Review of Algebraic Thinking and Operations

Intro to Algebra Lesson Review

By Greg Cimenski

What is an Algebraic Expression?

An algebraic expression in mathematics is an expression that is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms. 

Multiple Choice

What makes an algebraic expression?

• There is more than one operation

• There are variables (letters)

• There are only numbers

Variables, Coefficients, Constants & Terms

• In the expression pictured, x is a variable, whose value is unknown to us which can take any value.

• 5 is known as the coefficient of x, as it is a constant value used with the variable term and is well defined.

• 3 is the constant value term which has a definite value

• The whole expression has two terms. Terms are separated by addition and subtraction signs.

Multiple Choice

Identify the constant in the expression.

2y + x + 8 + 7p

• 7

• 2

• 1

• 8

Multiple Choice

Identify the coefficient in the expression.

6y + 7

• 6y

• 7

• 6

• 1

Multiple Choice

Identify the Variable in the expression 5y+7?

• x

• 5y

• y

• 7

Multiple Choice

How many terms are in the algebraic expression?

2y + x + 4 + y²

• 4

• 3

• 5

• 2

Multiple Choice

How many coefficients are in this expression?

• 1

• 2

• 3

• 4

Multiple Choice

What is 8 in the following expression?

72b - 8 + 9h + 2

• constant

• variable

• expression

• coefficient

Multiple Choice

How many terms are in the expression
3x + 2y + z

• 5

• 2

• 4

• 3

Multiple Select

Select all that apply. An expression can contain ...

• coefficients

• variables

• an equal sign

• constants

Multiple Choice

Determine whether the given value of the variable is a solution.

w + 19 = 49 for w=30

• Yes

• No

Multiple Choice

Determine whether the given value of the variable is a solution.

d + 27 = 81 for d = 44

• Yes

• No

Multiple Choice

Determine whether the given value of the variable is a solution.

101 = 144 - q for q = 38

• Yes

• No

Multiple Choice

Determine whether the given value of the variable is a solution.

$$105\ =\ p\ \times\ 7\ \ \ \ \ \ for\ p\ =\ 14$$  

• Yes

• No

Multiple Choice

Determine whether the given value of the variable is a solution.

$$49\ \div\ r\ =7\ \ \ \ for\ r\ =\ 7$$  

• Yes

• No

​Translating words in math...​

Here are some examples

3 minus the product of 8 and r is written 3 - 8r

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18 times w and the sum of 2 and t is written as 18w + 2t

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Notice that the coefficient and the variable are written next to each other with no operation sign between them. When you see this it is understood that the operation is multiplication.

Multiple Choice

Which operation do you use when writing an expression to describe this scenario? Joe collected $5 from his grandmother and $12 from his Aunt. How much did he receive in total?

• addition

• subtraction

• multiplication

• division

Multiple Choice

the product of x and sixteen

• x + 16

• x - 16

• 16x

• x/16

Multiple Choice

the difference between forty-six and a number

• 46 x n

• 46/n

• n-46

• 46 − n

Multiple Choice

46 less than a number

• 46 - n

• n - 46

• 46 + n

• n + 46

Multiple Choice

Translate this phrase into an algebraic expression.
8 less than the product of 4 and a number
Use the variable m to represent the unknown number.

• 8 - 4m

• 8m - 4

• 8m + 4

• 4m - 8

Multiple Choice

What is the expression used in the table?

• 5n + 1

• n + 13 

• 6n - 2

Multiple Choice

What is the expression used in the table?

• d + 13 

• 3d - 1 

• 2d + 6

Multiple Choice

What is the expression used in the table?

• 8g

• 32

• g/8

• 4

Multiple Choice

Find the expression.
x                  y
4                 8
8                16
3                 6
7                14

• x + 4
• 2x
• x + 2
• x - 4

using inverse operations (opposite)

​

isolate the variable

Solving Equations

• Use inverse operation to isolate the variable

• Keep the equation balanced by performing the operation to both sides of the equal sign.

Solve y +14=20

• The inverse operation of addition is subtraction.

• Subtract 14 from both sides of the equal sign

• 20-14=6

• y=6

Solve x -120 = 80

• The inverse operation of subtraction is addition

• Add 120 to both sides of the equal sign.

• 80 +120= 200

• x=200

Solve 3n=12

• The inverse operation of multiplication is division

• Divide both sides by 3

• 12/3=4

• n=4

• The inverse operation of division  is multiplication 

• Multiply both sides by 2

• 16(2)=32

• k=32

Multiple Choice

What is the inverse operation of Multiplication?

• addition

• subtraction

• multiplication

• division

Multiple Choice

What is the inverse operation of addition?

• addition

• subtraction

• multiplication

• division

Multiple Choice

What is the inverse operation of subtraction?

• addition

• subtraction

• multiplication

• division

Multiple Choice

What is the inverse operation of Division?

• addition

• subtraction

• multiplication

• division

Solving 1-step Equations

Fill in the Blanks

Vocabulary

• Parts of an expression are called terms.

• Like terms are terms that have the same variables raised to the same exponent.

• Constants are numbers. They are also like terms.

​Examples:

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​Non-Examples:

When they are "like terms" you can combine (add) them

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​Like Terms: terms that have the SAME variable(s)

​

​Example: 4x and 17x

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​Unlike Terms: terms that DO NOT have the same variable(s)

​

​Example: 4x and 17xy

​Vocabulary

​Combine Like Terms: take multiple like terms and make them one

​

​Another word used is SIMPLIFY.

​Vocabulary

Multiple Choice

Which of the following is equivalent to $$8m-10m$$  

• $$2m$$  

• $$18m$$  

• $$-2m$$  

• $$180m$$  

Multiple Choice

Which of the following expressions is equivalent to $$5x\ +\ 9x$$  ?

• $$-4x$$  

• $$45x$$  

• $$14x^2$$  

• $$14x$$  

Multiple Choice

Which of the following is equivalent to  $$12xy\ -3\ +4xy\ -xy\ +5$$  

• $$15xy+2$$  

• $$16xy+8$$  

• $$17x^2y$$  

• $$17xy+8$$  

Multiple Choice

Simplify the following expressions by combining like terms:

m + m + m + 5 + 4

• 9m

• 5m + 4

• 3m + 9

• 3m

Multiple Choice

Please simplify the following expression by combining like terms:

p + p + p

• 3p

• p + p + p

• 2P + 3

Multiple Choice

Please simplify the following expression by combining like terms:

8w - 6w + 3w

• 8w - 6w + 3w

• 2w + 3

• 14 + 3w

• 5w

Solving 2-step Equations

Our Goal

• Isolate the variable on one side of the equal sign

Our Strategy

• Keep it balanced

• What you do to one side, do to the other side

Use Inverse Operations to isolate the variable

• Inverse of addition - subtraction

• Inverse of subtraction - addition

• Inverse of multiplication - division

• Inverse of division - multiplication

Multiple Select

Check all of the equations that require you to use ADDITION to isolate the variable.

• g - 8 = 9

• y + 5 = 15

• d - 2 = 4

• r + 6 = 10

• m - 9 = 8

Multiple Select

Check all of the equations that require you to use SUBTRACTION to isolate the variable.

• g + 8 = 9

• y - 5 = 15

• d + 2 = 4

• r - 6 = 10

• m + 9 = 12

This next equation is going to look a little different...

We are not going to solve it completely yet, but I think we can figure out the first step.

Multiple Choice

How would you isolate "4x" in this equation?

4x - 3 = 17

• subtract 3 from both sides

• add 3 to both sides

• divide both sides by 3

• multiply both sides by 3

Multiple Choice

How do we isolate the "x" and get it all by itself in Step 2?

4x - 3 = 17

Step 2.... 4x = 20

• subtract 4 from both sides

• add 4 to both sides

• divide both sides by 4

• multiply both sides by 4

Multiple Choice

What is the first step to solving this problem? Remember, our first step involves ADDING or SUBTRACTING.

2x + 5 = 11

• subtract 5 from both sides

• add 5 to both sides

• divide both sides by 5

• multiply both sides by 5

Multiple Choice

What is the second step not that we have 2x = 6? How do we isolate the "x" and get it all by itself?

• subtract 2 from both sides

• add 2 to both sides

• divide both sides by 2

• multiply both sides by 2

Multiple Choice

When solving 2 step equations, what is our first step?

• undo addition and subtraction first

• undo multiplication and division second

Multiple Choice

What is the first step to solve this equation:

$$11-3x=44$$  

• Add 3 to both sides

• Subtract 11 from both sides

• Add 11 to both sides

• Divide 3 on both sides.