Mathematical Expressions Return to Table of Contents Slide 5 / - - PDF document

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7th Grade Math

Expressions

2015-11-17 www.njctl.org

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Mathematical Expressions Order of Operations The Distributive Property Like Terms Translating Words Into Expressions Evaluating Expressions Glossary & Standards

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Mathematical Expressions

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Slide 4 / 185 Expressions

Algebra extends the tools of arithmetic, which were developed to work with numbers, so they can be used to solve real world problems. This requires first translating words from your everyday language (i.e. English, Spanish, French) into mathematical expressions. Then those expressions can be operated on with the tools

• riginally developed for arithmetic.

Slide 5 / 185 Expressions

An Expression may contain: numbers, variables, mathematical operations Example: 4x + 2 is an algebraic expression.

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There are two terms: 4x; 2

What is a Term?

Terms of an expression are the parts of the expression which are separated by addition or subtraction. Circle the terms of this expression. Example: 4x + 2

Circle the terms and then click to check.

Slide 7 / 185 What is a Constant?

A constant is a fixed value, a number on its own, whose value does not change. A constant may either be positive

• r negative.

Example: 4x + 2 In this expression 2 is the constant.

Circle the constant and then click to check.

Slide 8 / 185 What is a Variable?

A variable is any letter or symbol that represents a changeable or unknown value. In this expression x is the variable. Example: 4x + 2

Circle the variable and then click to check.

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What is a Coefficient?

A coefficient is a number multiplied by a variable. It is located in front of the variable. In this expression 4 is the coefficient. Example: 4x + 2

Circle the coefficient and then click to check.

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If a variable contains no visible coefficient, the coefficient is 1. Example 1: x + 7 is the same as (1)x + 7 Example 2: -x + 7 is the same as (-1)x + 7

Coefficient Slide 11 / 185

1 In 2x - 12, the variable is "x". True False

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2 In 6y + 20, the variable is "y". True False

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3 In 3x + 4, the coefficient is 3. True False

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4 In 9x + 2, the coefficient is 2. True False

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5 What is the constant in 7x - 3? A 7 B x C 3 D

• 3

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6 What is the coefficient in - x + 3? A none B 1 C

• 1

D 3

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7 x has a coefficient. True False

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8 ) 19 has a coefficient. True False

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Order of Operations

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Slide 20 / 185 Order of Operations

Mathematics has its grammar, just like any language. Grammar provides the rules that allow us to write down ideas so that a reader can understand them. A critical set of those rules is called the order of operations.

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Order of Operations

The order of operations allows us to read an expression and interpret it as intended. It lets us understand what the author meant. For instance, the below expression could mean many different things without an agreed upon order of operations. How would you evaluate this expression? (5-8)(5)(3)-42÷2+8÷4+(3-2)

Slide 22 / 185 Use Parentheses

Parentheses will make your life much easier. Each time you do an operation, keep the result in parentheses until you use it for the next operation. You'll be able to read your own work, and avoid mistakes. When you're done, read each step you did and you should be able to check your work. Also, when you substitute a value into an expression, put it in parentheses first...that'll save you a lot of trouble.

Slide 23 / 185 Order of Operations

Do all operations in parentheses first. Then, do all exponents and roots. (5-8)(5)(3)-42÷2+8÷4+(3-2) (-3)(5)(3)-42÷2+8÷4+(1) (-3)(5)(3)-(16)÷2+8÷4+1 Then, do all multiplication and division. (-45)-(8)+(2)+1 Then, do all addition and subtraction.

• 50

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Order of Operations

One acronym used for the order of operations is PEMDAS which stands for: Parentheses Exponents/Roots Multiplication/Division Addition/Subtraction This order helps you read an expression...but it also helps you write expressions that others can read. Since parentheses are always done first, you can always eliminate confusion by putting parentheses around what you want to be done first. They may not be needed, but they don't ever hurt.

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Let's simplify this step by step... What should you do first? 5 - (-2) = 5 + 2 = 7 What should you do next? (-3)(7) = -21 What is your last step?

• 7 + (-21) = -28
• 7 + (-3)[5 - (-2)]

click to reveal click to reveal click to reveal

Order of Operations Slide 26 / 185

Let's simplify this step by step... What should you do first? What should you do second?

Click to Reveal Click to Reveal

Order of Operations Slide 27 / 185

Let's simplify this step by step... What should you do third? What should you do last?

Click to Reveal Click to Reveal

Order of Operations Slide 28 / 185

9 Simplify the expression.

• 12÷ 3(-4)

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10 Simplify the expression. [-1 - (-5)] + [7(3 - 8)]

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11 Simplify the expression. 40 - (-5)(-9)(2)

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12 Simplify the expression. 5.8 - 6.3 + 2.5

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13 Simplify the expression.

• 3(-4.7)(5-3.2)

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14 Simplify the expression.

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15 Complete the first step of simplifying. What is your answer? [3.2 + (-15.6)] - 6[4.1 - (-5.3)]

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16 Complete the next step of simplifying. What is your answer? [3.2 + (-15.6)] - 6[4.1 - (-5.3)]

• 12.4 - 6[4.1 - (-5.3)]

click to reveal step from previous slide

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17 Complete the next step of simplifying. What is your answer? [3.2 + (-15.6)] - 6[4.1 - (-5.3)]

• 12.4 - 6[9.4]
• 12.4 - 6[4.1 - (-5.3)]

click to reveal steps from previous slides

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18 Complete the next step of simplifying. What is your answer? [3.2 + (-15.6)] - 6[4.1 - (-5.3)]

• 12.4 - 56.4
• 12.4 - 6[9.4]
• 12.4 - 6[4.1 - (-5.3)]

click to reveal steps from previous slides

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20 Simplify the expression.

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21 Simplify the expression

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22 Simplify the expression

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23 Simplify the expression (-4.75)(3) - (-8.3)

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Solve this one in your groups.

Order of Operations Slide 44 / 185

How about this one?

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24 Simplify the expression

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25 Simplify the expression [(-3.2)(2) + (-5)(4)][4.5 + (-1.2)]

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26 Simplify the expression

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27 Simplify the expression

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28 Simplify the expression

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29 Evaluate the expression (9 - 13)2 ÷ 2(3 - 1) + 9 ∙ 8 - (5 + 6)

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30 Evaluate the expression 7 ∙ 9 − (7 − 4)3 ÷ 9 + (10 − 12)

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31 Evaluate the expression (7 + 3)2 ÷ 25 + 4 ∙ 2 - (7 + 8)

Slide 53 / 185 Order of Operations and Fractions

The simplest way to work with fraction is to imagine that the numerator and the denominator are each in their

• wn set of parentheses.

Before you divide the numerator by the denominator, you must have them both in simplest form. And, then you must be very careful about what you can do with them.

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Order of Operations and Fractions

For instance, a common error is shown below: I CANNOT divide the top and the bottom by x to get: Rather, I have to think of the denominator (1+x) as being in parentheses. Until I can simplify that further (which I can't) this is the simplest form. x 1+x 1 1+1 x (1+x) x 1+x

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How would you evaluate this expression? (4)(3)-32÷5+6÷2+(5-8) 7-8

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(4)(3)-32÷5+6÷2+(5-8) 7-8 (4)(3)-32÷5+6÷2+(5-8) (7-8) First, recognize that terms in a denominator act like they are in parentheses. Then, do all operations in parentheses first. (Keep all results in parentheses until the next operation.) Then, do all exponents and roots. (4)(3)-32÷5+6÷2+(-3) (-1) (4)(3)-(9)÷5+6÷2+(-3) (-1)

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Order of Operations

(4)(3)-9÷5+6÷2+(-3) (-1) Then, all multiplication and division Then, do all addition and subtraction. Then, divide the numerator by the denominator. (12)-(1.8)+(3)+(-3) (-1) (10.2) (-1) (-10.2)

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32 Simplify the expression.

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33 Evaluate the expression 3(5 − 3)3 + 5(7 + 5) − 9 2 ∙ 5 + 5

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34 Evaluate the expression 2(9 − 4)2 + 8 ∙ 6 − 3 3 ∙ 42 + 2

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35 Evaluate the expression −4(2 − 8)2 + 7(−3) + 15 5(25 − 12)

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36 Select the correct number from each group of numbers to complete the equation. A 2 B -2 C 3/4 D -4/3 E 2 F -2 G 4/3 H -3/4

_____ _____

From PARCC EOY sample test non-calculator #6

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The Distributive Property

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Slide 65 / 185 Area Model

4 x 2 Write an expression for the area of a rectangle whose width is 4 and whose length is x + 2

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Area Model

4 x 2 You can think of this as being two rectangles. One has an area of (4)(x) and the other has an area of (4)(2) An expression for the total area would be 4x + 8 Or as one large rectangle of area (4)(x+2).

Slide 67 / 185 Distributive Property

Finding the area of each rectangle demonstrates the distributive property. 4(x + 2) 4(x) + 4(2) 4x + 8 The 4 is distributed to each term of the sum (x + 2).

Slide 68 / 185 Distributive Property

Now you try: 6(x + 4) = 5(x + 7) =

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Write an expression equivalent to: 2(x - 1) 4(x - 8)

Distributive Property Slide 70 / 185 Distributive Property

a(b + c) = ab + ac Example: 2(x + 3) = 2x + 6 (b + c)a = ba + ca Example: (x + 7)3 = 3x + 21 a(b - c) = ab - ac Example: 5(x - 2) = 5x - 10 (b - c)a = ba - ca Example: (x - 3)6 = 6x - 18

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The Distributive Property can be used to eliminate parentheses, so you can then combine like terms.

Distributive Property

For example: 3(4x - 6) 3(4x) - 3(6) 12 x - 18

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The Distributive Property can be used to eliminate parentheses, so you can then combine like terms.

Distributive Property

For example:

• 2(x + 3)
• 2(x) + -2(3)
• 2x + -6
• 2x - 6

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The Distributive Property can be used to eliminate parentheses, so you can then combine like terms.

Distributive Property

For example:

• 3(4x - 6)
• 3(4x) - -3(6)
• 12x - -18
• 12x + 18

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38 Simplify 4(7x + 5) using the distributive property. A 7x + 20 B 28x + 5 C 28x + 20

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39 Simplify -6(2x + 4) using the distributive property. A 12x + 4 B -12x + 24 C 12x - 4 D -12x - 24

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40 Simplify -3(5m - 8) using the distributive property. A -35m - 8 B -15m + 24 C 15m - 24 D -15m - 24

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A negative sign outside of the parentheses represents a multiplication by (-1).

Distributing a Negative Sign

For example:

• (3x + 4)

(-1)(3x + 4) (-1)(3x) + (-1)(4)

• 3x - 4

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41 Use the Distributive Property to simplify the expression.

• (6x - 7)

A -6x + 7 B -6x - 7 C 6x - 7 D 6x + 7

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42 Use the Distributive Property to simplify the expression.

• (-x - 9)

A -x + 9 B x - 9 C -x - 9 D x + 9

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43 Use the Distributive Property to simplify the expression.

• (2x + 5)

A -2x + 5 B -2x - 5 C 2x - 5 D 2x + 5

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44 Use the Distributive Property to simplify the expression.

• (-5x + 3)

A -5x + 3 B -5x - 3 C 5x - 3 D 5x + 3

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45 ) 4(x + 6) is the same as 4 + 4(6). True False

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46 Use the distributive property to rewrite the expression without parentheses. 2(x + 5) A 2x + 5 B 2x + 10 C x + 10 D 7x

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47 Use the distributive property to rewrite the expression without parentheses. 3(x - 6) A 3x - 6 B 3x - 18 C x - 18 D 15x

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48 Use the distributive property to rewrite the expression without parentheses.

• 4(x - 9)

A

• 4x - 36

B 4x - 36 C

• 4x + 36

D 32x

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49 Use the distributive property to rewrite the expression without parentheses.

• (4x - 2)

A

• 4x - 2

B 4x - 2 C

• 4x + 2

D 4x + 2

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50 Use the distributive property to rewrite the expression without parentheses. 0.6(3.1x + 17) A B C D 1.86x + 10.2 186x + 102 1.86x + 17 .631x + .617

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51 Use the distributive property to rewrite the expression without parentheses. 0.5(10x - 15) A B C D 5x - 7.5 5x - 15 10x - 7.5 5x - 75

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52 Use the distributive property to rewrite the expression without parentheses. 1.3(6x + 49) A B C D 7.8x + 63.7 78x + 637 7.8x + 49 1.36x + 1.349

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Like Terms

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Like Terms: Terms in an expression that have the same variable(s) raised to the same power Like Terms 6x and 2x 5y and 8y 4x2 and 7x2 NOT Like Terms 6x and x2 5y and 8 4x2 and x4

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53 Identify all of the terms like 5y. A 5 B 4y2 C 18y D 8y E

• 1y

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54 Identify all of the terms like 8x. A 5x B 4x2 C 8y D 8 E

• 10x

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55 Identify all of the terms like 8xy. A 5x B 4x2y C 3xy D 8y E

• 10xy

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56 Identify all of the terms like 2y. A 51y B 2w C 3y D 2x E

• 10y

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57 Identify all of the terms like 14x2. A 5x B 2x2 C 3y2 D 2x E

• 10x2

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58 Identify all of the terms like 0.75x5. A 75x B 75x5 C 3y2 D 2x E

• 10x5

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59 Identify all of the terms like A 5x B 2x2 C 3y2 D 2x E

• 10x2

2 3 x

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60 Identify all of the terms like A 5x B 2x C 3x2 D 2x2 E

• 10x

1 4 x2

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Simplify by combining like terms 6x + 3x (6 + 3)x 9x Notice when combining like terms you add/subtract the coefficients but the variable remains the same.

Combining Like Terms Slide 101 / 185

Simplify by combining like terms 4 + 5(x + 3) 4 + 5(x) + 5(3) 4 + 5x + 15 5x + 19 Notice when combining like terms you add/subtract the coefficients but the variable remains the same.

Combining Like Terms Slide 102 / 185

Simplify by combining like terms 7y - 4y (7 - 4)y 3y Notice when combining like terms you add/subtract the coefficients but the variable remains the same.

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61 Simplify the expression 8x + 9x. A x B 17x C -x D cannot be simplified

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62 Simplify the expression 7y - 5y. A 2y B 12y C -2y D cannot be simplified

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63 Simplify the expression 6 + 2x + 12x. A 6 + 10x B 20x C 6 + 14x D cannot be simplified

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64 Simplify the expression 7x + 7y. A 14xy B 14x C 14y D cannot be simplified

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Teachers: Use the Math Practice tab to assist with questioning on the next 10 slides

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65 ) 8x + 3x is the same as 11x. True False

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66 ) 7x + 7y is the same as 14xy. True False

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67 ) 4x + 4x is the same as 8x2. True False

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68 ) -12y + 4y is the same as -8y. True False

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69 ) -3 + y + 5 is the same as 2y. True False

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70 ) -3y + 5y is the same as 2y. True False

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71 ) 7x - 3(x - 4) is the same as 4x +12. True False

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72 ) 7 + 5(x + 2) is the same as 5x + 9. True False

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73 ) 4 + 6(x - 3) is the same as 6x -14. True False

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74 ) 3x + 2y + 4x + 12 is the same as 9xy + 12. True False

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75 The lengths of the sides of home plate in baseball are represented by the expressions in the accompanying figure. Which expression represents the perimeter of the home plate? A 5xyz B 2x + 2yz C 2x + 3yz D 2x + 2y + yz yz y y x x

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x x+2 x+3

7

x x+2 x+3

7

76 Find an expression for the perimeter of the octagon. A x +24 B 6x + 24 C 24x D 30x

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Translating Words Into Expressions

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Slide 121 / 185 Translating Between Words and Expressions

Key to solving algebra problems is translating words into mathematical expressions. The two steps to doing this are: 1. Taking English words and converting them to mathematical words. 2. Taking mathematical words and converting them into mathematical symbols. We're going to practice the second of these skills first, and then the first...and then combine them.

Slide 122 / 185 Addition

List words that indicate addition.

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Subtraction

List words that indicate subtraction.

Slide 124 / 185 Multiplication

List words that indicate multiplication.

Slide 125 / 185 Division

List words that indicate division.

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Be aware of the difference between "less" and "less than". For example: "Eight less three" and "three less than eight" are equivalent expressions, so what is the difference in wording? Eight less three: 8 - 3 Three less than eight: 8 - 3 When you see "less than", take the second number minus the first number.

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As a rule of thumb, if you see the words "than" or "from" it means you have to reverse the order

• f the two numbers or variables when you write the expression.

Reverse the Order

Examples: · 8 less than b means b - 8 · 3 more than x means x + 3 · x less than 2 means 2 - x

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The many ways to represent multiplication. How do you represent "three times a"? (3)(a) 3(a) 3 a 3a The preferred representation is 3a. When a variable is being multiplied by a number, the number (coefficient) is always written in front of the variable. The following are not allowed: 3xa ... The multiplication sign looks like another variable a3 ... The number is always written in front of the variable

Multiplication Slide 129 / 185

How do you represent "b divided by 12"? b ÷ 12 b ∕ 12 b 12

Representation of Division Slide 130 / 185 Sort the words by operation.

Quotient Product Sum Total Ratio Difference Less Than More Fraction Multiply Per

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Three times j Eight divided by j j less than 7 5 more than j 4 less than j

1 2 3 4 5 6 7 8 9 + - . ÷

Translate the Words into Algebraic Expressions Using the Red Characters

j Slide 132 / 185

The sum of twenty-three and m

Write the Expression Slide 133 / 185

The product of four and k

Write the Expression Slide 134 / 185

Twenty-four less than d

Write the Expression Slide 135 / 185

**Remember, sometimes you need to use parentheses for a quantity.** Four times the difference of eight and j

Write the Expression Slide 136 / 185

The product of seven and w, divided by 12

Write the Expression Slide 137 / 185

The square of the sum of six and p

Write the Expression Slide 138 / 185

77 The sum of 100 and h A 100 h B 100 + h C 100 - h D 100 + h 200

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78 The quotient of 200 and the quantity of p times 7 A 200 7p B 200 - (7p) C 200 ÷ 7p D 7p 200

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79 Thirty five multiplied by the quantity r less 45 A 35r - 45 B 35(45) - r C 35(45 - r) D 35(r - 45)

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80 a less than 27 A 27 - a B a 27 C a - 27 D 27 + a

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Now, we know how to translate a mathematical sentence in words to a mathematical expression in symbols. Next, we need to practice translating from English sentences to mathematical sentences. Then, we can translate from English sentences to mathematical expressions.

Translating English Sentences to Mathematical Sentences Slide 143 / 185

Write a mathematical sentence, in words, for the below. Then translate that into a mathematical expression. The total amount of money my friends have, if each

• f my seven friends has x dollars.

Translating From English Sentences

7 multiplied by x 7x

click for mathematical sentence click for mathematical expression

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Write a mathematical sentence, in words, for the below. Then translate that into a mathematical expression.

Translating From English Sentences

12 added to x x + 12 click for mathematical sentence click for mathematical expression My age if I am x years older than my 12 year old brother

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Write a mathematical sentence, in words, for the below. Then translate that into a mathematical expression.

Translating From English Sentences

The total of 15 minus 5 divided by 2 (15-5)/2 click for mathematical expression click for mathematical sentence How many apples each person gets if starting with 15 apples, 5 are eaten and the rest are divided equally by 2 friends.

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Write a mathematical sentence, in words, for the below. Then translate that into a mathematical expression.

Translating From English Sentences

d divided by s d/s click for mathematical expression click for mathematical sentence My speed if I travel d meters in s seconds

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Write a mathematical sentence, in words, for the below. Then translate that into a mathematical expression.

Translating From English Sentences

r multiplied by 28 28r click for mathematical expression click for mathematical sentence How much money I make if I earn r dollars per hour and work for 28 hours

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Write a mathematical sentence, in words, for the below. Then translate that into a mathematical expression.

Translating From English Sentences

6 less than two times h 2h - 6 click for mathematical expression click for mathematical sentence My height if I am 6 inches less than twice the height of my sister, who is h inches tall

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81 The total number of jellybeans if Mary had 5 jellybeans for each of 4 friends. A 5 + 4 B 5 - 4 C 5 x 4 D 5 ÷ 4

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82 If n + 4 represents an odd integer, the next larger

• dd integer is represented by

A n + 2 B n + 3 C n + 5 D n + 6

From the New York State Education Department. Office of Assessment Policy, Development and

• Administration. Internet. Available from www.nysedregents.org/IntegratedAlgebra; accessed 17, June, 2011.

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83 Jenny earns $15 an hour waitressing plus $150 in tips

• n a Friday night. What expression represents her

total earnings? A 150 - 15h B h 150 C 15h + 150 D 15 + h

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84 Bob's age if he is 2 years less than double the age of his brother who is z years old? A 2z + 2 B z 2 C 2z - 2 D z - 2 Answer

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When choosing a variable, there are some letters that are often avoided: l, i, t, o, O, s, S Why might these letters be avoided? It is best to avoid using letters that might be confused for numbers or operations. In the case above (1, +, 0, 5) Click

Variables Slide 154 / 185

85 Bob has x dollars. Mary has 4 more dollars than Bob. Write an expression for Mary's money. A 4x B x - 4 C x + 4 D 4x + 4

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86 The width of the rectangle is five inches less than its length. The length is x inches. Write an expression for the width. A 5 - x B x - 5 C 5x D x + 5

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87 Frank is 6 inches taller than his younger brother, Pete. Pete's height is P. Write an expression for Frank's height. A 6P B P + 6 C P - 6 D 6

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88 A dog weighs three pounds more than twice the weight of a cat, whose weight is c pounds. Write an expression for the dog's weight. A 2c + 3 B 3c + 2 C 2c + 3c D 3c

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89 Write an expression for Mark's test grade, given that he scored 5 less than Sam who earned a score of x. A 5 - x B x - 5 C 5x D 5

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90 Tim ate four more cookies than Alice. Bob ate twice as many cookies as Tim. If x represents the number of cookies Alice ate, which expression represents the number of cookies Bob ate? A 2 + (x + 4) B 2x + 4 C 2(x + 4) D 4(x + 2)

From the New York State Education Department. Office of Assessment Policy, Development and Administration.

• Internet. Available from www.nysedregents.org/IntegratedAlgebra; accessed 17, June, 2011.

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Evaluating Expressions

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Slide 161 / 185 Evaluating Expressions

When evaluating algebraic expressions, the process is fairly straight forward.

• 1. Write the expression.
• 2. Substitute in the value of the variable (in parentheses).
• 3. Simplify/Evaluate the expression.

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Evaluate (4n + 6)2 for n = 1

Write: Substitute: Simplify: (4n + 6)2 (4(1) + 6)2 (4 + 6)2 (10)2 100

Slide 163 / 185 Evaluate 4(n + 6)2 for n = 2

Write: Substitute: Simplify: 4(n + 6)2 4((2) + 6)2 4(8)2 4(64) 256

Slide 164 / 185 Evaluate (4n + 6)2 for n = -1

Write: Substitute: Simplify: (4n + 6)2 (4(-1) + 6)2 ((-4) + 6)2 (2)2 4

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108 114 130 128 118 116 106

Let x = 8, then use the magic looking glass to reveal the correct value of the expression

12x + 23

104

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118 128 130 114 20 800 72

4x + 2x3

24 Let x = 2, then use the magic looking glass to reveal the correct value of the expression

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91 Evaluate 3h + 2 for h = 3

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92 Evaluate 2(x + 2)2 for x = -10

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93 Evaluate 2x2 for x = 3

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94 Evaluate 4p - 3 for p = 20

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95 Evaluate 3x + 17 when x = -13

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96 Evaluate 3a for a = -12 9

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97 Evaluate 4a + for a = 8, c = -2 c a

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98 If t = -3, then 3t2 + 5t + 6 equals A

• 36

B

• 6

C 6 D 18

From the New York State Education Department. Office of Assessment Policy, Development and Administration.

• Internet. Available from www.nysedregents.org/IntegratedAlgebra; accessed 17, June, 2011.

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99 Evaluate 3x + 2y for x = 5 and y = 1 2

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100 Evaluate 8x + y - 10 for x = and y = 50 1 4

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Glossary & Standards

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Back to Instruction

Coefficient

The number multiplied by the variable and is located in front of the variable.

4x + 2 These are not coefficients. These are constants! Tricky! 1x + 7

• 1x2 +18

When not present, the coefficient is assumed to be 1. 7 3 5

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Constant

A fixed number whose value does not

• change. It is either positive or negative.

4x + 2 7x 3y 3z

These are not

• constants. These

are coefficients!

Tricky! 7 4 69 110 8 0.45 1/2 π

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The Distributive Property

A property that allows you to multiply all the terms on the inside of a set of parenthesis by a term on the outside of the parenthesis. a(b + c) = ab + ac a(b + c) = ab + ac a(b - c) = ab - ac 3(2 + 4) = (3)(2) + (3)(4) = 6 + 12 = 18 3(2 - 4) = (3)(2) - (3)(4) = 6 - 12 = -6 3(x + 4) = 48 (3)(x) + (3)(4) = 48 3x + 12 = 48 3x = 36 x = 12

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Expression

An expression contains: number, variables, and at least one operation.

4x + 2 7x = 21 11 = 3y + 2 11 - 1 = 3z + 1 Remember! 7x "7 times x" "7 divided by x" 7 x

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Like Terms

Terms in an expression that have the same variable raised to the same power.

3x 5x 15.7x x 1/2x

• 2.3x

27x3

• 2x3

x3 1/4x3

• 5x3

2.7x3 5x3 5x 5x2 5 5x4 NOT LIKE TERMS!

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Variable

Any letter or symbol that represents a changeable or unknown value.

4x + 2 l, i, t, o, O, s, S x y z u v any letter towards end of alphabet!

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Standards for Mathematical Practices Click on each standard to bring you to an example of how to meet this standard within the unit. MP8 Look for and express regularity in repeated reasoning. MP1 Make sense of problems and persevere in solving them. MP2 Reason abstractly and quantitatively. MP3 Construct viable arguments and critique the reasoning of others. MP4 Model with mathematics. MP5 Use appropriate tools strategically. MP6 Attend to precision. MP7 Look for and make use of structure.

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