theorem
• Polynomial equations
• Basic shape of graphs of polynomials
• Graphing polynomial functions
• The Binomial Theorem
• Evaluating functions
• Function operations
• Inverse functions
• Simplifying radicals
• Operations with radical expressions
• Dividing radical expressions
• Radicals and rational exponents
• Simplifying rational exponents
• Square root equations
• Rational exponent equations
• Graphing radicals
• Graphing & properties of parabolas
• Equations of parabolas
• Graphing & properties of circles
• Equations of circles
• Graphing & properties of ellipses
• Equations of ellipses
• Graphing & properties of hyperbolas
• Equations of hyperbolas
• Classifying conic sections
• Eccentricity
• Systems of quadratic equations
• Graphing simple rational functions
• Graphing general rational functions
• Simplifying rational expressions
• Multiplying / dividing rational expressions
• Adding / subtracting rational expressions
• Complex fractions
• Solving rational equations
• The meaning of logarithms
• Properties of logarithms
• The change of base formula
• Writing logs in terms of others
• Logarithmic equations
• Inverse functions and logarithms
• Exponential equations not requiring logarithms
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• Graphing logarithms
• Graphing exponential functions
• Discrete exponential growth and decay word problems
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• General sequences
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• Comparing Arithmetic/Geometric Sequences
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• Right triangle trig: Evaluating ratios
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• Exact trig ratios of important angles
• The Law of Sines
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• Double-/Half-Angle Identities
• Sample spaces and The Counting Principle
• Independent and dependent events
• Mutualy exclusive events
• Permutations
• Combinations
• Permutations vs combinations
• Probability using permutations and combinations

Simplifying Algebraic Expressions (Algebra 2)

In Algebra 2, algebraic expressions are one of the most important concepts students encounter. They learn how to simplify them or rewrite them in a simplified way. To achieve this, they apply the properties of real numbers and produce an equivalent form of an expression.

Indeed, all the x’s and y’s can come across as tricky, but they’re certainly not impossible to learn! Math teachers can adopt various strategies to support students in becoming fluent in simplifying algebraic expressions. Read on to find out more.

Algebraic Expressions Definition

For starters, remind students of the definition of an algebraic expression. By now, most students should be able to tell you that an algebraic expression is a mathematical expression comprising constants, variables, and operations (such as addition, subtraction, multiplication, etc.).

Give an example, such as 8x + 4. This is a simple algebraic expression, as it contains two constants (the number 8 and 4 which don’t change), a variable (the letter x, which can change), and an operation (subtraction).

Remind children that when algebra problems come as word problems, we must transform these words into algebraic expressions, known as writing algebraic expressions. Substituting a number for each variable and doing the operation is called evaluating algebraic expressions.

Finally, explain that simplifying an algebraic expression means that we’re turning a long expression into something that we can easily make sense of. Then, you can provide an example. For instance, you can say that by using simplification, we can turn 2x 5y – y2 into 4xy.

You may also want to check out our article on writing and evaluating algebraic expressions.

Teaching How to Simplify Algebraic Expressions

Bell-work activity.

In order for students to be able to simplify an algebraic expression, they need to have a solid grasp of the properties of real numbers. This is why it’s advisable to do a few exercises so that you can review previously acquired knowledge in this regard.

You can use this simple Bell-Work Worksheet for this purpose. Print out a sufficient number of copies and distribute them to each student. The worksheet contains exercises on properties of real numbers, such as the distributive property, the commutative property, associative property, etc.

Simplifying Algebraic Expressions

Start by writing an easier example on the whiteboard, such as:

5x – 8 + 3 (2x – 5) = ?

Explain that by applying the distributive property, we’ll get the following expression:

5x – 8 + 6x – 15

Point out to students that when we simplify an algebraic expression, we also need to combine similar terms. Illustrate the like expressions in the above example. You can use a marker to highlight the like expressions in different colors. That is:

That means that:

5x + 6x = 11x

– 8 – 15 = – 23

11x – 23

You can use this video in your classroom to present the process of simplifying algebraic expressions. It starts with simpler examples and gradually moves on to more complicated expressions.

Finally, distribute this Guided Notes Worksheet for even more challenging expressions.

Activities to Practice Simplifying Algebraic Expressions

In Algebra 2, algebraic expressions and their simplification can be mastered with the help of different engaging activities in your classroom. Use the following activities for group work, or adjust them to individual work if you’re a homeschooling parent.

Online Game

Divide children into pairs and explain that they’ll play an online game to practice how to simplify algebraic expressions. Make sure that each student has a suitable device.

Explain to students that each person in the pair will play the game individually on their device. The game consists of answering different math questions related to simplifying algebraic expressions, such as:

Simplify the following expression:

-3(x + y) + 5(x – y)

The game usually offers multiple answers from which the student needs to select one. For each question that a student answers correctly, they score points. In the end, the students compare their scores and the one with the highest score wins the game.

To implement this activity in your classroom, print out enough copies of this Assignment Worksheet , depending on the number of students in your class. Then, divide students into groups of three or four and hand out the copies.

The worksheet contains math problems connected to simplifying algebraic expressions or writing an algebraic expression to the given verbal expression. Each group works together to solve the math problems in the worksheet.

In the end, each group selects one representative to present their answers in front of the class, as well as explain how they reached a specific solution. This activity will encourage cooperation within a group, as well as reinforce presentation skills.

Before You Leave…

In algebra 2, algebraic expressions and the process of simplifying them can be an engaging experience for children if you’re equipped with the right resources!

So, if you liked our math strategies in this article, make sure to check out our resources on simplifying algebraic expressions:

• 1-2 Assignment (PDF)
• 1-2 Assignment SE (PDF)
• 1-2 Bell Work (PDF)
• 1-2 Bell Work SE (PDF)
• 1-2 Exit Quiz – (PDF)
• 1-2 Exit Quiz SE (PDF)
• 1-2 Guided Notes SE (PDF)
• 1-2 Guided Notes TE (PDF)
• 1-2 Lesson Plan (PDF)
• 1-2 Online Activity (PDF)
• 1-2 Slide Show (PDF)

To get the Editable versions of these files, join us inside the Math Teacher Coach Community:

• 1-2 Assignment ( Doc – Members Only )
• 1-2 Bellwork ( Doc – Members Only )
• 1-2 Exit Quiz ( Doc – Members Only )
• 1-2 Guided Notes SE ( Doc – Members Only )
• 1-2 Guided Notes TE ( Doc – Members Only )
• 1-2 Lesson Plan ( Doc – Members Only )
• 1-2 Online Activity ( Doc – Members Only )
• 1-2 Slide Show (PPT – Members Only )

This article is based on:

Unit 1 – Tools of Algebra

• 1-1 Properties of Real Numbers
• 1-2 Algebraic Expressions
• 1-3 Solving Equations
• 1-4 Solving Inequalities
• 1-5 Absolute Value Equations and Inequalities
• 1-6 Probability

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Solve equations and simplify expressions

• Solving equations I
• Solving equations II
• Solving equations III

In algebra 1 we are taught that the two rules for solving equations are the addition rule and the multiplication/division rule. The addition rule for equations tells us that the same quantity can be added to both sides of an equation without changing the solution set of the equation.

$$\begin{array}{lcl} 4x-12 & = & 0\\ 4x-12+12 & = & 0+12\\ 4x & = & 12\\ \end{array}$$

Adding 12 to each side of the equation on the first line of the example is the first step in solving the equation. We did not change the solution by adding 12 to each side since both the second and third equations have the same solution. Equations that have the same solution sets are called equivalent equations.

The multiplication/division rule for equations tell us that every term on both sides of an equation can be multiplied or divided by the same term (except zero) without changing the solution set of the equation.

$$\begin{array}{lcl} 4x-12 & = & 0\\ 4x-12+12 & = & 0+12\\ 4x & = & 12\\ \frac{4x}{4} & = & \frac{12}{4}\\ x & = & 3\\ \end{array}$$

When we simplify an expression we operate in the following order:

• Simplify the expressions inside parentheses, brackets, braces and fractions bars.
• Evaluate all powers.
• Do all multiplications and division from left to right.
• Do all addition and subtractions from left to right.

A useful rule is the denominator-numerator rule which states that the denominator and numerator may be multiplied by the same quantity without changing the value of the fraction.

$$\frac{(2^{2}-2)}{\sqrt{2}}$$

First we simplify the expression inside the parentheses by evaluating the powers and then do the subtraction within it.

$$\frac{(4-2)}{\sqrt{2}}$$

$$\frac{(2)}{\sqrt{2}}$$

We then remove the parentheses and multiply both the denominator and the numerator by √2.

$$\frac{2\cdot \sqrt{2}}{\sqrt{2}\cdot \sqrt{2}}$$

As a last step we do all multiplications and division from left to right.

$$\frac{2\cdot \sqrt{2}}{2}$$

$$\sqrt{2}$$

Video lesson

Solve the given equation

$$12a\left(\frac{3b-b}{4a}\right)=36$$

• Functions and linear equations
• Graph functions and relations
• Graph inequalities
• Solving systems of equations in two variables
• Solving systems of equations in three variables
• Matrix properties
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• Simplify expressions
• Polynomials
• Factoring polynomials
• Solving radical equations
• Complex numbers
• How to graph quadratic functions
• How to solve quadratic equations
• The Quadratic formula
• Standard deviation and normal distribution
• Distance between two points and the midpoint
• Equations of conic sections
• Basic knowledge of polynomial functions
• Remainder and factor theorems
• Roots and zeros
• Descartes' rule of sign
• Composition of functions
• Operate on rational expressions
• Exponential functions
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• Logarithm property
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Algebra II : Simplifying Expressions

Study concepts, example questions & explanations for algebra ii, all algebra ii resources, example questions, example question #1 : simplifying expressions.

Simplify x(4 – x) – x(3 – x).

You must multiply out the first set of parenthesis (distribute) and you get 4x – x 2 . Then multiply out the second set and you get –3x + x 2 . Combine like terms and you get x.

x(4 – x) – x(3 – x)

4x – x 2  – x(3 – x)

4x – x 2 – (3x – x 2 )

4x – x 2 – 3x + x 2 = x

Example Question #1 : How To Divide Trinomials

Factor the numerator and denominator:

Cancel the factors that appear in both the numerator and the denominator:

Example Question #3 : How To Divide Monomial Quotients

Example Question #2 : Simplifying Expressions

Simplify the following:

First, let us factor the numerator:

Example Question #1 : Monomials

Find the product:

First, mulitply the mononomial by the first term of the polynomial:

Second, multiply the monomial by the second term of the polynomial:

Add the terms together:

Example Question #4 : Simplifying Expressions

Multiply, expressing the product in simplest form:

Cross-cancel the coefficients by dividing both 15 and 25 by 5, and both 14 and 21 by 7:

Now use the quotient rule on the variables by subtracting exponents:

Example Question #5 : Simplifying Expressions

In this problem, you have two fractions being multiplied. You can first simplify the coefficients in the numerators and denominators. You can divide and cancel the 2 and 14 each by 2, and the 3 and 15 each by 3:

You can multiply the two numerators and two denominators, keeping in mind that when multiplying like variables with exponents, you simplify by adding the exponents together:

Any variables that are both in the numerator and denominator can be simplified by subtracting the numerator's exponent by the denominator's exponent. If you end up with a negative exponent in the numerator, you can move the variable to the denominator to keep the exponent positive:

Example Question #3 : How To Factor A Variable

Factor the expression:

To find the greatest common factor, we need to break each term into its prime factors:

Example Question #2 : Monomials

To expand, multiply 8x by both terms in the expression (3x + 7).

8x multiplied by 3x is 24x².

8x multiplied by 7 is 56x.

Therefore, 8x(3x + 7) = 24x² + 56x.

None of the other answers are correct.

First, distribute –5 through the parentheses by multiplying both terms by –5.

Then, combine the like-termed variables (–5x and –3x).

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Unit 6: Rational exponents and radicals

About this unit.

We previously learned about integer powers—first positive and then also negative. But what does it mean to raise a number to the 2.5 power? In Algebra 2, we extend previous concepts to include rational powers. We'll define how they work, and use them to rewrite exponential expressions in various ways.

Rational exponents

• Intro to rational exponents (Opens a modal)
• Rewriting roots as rational exponents (Opens a modal)
• Exponential equation with rational answer (Opens a modal)
• Unit-fraction exponents Get 3 of 4 questions to level up!
• Fractional exponents Get 3 of 4 questions to level up!
• Rational exponents challenge Get 3 of 4 questions to level up!

Properties of exponents (rational exponents)

• Rewriting quotient of powers (rational exponents) (Opens a modal)
• Rewriting mixed radical and exponential expressions (Opens a modal)
• Properties of exponents intro (rational exponents) Get 3 of 4 questions to level up!
• Properties of exponents (rational exponents) Get 3 of 4 questions to level up!

Evaluating exponents & radicals

• Evaluating fractional exponents (Opens a modal)
• Evaluating fractional exponents: negative unit-fraction (Opens a modal)
• Evaluating fractional exponents: fractional base (Opens a modal)
• Evaluating quotient of fractional exponents (Opens a modal)
• Evaluating mixed radicals and exponents (Opens a modal)
• Evaluate radical expressions challenge Get 3 of 4 questions to level up!

Equivalent forms of exponential expressions

• Rewriting exponential expressions as A⋅Bᵗ (Opens a modal)
• Equivalent forms of exponential expressions (Opens a modal)
• Rewrite exponential expressions Get 3 of 4 questions to level up!
• Equivalent forms of exponential expressions Get 3 of 4 questions to level up!

Solving exponential equations using properties of exponents

• Solving exponential equations using exponent properties (Opens a modal)
• Solving exponential equations using exponent properties (advanced) (Opens a modal)
• Rational exponents and radicals: FAQ (Opens a modal)
• Solve exponential equations using exponent properties Get 3 of 4 questions to level up!
• Solve exponential equations using exponent properties (advanced) Get 3 of 4 questions to level up!

Algebra 2 Worksheets with answer keys

Enjoy these free printable math worksheets . Each one has model problems worked out step by step, practice problems, as well as challenge questions at the sheets end. Plus each one comes with an answer key.

• Absolute Value Equations
• Simplify Imaginary Numbers
• Adding and Subtracting Complex Numbers
• Multiplying Complex Numbers
• Dividing Complex Numbers
• Dividing Complex Number (advanced)
• End of Unit, Review Sheet
• Exponential Growth (no answer key on this one, sorry)
• Compound Interest Worksheet #1 (no logs)
• Compound Interest Worksheet (logarithms required)
• Simplify Rational Exponents
• Solve Equations with Rational Exponents
• Solve Equations with variables in Exponents
• Factor by Grouping
• 1 to 1 functions
• Evaluating Functions
• Composition of Functions
• Inverse Functions
• Operations with Functions
• Functions Review Worksheet
• Product Rule of Logarithms
• Power Rule of Logarithms
• Quotient Rule of Logarithms
• Logarithmic Equations Worksheet
• Dividing Polynomials Worksheet
• Solve Quadratic Equations by Factoring
• Solve Quadratic Equations by Completing the Square
• Quadratic formula Worksheet (real solutions)
• Quadratic Formula Worksheet (complex solutions)
• Quadratic Formula Worksheet (both real and complex solutions)
• Discriminant Worksheet
• Sum and Product of Roots
• Radical Equations
• Rationalizing the Denominator
• Simplify Rational Expressions Worksheet
• Dividing Rational Expressions
• Multiplying Rational Expressions
• Adding and Subtracting Rational Expressions (with like denominators)
• Adding and Subtracting Ratioal Expressions with Unlike Denominators
• Mixed Review on Rational Expressions

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• Newton Raphson
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• Difference of Squares
• Difference of Cubes
• Sum of Cubes
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• FOIL method
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• Expand Power Rule
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• Exponent Rules
• Exponential Form
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• Absolute Value
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• Powers of i
• Complex Form
• Partial Fractions
• Is Polynomial
• Leading Coefficient
• Leading Term
• Standard Form
• Complete the Square
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• Rationalize Denominator
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• Identify Type
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• How do you solve algebraic expressions?
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• The basics of algebra are the commutative, associative, and distributive laws.
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• The basic rules of algebra are the commutative, associative, and distributive laws.
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• The golden rule of algebra states Do unto one side of the equation what you do to others. Meaning, whatever operation is being used on one side of equation, the same will be used on the other side too.
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• The basic laws of algebra are the Commutative Law For Addition, Commutative Law For Multiplication, Associative Law For Addition, Associative Law For Multiplication, and the Distributive Law.

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2.2: Use the Language of Algebra (Part 2)

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Simplify Expressions Using the Order of Operations

We’ve introduced most of the symbols and notation used in algebra, but now we need to clarify the order of operations. Otherwise, expressions may have different meanings, and they may result in different values. For example, consider the expression: \[4 + 3 \cdot 7 \nonumber\]

Imagine the confusion that could result if every problem had several different correct answers. The same expression should give the same result. So mathematicians established some guidelines called the order of operations, which outlines the order in which parts of an expression must be simplified.

Definition: Order of Operations

When simplifying mathematical expressions perform the operations in the following order:

• P arentheses and other Grouping Symbols
• Simplify all expressions inside the parentheses or other grouping symbols, working on the innermost parentheses first.
• Simplify all expressions with exponents.
• M ultiplication and D ivision
• Perform all multiplication and division in order from left to right. These operations have equal priority.
• A ddition and S ubtraction
• Perform all addition and subtraction in order from left to right. These operations have equal priority.

Students often ask, “How will I remember the order?” Here is a way to help you remember: Take the first letter of each key word and substitute the silly phrase. P lease E xcuse M y D ear A unt S ally.

It’s good that ‘ M y D ear’ goes together, as this reminds us that m ultiplication and d ivision have equal priority. We do not always do multiplication before division or always do division before multiplication. We do them in order from left to right.

Similarly, ‘ A unt S ally’ goes together and so reminds us that a ddition and s ubtraction also have equal priority and we do them in order from left to right.

Example \(\PageIndex{8}\): simplify

Simplify the expressions:

• \(4 + 3 • 7\)
• \((4 + 3) • 7\)

exercise \(\PageIndex{15}\)

• \(12 − 5 • 2\)
• \((12 − 5) • 2\)

exercise \(\PageIndex{16}\)

• \(8 + 3 • 9\)
• \((8 + 3) • 9\)

Example \(\PageIndex{9}\): simplify

• \(18 ÷ 9 • 2\)
• \(18 • 9 ÷ 2\)

exercise \(\PageIndex{17}\)

Simplify: \(42 ÷ 7 • 3\)

exercise \(\PageIndex{18}\)

Simplify: \(12 • 3 ÷ 4\)

Example \(\PageIndex{10}\): simplify

Simplify: \(18 ÷ 6 + 4(5 − 2)\).

exercise \(\PageIndex{19}\)

Simplify: \(30 ÷ 5 + 10(3 − 2)\)

exercise \(\PageIndex{20}\)

Simplify: \(70 ÷ 10 + 4(6 − 2)\)

When there are multiple grouping symbols, we simplify the innermost parentheses first and work outward.

Example \(\PageIndex{11}\): simplify

Simplify: \(5 + 2^3 + 3[6 − 3(4 − 2)]\).

exercise \(\PageIndex{21}\)

Simplify: \(9 + 5^3 − [4(9 + 3)]\)

exercise \(\PageIndex{22}\)

Simplify: \(7^2 − 2[4(5 + 1)]\)

Example \(\PageIndex{12}\): simplify

Simplify: \(2^3 + 34 ÷ 3 − 5^2\).

exercise \(\PageIndex{23}\)

Simplify: \(3^2 + 2^4 ÷ 2 + 4^3\)

exercise \(\PageIndex{24}\)

Simplify: \(6^2 − 5^3 ÷ 5 + 8^2\)

Access Additional Online Resources

• Order of Operations
• Order of Operations – The Basics
• Ex: Evaluate an Expression Using the Order of Operations
• Example 3: Evaluate an Expression Using The Order of Operations

Key Concepts

• \(a=b\) is read as \(a\) is equal to \(b\)
• The symbol \(=\) is called the equal sign.
• \(a<b\) is read \(a\) is less than \(b\)

• \(a>b\) is read \(a\) is greater than \(b\)

• For any expression \(a^n\) is a factor multiplied by itself \(n\) times, if \(n\) is a positive integer.

• The expression of \(a^n\) is read \(a\) to the \(n^{th}\) power.

Order of Operations When simplifying mathematical expressions perform the operations in the following order:

• Parentheses and other Grouping Symbols: Simplify all expressions inside the parentheses or other grouping symbols, working on the innermost parentheses first.
• Exponents: Simplify all expressions with exponents.
• Multiplication and Division: Perform all multiplication and division in order from left to right. These operations have equal priority.
• Addition and Subtraction: Perform all addition and subtraction in order from left to right. These operations have equal priority.

An expression is a number, a variable, or a combination of numbers and variables and operation symbols.

An equation is made up of two expressions connected by an equal sign.

Practice Makes Perfect

Use variables and algebraic symbols.

In the following exercises, translate from algebraic notation to words.

• 16 − 9
• 25 − 7
• 28 ÷ 4
• 45 ÷ 5
• y − 1 > 6
• y − 4 > 8
• 2 ≤ 18 ÷ 6
• 3 ≤ 20 ÷ 4
• a ≠ 7 • 4
• a ≠ 1 • 12

Identify Expressions and Equations

In the following exercises, determine if each is an expression or an equation.

• 9 • 6 = 54
• 7 • 9 = 63
• 5 • 4 + 3
• 6 • 3 + 5
• y − 5 = 25
• y − 8 = 32

Simplify Expressions with Exponents

In the following exercises, write in exponential form.

• 3 • 3 • 3 • 3 • 3 • 3 • 3
• 4 • 4 • 4 • 4 • 4 • 4
• x • x • x • x • x
• y • y • y • y • y • y

In the following exercises, write in expanded form.

In the following exercises, simplify.

• (a) 3 + 8 • 5 (b) (3+8) • 5
• (a) 2 + 6 • 3 (b) (2+6) • 3
• 2 3 − 12 ÷ (9 − 5)
• 3 2 − 18 ÷ (11 − 5)
• 3 • 8 + 5 • 2
• 4 • 7 + 3 • 5
• 2 + 8(6 + 1)
• 4 + 6(3 + 6)
• 4 • 12 / 8
• 2 • 36 / 6
• 6 + 10 / 2 + 2
• 9 + 12 / 3 + 4
• (6 + 10) ÷ (2 + 2)
• (9 + 12) ÷ (3 + 4)
• 20 ÷ 4 + 6 • 5
• 33 ÷ 3 + 8 • 2
• 20 ÷ (4 + 6) • 5
• 33 ÷ (3 + 8) • 2
• 3(1 + 9 • 6) − 4 2
• 5(2 + 8 • 4) − 7 2
• 2[1 + 3(10 − 2)]
• 5[2 + 4(3 − 2)]

Everyday Math

• Basketball In the 2014 NBA playoffs, the San Antonio Spurs beat the Miami Heat. The table below shows the heights of the starters on each team. Use this table to fill in the appropriate symbol (=, <, >).
• Height of Tim Duncan____Height of Rashard Lewis
• Height of Boris Diaw____Height of LeBron James
• Height of Kawhi Leonard____Height of Chris Bosh
• Height of Tony Parker____Height of Dwyane Wade
• Height of Danny Green____Height of Ray Allen
• Elevation In Colorado there are more than 50 mountains with an elevation of over 14,000 feet. The table shows the ten tallest. Use this table to fill in the appropriate inequality symbol.
• Elevation of La Plata Peak____Elevation of Mt. Antero
• Elevation of Blanca Peak____Elevation of Mt. Elbert
• Elevation of Gray’s Peak____Elevation of Mt. Lincoln
• Elevation of Mt. Massive____Elevation of Crestone Peak
• Elevation of Mt. Harvard____Elevation of Uncompahgre Peak

Writing Exercises

• Explain the difference between an expression and an equation.
• Why is it important to use the order of operations to simplify an expression?

(a) After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

(b) If most of your checks were:

…confidently. Congratulations! You have achieved the objectives in this section. Reflect on the study skills you used so that you can continue to use them. What did you do to become confident of your ability to do these things? Be specific.

…with some help. This must be addressed quickly because topics you do not master become potholes in your road to success. In math, every topic builds upon previous work. It is important to make sure you have a strong foundation before you move on. Who can you ask for help? Your fellow classmates and instructor are good resources. Is there a place on campus where math tutors are available? Can your study skills be improved?

…no—I don’t get it! This is a warning sign and you must not ignore it. You should get help right away or you will quickly be overwhelmed. See your instructor as soon as you can to discuss your situation. Together you can come up with a plan to get you the help you need.

Contributors and Attributions

• Lynn Marecek (Santa Ana College) and MaryAnne Anthony-Smith (formerly of Santa Ana College). This content produced by OpenStax and is licensed under a  Creative Commons Attribution License 4.0  license.