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1

UNIT 1

NAME:______________________

PERIOD:_____________________

TEACHER: Ms. Schmidt _

2

Adding and Subtracting Integers

What are integers? _________________________________________________________________________

Part 1: Introduction to Integers:

Name the Integer.

1. a loss of 2 yards _____

2. a withdrawal of $25 _____

3. a deposit of $25 _____

4. 3 inches of rainfall _____

Order these from least to greatest.

5. 3, -8, 0, 11, -7 ____________________________

6. -11, 12, 9, -8, -1 ____________________________

Compare the following using the inequality symbols. Inequality Symbols

7. -2 ____-8 11. 2 ____-8

8. 0 ____-6 12. 0 ____-6

9. -5____-2 13. -5____-2

10. -8____-10 14. -8____-10

Part 2: Adding Numbers

Signs Same Signs Different

1) _______________________

2) _______________________

1) ____________________________

2) ____________________________

Examples:

1. -2 + -3 = 2. -2 + 8 = 3. -6 + 1 =

3


Use the integer rules to solve.

1. -4 + 4 2. 6 + (-3) 3. 10 + -5 + 3

4. 8 + -7 5. – 8 + 2 6. -1 + -7

7. -3 + (-3) 8. 6 + (-6) 9. -2 + - 5 + 3

Part 3: Rules for Subtracting Integers

1) _______________________________________________

2) _______________________________________________

Examples:

1. 6 – 10 2. -3 – 8 3. 4 - -6

Use the integer rules to solve.

1. -2 - -2 2. 7 + -3 3. -12 - 7 + 4

4. -5 – 6 + 2 – 11 5. 5 - 12 6. 8 – (-9)

7. -7 – (-10) 8. -4 - (- 4) 9. -8 + 12 – 9 + 4

More Practice:

1. 9 + -11 2. 13 – 14 3. -15 – 10 4. 20 + - 13

5. -5 + 9 + -6 6. -16 + 21 – 9 7. -5 + 9 + (-6) 8. -8 + 12 – 3

9. ) A football team had a 3 yard gain followed by a 7 yard loss. Find the resulting gain or loss.

4


Write the number that describes each situation:

1. loss of 5 kg _____

2. gain of 3 kg _____

Put in order from least to greatest

3. 10, -5, 1, 12, 0 _________________________________

4. Compare each inequality using the correct symbol

a. 7 __ 4 b. 6 __-13

c. -6 __ -3 d. 7 __ -3

Solve each of the following using the integer rules.

5. -4 + (-4) 6. 8 + (-8)

7. -3 - (-8) 8. 5 - 9

9. 7 – 9 – 8 – 5 10. 7 – 15 – 2

11. -14 + 16 – 1 12. -5 + 1 – 8 + 7

13. In the morning, Mrs. Boxer deposited $135 to her bank account. She withdrew $235 in the afternoon.

What number describes her account’s net change?

5

Multiply and Divide Integers

Rules for Multiplying and Dividing Integers:

Odd number of negative signs Answer – Negative

Even number of negative signs

Answer – Positive

Steps for Multiplying and Dividing

1) ___________________________________________________________

2) ___________________________________________________________

Examples:

1. (-6)(-2) 2. (5)(-3) 3. (-5)(0)

4. -25

5 5. -36 ÷ -9 6.

0

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When 0 is in the numerator of a fraction the answer is _________________.

When 0 is in the denominator of a fraction the answer is _______________.

*** Remember ….. When 0 is Underneath the answer is U____________

Practice:

1. (7)(5) 2. (4)(-9) 3. -32

4 4. 4.5 ÷ -0.9

5. -28

2 6. (-8)(-5) 7.

-3

0 8. (-6)(7)

9. 0

5 10. (-2)(5)(-3)(-2)(6)(-4) 11. -2 ÷ 0 12. (-38)(24)(96)(0)

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What about fractions?

Examples: USE THE CALCULATOR!

1. 3

11+

7

20 2. −

5

4−

3

4 3. −

2

3×

5

4 4.

1

9÷ −1

1

3

Practice: (only use the calculators for fractions!!)

1. 3

7−

1

2 2.

1

3− (−

1

3) 3.

4

9×

7

4 4. -2 ÷ −3

4

5

5. (6)(-7) 6. (-3)(-9) 7. (-9)(0) 8. (-4.2)(0.3)

9. -100 ÷ -10 10. 35÷ -7 11. -12 ÷ 0 12. 0 ÷ 17

13. 6 −1

6 14. −3

5

9 ÷ 3 15. −2

2

3 × 4

1

10 16.

4

5 + 0

7


Simplify.

1. (-3)(9) 2. (-5)(-1)

3. (-9)(0) 4. -52

5

5. (7)(-1)(6)(-8) 6. (-4)(-2)

7. -18 ÷ -9 8. 0

7

Use a calculator for the following.

9. 1

3÷ (−

1

3) 10.

5

9 ×

7

15

11. 1

5+ (−

1

5) 12.

7

6−

5

6

13. 4

7 of birthday cake was eaten on your birthday. The next day your dad ate

1

2 of what was left. You get to

finish the cake. How much was left?

8

Order of Operations

Some mathematical expressions involve several operations. Does the order in which these operations are done

make a difference?

6 + 3 x 4 6 + 3 x 4

9 x 4 = 36 6 + 12 = 18 Which is correct, and why?

Examples:

1. 5 + 2 x 6 2. 10 ÷ 5 x 2 3. 7(1 + 2) – 5 ÷ 5 4. 3 · 4 + 8

15 – 2 · 5

Activity:

1. 2. 3. 4.

5. 6. 7. 8.

9. 10. 11. 12.

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Order of Operations

Simplify each of the following using the order of operations.

1. 2 + 7 x 4 – 15 ÷ 3 + 7 2. 20 ÷ 4 + 3 x 6 – 12 ÷ 4 3. 8(4) + 9 ÷ 3 – 1 x 5

4. 3(8 – 4) + 6 5. (7 – 5)6 + 4 6. 10 – 3(5 – 2)

7. 735)43(2 8. 54215 3 9. 24 ÷ 6 + 33 – 5(2) + (36 ÷ 4)

10. 5(9)+18÷3

2+3(5) 11. (0.9)(0.2) + (0.6)(0.4) 12. (

4

5)(35) – 14 ÷ 7

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Evaluate Expressions

Vocabulary:

Expression - _______________________________________________________________

Equation - _________________________________________________________________

Evaluate - _________________________________________________________________

Name the coefficient: _______ Coefficient - ______________________________________

Name the variable: _______ Variable – ________________________________________

Name the exponent: _______ Exponent – _______________________________________

Steps to Evaluating Algebraic Expressions Problems

1 - __________________________________________________________________________

2 - __________________________________________________________________________

3 - __________________________________________________________________________

Examples:

1. 3x - 2 for x = 4 2. 5(x + 3) when x = 2 3. 3𝑎 + 6

2𝑏 −3𝑐 if a = 8, b = 6, c = 2

Practice:

1. 2a5 if a = 3 2. (2a)5 when a = 3 3. -13 - 5x if x = -2

4. 5x – 2y if x = 3; y = 6 5. 2

5 x + 3 for x = 20 6. 3x + 5y - 8 for x = 3.1; y = -.8

3𝑥2

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Conversion Formulas

Fahrenheit Celsius Celsius Fahrenheit

)32(9

5 FC 32

5

9 CF

Convert the following temperatures:

7. 50 ° C = _____ F 8. 113 ° F = _____ C

9. 19 - 2m for m = 6 10. ab4 if a = 3; b = 2 11. 3x2 if x = 4

12. (3x)2 when x = 4 13. 2x - 3y for x = -8, y = -4 14. 3𝑎−8

2𝑏+4 for a = -2 and b = -3

15. -5m - 6p + 8k for m = -1, p = -2, k = -0.3 16. (4x + 3y)2 + 9 for x = -1

2 and y = -

2

3

Convert the following temperatures:

17. 77 ° F = _____ C 18. 35 ° C = _____ F

12


Evaluate the following expressions:

1. 3x + 4 for x = 6 2. 10 – 3y for y = 2 3. 8 + 6a for a = 3

4. 3a – 2 + 5b for a = 6, b = 2 5. 5a – 4b + 9 for a = 7, b = 2 6. 2

5 a – 3 for a = 10

7. 3d – 6e for d = 5, e = 0.2 8. 6x – 4y for x = −2

3, y = -3 9.

3x+2y

2x+y for x = -4, y = 3

Conversion Formulas

Fahrenheit Celsius Celsius Fahrenheit

)32(9

5 FC 32

5

9 CF

10. What is 194 ° F in Celsius? 11. What is 120 ° C in Fahrenheit?

12. Use the formula h = 60t – 5t2, to answer the following question. If an object is shot upward from the

ground, what is its height (h) above the ground after 5 seconds (t)?

13

Translating Algebraic Expressions

Vocabulary: Sum - _____________________________________________________________________________

Difference - ________________________________________________________________________

Product - __________________________________________________________________________

Quotient - __________________________________________________________________________

x + 5

x – 5

5x

5

x

Remember….

Examples:

1) 3 times a number plus 6 _______ 2) 4 less than a number times 2 _______

3) x divided by 8 _______ 4) 12 subtracted by x ______

Try These: Matching

___ 1) n increased by 11 A) n – 19

___ 2) 11 less than n B) n + 11

___ 3) the sum of n and 19 C) n + 19

___ 4) 11 more than n D) n – 11

___ 5) n increased by 19 E) 19 – n

F) 11 - n

More Than / Less Than

___________________

From

___________________

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Practice:

Write each as an algebraic expression

________ 1) m increased by 8

________ 2) 4 less than c

________ 3) the sum of b and 14

________ 4) 7 decreased by k

________ 5) 3 more than twice d

________ 6) 17 increased by 5 times r

________ 7) 4 less than 6 times w

________ 8) 8 increased by 7 times a number

________ 9) twice Don’s age increased by 8

________ 10) 40 more than Meg’s bowling score

________ 11) the sum of 32 and twice a number

________ 12) Abe’s savings decreased by $540

________ 13) 24 decreased by 4 times a number

________ 14) Bill’s batting average increased by 12

________ 15) 8 times a number, decreased by 14

________ 16) the product of x and y

________ 17) 11 more than x times y

________ 18) the quotient of x and 8

________ 19) the difference of x and 7

________ 20) 3 less than 4 times a number

15


Translate and solve each of the following.

1. The difference of 8 and -9 2. The quotient of -36 and 12

3. The sum of -5 and -8 4. The product of -2 and -6

5. 7 subtracted from -10 6. 8 less than 10

7. 13 less than 6 times 5 8. 20 divided by 2, increased by 4

9. An elevator began on the fourth floor. It went up 6 floors, dropped 3 floors, and then went up another two

floors. What floor did the elevator stop on?

10. On Monday afternoon the temperature was 6°. That night it dropped 8°. What was the temperature on

Tuesday morning?

16

Combine Like Terms

Vocabulary:

Polynomial - ___________________________________________________________________________

Monomial - ____________________________________________________________________________

Binomial - _____________________________________________________________________________

Trinomial - ____________________________________________________________________________

Like terms - ___________________________________________________________________________

Perimeter - ____________________________________________________________________________

Determine if the following are like terms or unlike terms:

1) 3x + 2x² 2) 5xy + x 3) x²y - xy² 4) 4y² - 2y²

5) 0.1ab and 4ab 6) x2y and -5x2y 7) -2ab2 and -2a2b 8) 3x2 and 5x4

Rule:

______________________________________

Examples:

1. 6x + 3x 2. 5x + x 3. 2x + 7 4. -9x + 4x

5. Find the perimeter 6. Find the perimeter 7. Express the perimeter in terms of x:

x

3x - 1

2x + 3

4x + 3

6x + 2

5

9

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Combine Like Terms

Practice:

1. What is the coefficient of p in a + 7p – 21? ______

2. What are the like terms of 7r + 5 + 3r? __________

3. What is the coefficient of a in the expression 4c + 5 + a? __________

4. What are the steps in simplifying 8x + 3 + x + 9? _______________________________________________

Simplify by combining like terms:

5. 2r + 8 + r 6. 8 + 4z + 8k 7. 9 + 3m + m

8. 7 + 6y – 2 – 4y 9. 8 + 11m – 5 – 7m 10. –x – x + 2x

11. x + 9 + x – 8 + 3c 12. 8xy + 4a – 9xy – 6a – 7a 13. 6g + 14 + 3g + g – 5

14. What is the perimeter of a quadrilateral whose sides are 7x - 10, 4x + 8, 2x + 12, and 5x – 10

Express the perimeter in terms of x:

15. 16.

2x + 3

5x – 7y

4x + 3y

x

2x + 3

2x + 1

2x + 1

18

Combine Like Terms

Simplify.

1. g – 5 – 2g + 10 2. -7 – z – 3z + 2

3. c + 8 – 2c – 9 4. -6a + 7b – a – 8b

5. -2d + 9f – 6f + d 6. 8y + z – 9y – 2z + 3

Express the perimeter in terms of x:

7. 8.

Mixed Review:

9. Evaluate 5x – 2y – 7 for x = -2, y = 4 10. -1 – 5 11. -8 x -4

19

Distributive Property

Vocabulary:

Distributive Property - _____________________________________________________________________

Area - ___________________________________________________________________________________

Examples: Simplify each of the following.

1. 2(x + 3) 2. 2(4x – 5y) 3. 3(4x + 5y – 6z + 8)

4. - (-2x + 4) 5. -6(7k + .5) 6. 1

3 (15x + 27)

7. 3

4 (7n + 1) 8. -4(1 + 11x) + 20x 9. -3(5x – 1) -8x

10. Find the area: 11. Find the area of a rectangle whose width is 6 and length is (x + 7).

5

2x + 3

20


Practice:

1. 3(4 + 3y) 2. -2(6x - 8) 3. 1

2 (8n + 2) 4. - (-2 – n)

5. -3(x – 2.6) 6. 8 + 1

7 (7n – 14) 7. 4x + 5(3x – 3) 8. 5(-8n + 5) – 4n

9. -4(3x – 3) + 9(x + 1) 10. 10.8(x - 3.6) 11. – 5

4 ( 4n – 3) 12. -2( -8x – 10)

Express the area in terms of x:

13. 14.

2

2x

+

1

x

x + 6

21


1. - (-6x + 9) 2. -2(3x + .6) 3. 3

4 (7n + 1) 4. 2(1 – 4.3k) – 2

5. -9(3 – 10n) – 3 6. 4(7 – 5n) – 2(3n + 4) *Challenge* 7. 7(2x2 – 3x ) + 10x

8. Find the area of the rectangle. 9. Find the perimeter of the triangle.

10. If Lisa’s yard has a length of 9 and a width of x – 2.

A) Express the amount fertilizer she will need in terms of x.

B) Express the amount of fence she would need to enclose her yard in terms of x.

9x + 7

4 5x - 6 2x - 8

3x

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