+/-

(-5)(-9) =

45

The exponential form of 2 x 2 x 2 x 2 is

2 to the fourth power

Evaluate: 2y2 for y = -6

2(-6)2 = 2(36) = 72

Evaluate: A decorator wishes to put a wallpaper boarder around a rectangle room that measures 17 ft. x 20 ft. Find the room perimeter.

2(17) + 2(20) = 34 + 40 = 74 feet

To evaluate 2a + 3b -5 for a = 2 and b = 3, which expression shows the CORRECT first step? a. 2(2) + 3(2) -5 b. 2(3) + 3(3) -5 c. 2(3) + 3(2) -5 d. 2(2) + 3(3) -5

2(2) + 3(3) -5

Which of the following is an example of the Distributive Property? a. 2(x + 3) = 2(3 + x) b. 2(x + 3) = 2x + 6 c. 2x + 3 = 3 + 2x d. 2 + (x + 3) = (2 + x) + 3

2(x + 3) = 2x + 6

Identify the like terms. 2, 7d, 3, -9

2, 3, and -9

Simplify the expression. 5 (4x - 1) / 3 (1x - 1) =

20x - 5 / 3x - 3

(2)(4)(-6)(-5) = (8)(-6)(-5) = (-48)(-5) =

240

Two-thirds of a number subtracted from twenty-five =

25 - (2/3x)

Thirty-nine divided by the sum of a number and four =

39 / (x + 4)

Nineteen times a number =

19y

-154 / -55 =

2 4/5

Which multiplication property states the rule listed below? Changing the grouping when multiplying numbers does not change the product. a. Commutative Property b. Distributive Property c. Identity Property d. Associative Property

Associative Property

Which property justifies the following statement? (2 x y) x 8 = 2 x (y x 8) =

Associative Property

Which property justifies the following statement? 3 x (2 x 6) = (3 x 2) x 6 =

Associative Property

Exponent Expressions with Negative Signs

Be careful how you read expressions with exponents and negative signs.

Identify the terms as like or unlike. 5r, -18r

The terms are like terms

Identify the terms as like or unlike. 7p, -11r

The terms are unlike terms

Identify the terms as like or unlike. 8, 3x, -19

The terms are unlike terms

Identify the terms as like or unlike. h, k

The terms are unlike terms

2x2 + 3x

These are NOT like terms

How are the rules for determining the sign when dividing real numbers related to the rules for determining the sign when multiplying real numbers? a. The answer will have the same sign as the dividend. b. The answer will have the same sign as the divisor. c. If both numbers have the same sign, the answer will be negative, and if both numbers have different signs, the answer will be positive. d. They are the same when working with two numbers with the same sign or two numbers with different signs.

They are the same when working with two numbers with the same sign or two numbers with different signs.

The Distributive Property is most useful when it does not conflict with the order of operations.

That is, it is mostly used when you cannot perform the operations inside the parentheses. The Distributive Property can be used to remove the parentheses.

Evaluate: z/2x for 4 = 4 and z = 1

z/2x = 1/2(4) = 1/8

Division: "a / 7"

• A number divided by seven • A quotient of a number and seven • A number out of seven

Multiplication: "2x"

• Double a number • Twice a number • The product of two and a number • Two times a number • Two of a number

Subtraction: "a - 6"

• The difference between a number and 6 • Six is subtracted from a number • A number decreased by six • Six less than a number • Six smaller than a number • A number minus six

Addition: "x + 4"

• The sum of a number and four • A number increased by four • Four more than a number • Four is added to a number • Four greater than a number • A number plus four

Like Terms

are terms that have the same variables raised to the same powers. In other words, like terms have exactly the same variable factors.

To find the reciprocal of a fraction...

invert, or flip, the fraction

Algebraic Expression

is a combination of numbers and variables, operation symbols, and grouping symbols.

Term

is any number, variable, or product of numbers and/or variables. Terms are the parts of an algebraic expression separated by a plus sign (+) or a minus sign (-)

Quotient

is the answer to a division problem.

Dividend

is the number being divided.

Divisor

is the number you are dividing by.

Division

is the operation of splitting a quantity or number into equal parts. Dividend ÷ Divisor = Quotient

Exponent

is used as a shortcut for repeated multiplication.

1. Which answer CORRECTLY finishes the statement? Terms that have the same variables raised to the same powers are called _____. a. algebraic expressions b. unlike terms c. like terms d. variables

like terms

When multiplying signed numbers, how do you determine the sign of the product? a. look at the number of positive factors b. the sign of the answer cannot be determined before doing the actual multiplication c. look at the number of negative factors d. look at the sign of the number with the largest numerical part

look at the number of negative factors

1. When is an algebraic expression simplified? a. when you know the value of the variable b. when none of its terms can be combined and no parentheses remain c. after the Distributive Property has been applied d. after you have performed the multiplication

when none of its terms can be combined and no parentheses remain

A number increased by six =

x + 6

Eighteen subtracted from a number =

x - 18

A number decreased by two =

x - 2

Which answer CORRECTLY finishes the statement? The difference between a number and 2 translates to _____. a. x + 2 b. 2 - x c. 2x d. x - 2

x - 2

Six subtracted from a number =

x - 6

The first angle of a triangle is 19° less than the second angle. The third angle of a triangle id four times the second angle. The first angle is _____? The second angle is _____? The third angle is _____?

x -19°, x, and 4x

A number divided by ten =

x / 10

Values have been substituted for the variables x, y, and z in the following expression. 10(2)2 - 3(6) 9(-4) What are the most likely values for each variable? a. x = 2, y = 6, and z = -4 b. x = 10, y = -3, and z = -4 c. x = 10, y = 3, and z = 9 d. The answer cannot be determined from the given information

x = 2, y = 6, and z = -4

Simplify the expression. 3 (3a - b) - 8 (6b -7a) =

(3)(3a) + (3)(-1b) + (-8)(6b) + (-8)(-7a) = 9a + (-3b) + (-48b) + 56a 65a -51b

Simplify the expression. 3 (3a - b) -6 (2b - 2a)

(3)(3a) + (3)(1b) + (-6)(2b) + (-6)(-2a) = 9a + (-3b) + (-12b) + 12a 21a + (-15b) = 21a -15b

Simplify the expression. 3 (5k + 9) -2 (k - 3) =

(3)(5k) + (3)(9) + (-2)(k) + (-2)(-3) = 15k + 27 + (-2k) + 6 = 13k + 33

Simplify the expression. 4 (2x + 1)/3 (1x - 8) =

(4)(2x) + (4)(1) / (3)(1x) + (3)(-8) = 8x + 4 / 3x - 24

After the first quarter of last year, a company posted a net income of $655 million. If this had continued, what would the company's net income have been after all four quarters?

(655)(4) = 2,620

For which of the following expressions could the Distributive Property NOT be used? a. -4(x - 5) b. (x)2 c. 8(3z + 4b -5c) d. (x + 3)(1/4)

(x)2

0.18 / (-0.9) =

-0.2

-5.4 / 6 =

-0.9

Evaluate (-1)5 =

-1

Simplify the expression. -(3y - 7) + 11 =

-1 (3y - 7) + 11 = (-1)(3y) + (-1)(-7) + 11 = -3y + 7 + 11 = -3y + 18

Multiply using the Distributive Property... -(x + 7y) =

-1(x) + -1(7y) = -1x + (-7y)

-20 = -20/1 =

-1/20

-1/10 = -10/1 =

-10

-40 / 4 =

-10

Combine like terms: -5b2 -5b2 =

-10b2

Combine like terms: 4y2 -8y + - -15y2 -8y =

-11y2 -16y + 11

Combine like terms: 3/5x -4/7y -3x + 5/7y =

-12/5x + 1/7y

-5(-6)(-2)(2) = (30)(-2)(2) = (-60)(2) =

-120

182 / (-13) =

-14

-3/14 =

-14/3

(-3.9)(4.1) =

-15.99

-5/8 / 8/27 = -5/8 x 27/8 = -135/64 =

-15/8

-7.5 / (0.05) =

-150

Evaluate (-5)3 + 7(-8) = -125 + 7(-8) = -125 + (-56) =

-181

(9/10)(-3) = (9/10)(-3/1) = -27/10 =

-2 7/10

8/3 / -4 =

-2/3

A negative fraction can be written in three different, but equivalent ways:

-2/5 = -2/5 = 2/-5 A negative fraction is typically written with the negative sign even with the fraction bar.

-7.45 = -7.45/1 = -1/7.45 = (-1/7.45)(10/10) = -10/74.5 = (-10/74.5)(10/10) = -100/745 =

-20/149

(6)(-6) =

-36

-3(6)(4)(-1)(-5) = (-18)(4)(-1)(-5) = (-72)(-1)(-5) = (72)(-5) =

-360

Combine like terms: 6m + (-9m) =

-3m

Combine like terms: 3rs -6r + 4s -6rs + 12r -4s =

-3rs + 6r

Combine like terms: 1.1x -2.5y -4.1x -6.4y =

-3x -8.9y

Which of the following is an example of the Identity Property of Multiplication? a. -4(1) - -4 b. -4(3 + 1) = -12 + (-4) c. -4(1) = 1(-4) d. -4 + 0 = -4

-4(1) - -4

Evaluate a. -22 = b. (-2)2 =

-4; 4

Simplify the expression. -1/2 (8x + 6) + 1/6 (42x + 30) =

-4x + (-3) + 7x + 5 = 3x + 2

-4x + 5 - 2x - 7

-4x and -2x are like terms, and 5 and -7 are like terms

Combine like terms: 3xy + 2z -7xy -7z =

-4xy -5z

-0.2 = -0.2/1 = -1/0.2 = (-1/0.2)(10/10) = -10/2 =

-5

Simplify the expression. -5 (6n - 6) + 2n =

-5 (6n - 6) + 2n = (-5)(6n) + (-5)(-6) + 2n = -30n + 30 + 2n = -28n + 30

Evaluate: -5x + 3 for x = 5

-5(5) + 3 = -25 + 3 = -22

-16/5 =

-5/16

(-5/7) / (6/7) = -5/7 x 7/6 = -5/1 x 1/6 =

-5/6

Combine like terms: -5 -4x + 3 -1x =

-5x -2

Combine like terms: 2x -8y -7x + 4y =

-5x -4y

-1 5/6 = -11/6 =

-6/11

-4(-5)(1/4)(-3)(4) = (20)(1/4)(-3)(4) = (5)(-3)(4) = (-15)(4) =

-60

4. Consider -6x2y -xy2 -5xy + 1x2y + 3xy2 + 8xy. Which expression shows the like terms grouped together? a. -6x2y -xy2 + x2y + 3xy2 + 8xy -5xy b. -6x2y -xy2 -5xy + x2y + 3xy2 + 8xy c. -6x2y -x2y + xy2 + 3xy2 -5xy + 8xy d. -6x2y + x2y -xy2 + 3xy2 -5xy + 8xy

-6x2y + x2y -xy2 + 3xy2 -5xy + 8xy

Evaluate (-7.1)1 =

-7.1

Multiply. -5 x 14 x 1/5 =

-70 x 1/5 = -70/5 = -14

Multiply. 8/5 x (-9/2) x 5 x 2 =

-72

Evaluate: x2 -5x for x = -7

-72 -5(-7) = 49 -5(-7) = 49 - (-35) = 49 + 35 = 84

Combine like terms: 7a3 -8a2 + 2a3 =

-9a3 -8a2

3. For the expression -[2 (3x -6)], the Distributive Property must be used twice. Which of the following expressions is the result after it is used the first time? a. -[6x -6] b. -[6x -12] c. -2 (3x -6) d. -6x + 12

-[6x -12]

0(-38) =

0

Multiply using the Distributive Property... 1/2(8x - 6y + 10z) =

0.5(8x) - 0.5(6y) + 0.5(10z) = 4x - 3y + 5z

Evaluate 0.7 + 0.3(0.6 -0.5)2 = 0.7 + 0.3(0.1)2 = 0.7 + 0.3(0.01) = 0.7 + 0.003 =

0.703

Evaluate (5 + 2)2 / (9 - 2)2 = 72 / 72 = 49 / 49 =

1

Evaluate (-8)0 =

1

What is the product of a number and its reciprocal? a. the original number b. 1 c. 0 d. -1

1

8a - 7b + 3b + 2b + a

8a and a are like terms, -7b, 3b, and 2b are all like terms

Simplify the expression. 1/2 (8x + 2) + 18 =

(1/2)(8x) + (1/2)(2) + 18 = 4x + 1 + 18 = 4x + 19

Evaluate: (y - 5)/6 for y = 17

(17 - 5)/6 = 12/6 = 6/3 = 2/1 = 2

Simplify the expression. 2 (6 - x) -4 (-5 -9x) =

(2)(6) + (2)(-1x) + (-4)(-5) + (-4)(-9x) = 12 + (-2x) + 20 + 36x = 34 x + 32

Simplify the expression. 2 [-5 (2x + 5) + 3 (5x - 5)] =

(-5)(2x + (-5)(5) + (3)(5x) + (3)(-5) = -10x + (-25) + 15x + (-15) = 2 [5x - 40] = 10x + (-80) = 10x -80

During one quarter last year, a company posted a net income of -$562 million. If this continued, what would the company's net income have been after four quarters?

(-562)(4) = -2,248

Multiply using the Distributive Property... -6(-6.3x + 7) =

(-6)(-6.3x) + (-6)(7) = 37.8x + (-42) = 37.8x - 42

Simplify the expression. -6 (x + 5) + 6 (2x + 1) =

(-6)(1x) + (-6)(5) + (6)(2x) + (6)(1) = -6x + (-30) + 12x + 6 = 6x + (-24) = 6x - 24

Write using exponential notation... (-8)(-8)(-8) =

(-8)3

Use the Distributive Property to rewrite the expression, then simplify... -9(8 + 4) =

(-9)(8) + (-9)(4) = -72 + (-36) = -72 - 36 = -108

Use the appropriate properties of multiplication as needed to rewrite the given expression, then simplify. 1/2(12z) =

(1/2 x 12) x z = 6z

Multiplying Signed Numbers These rules apply to both multiplication and division.

(+)(+) = (+) (+)(-) = (-) (-)(+) = (-) (-)(-) = (+)

Write using exponential notation... (-1/6)(1/6)(1/6)(1/6) =

(-1/6)4

Multiply using the Distributive Property... -14(x - 3) =

(-14)(x) - (-14)(3) = -14x - (-42) = -14x + 42

Multiply using the Distributive Property... -15(6x - 8y + 3z) =

(-15)(6x) - (-15)(8y) + (-15)(3z) = -90x - 120y + (-45z) = -90x - 120y - 45z

Use the Commutative Property to rewrite the following expression. (-19) x 11

(-19) x 11 = 11(-19)

Multiply using the Distributive Property... -2(-10x - 8 + 2m) =

(-2)(-10x) - (-2)(8) + (-2)(2m) = 20x + 16 - 4m

Use the Distributive Property to rewrite the expression, then simplify... -2(9 - 7) =

(-2)(9) - (-2)(7) = -18 - (-14) = -18 + 14 = -4

Simplify the expression. 3 [7x - 4 (y - 3)]

(-4)(1y) + (-4)(-3) = (-4y + 12) 3 [7x + (-4y) + 12] (3)(7x) + (3)(-4y) + (3)(12) = 21x + (-12y) + 36

Simplify the expression. 4 [ 5x - 4 (7x + y)] =

(-4)(7x) + (-4)(1y) = (-28x - 4y) 4 [5x - 28x - 4y] = (4)(5x) + (4)(-28x) + (4)(-4y) = 20x + (-112x) + -16y) = -92x + (-16y) = -92x -16y

Use the appropriate properties of multiplication as needed to rewrite the given expression, then simplify. -5(7y)

(-5 x 7) x y = -35y

-1 7/8 / -1 1/4 =

1 1/2

To multiply two numbers with different signs:

1. Multiply the absolute values, or the numerical parts 2. Your answer will ALWAYS be NEGATIVE

To multiply two numbers with the same signs:

1. Multiply the absolute values, or the numerical parts 2. Your answer will ALWAYS be POSITIVE

Order of Operations Please Excuse My Dear Aunt Sally

1. Parentheses - evaluate what is inside the parentheses 2. Exponents - evaluate any exponents 3. MD - Multiply and Divide - perform multiplication and division left to right, whichever comes first 4. AS - Add and Subtract - perform addition and subtraction left to right, whichever comes first

Evaluating Algebraic Expressions The value of an expression depends on the value of the variable.

1. Substitute the given value for each variable. 2. Simplify the expression.

Finding the Reciprocal of a Decimal

1. To find the reciprocal of a decimal, write it as a fraction by putting the decimal over 1. 2. Invert, or flip, the fraction. 3. Simplify the fraction.

Finding the Reciprocal of a Mixed Number

1. To find the reciprocal of a mixed number, write it as an improper fraction. 2. Invert, or flip, the fraction.

Finding the Reciprocal of an Integer

1. To find the reciprocal of an integer, first write it as a fraction by putting the number over 1. 2. Invert, or flip, the fraction The number zero does not have a reciprocal. 0 = 0/1 is 1/0 = undefined.

Simplifying Algebraic Expressions

1. Use the Distributive Property to remove the innermost grouping symbols. 2. Remove each set of grouping symbols, working from the inside to the outside. 3. Combine like terms.

(-1.86)(-0.7) =

1.302

13 = 13/1 =

1/13

Multiply using the Distributive Property... 1/20(x - 3y - 5z) =

1/20(x) - 1/20(3y) - 1/20(5z) = 1/20x - 3/20y - 1/4z

(-4/7)(-7/12) = 28/84 =

1/3

Evaluate (-1/2)2 = (-1/2)(-1/2) =

1/4

Combine like terms: 2.7x -2.1y + 7.4x -0.5y =

10.1x -2.6y

Identify the like terms. 10c, 6c, 4c, 2, 9c

10c, 6c, 4c, and 9c

Evaluate: x2 -2y + x for x = 12 and y = 7

122 - 2(7) + 12 = 144 - 2(7) + 12 = 144 - 14 + 12 = 130 + 12 = 142

Evaluate: x/z + 2y for x = 15, y = 3, and z = 5

15/5 + 2(3) = 3/1 + 2(3) = 3 + 2(3) = 3 + 6 = 9

Evaluate: (5x)2 + x for x = 3

152 + 3 = 225 + 3 = 228

15x3 + 2 -8x2 + 1x3 -9x + 13x2 -3 =

15x3 + 1x3 -8x2 +13x2 -9x + 2 -3 = 16x3 + 5x2 -9x -1

Sixteen more than a number =

16 + x

Which of the following expressions have a negative quotient? a. -48 / -6 b. 0 / -12 c. 16 / -8 d. 35 / 7

16 / -8

16x2y -3xy2 + 5xy -2x2y -4xy2 =

16x2y -2x2y -3xy2 -4xy2 + 5xy = 14 x2y -7 xy2 + 5xy

Evaluate: (x + 9)/5 for x = 16

25/5 = 5/1 = 5

2a + 32b -25c -12b + 15a + 13c =

2a + 15a + 32b -12b -25c + 13c = 17a + 20b -12c

Twice a number increased by nineteen =

2x + 19

2x2 + 3x - 1 + 6x2 - 9x + 8

2x2 and 6x2 are like terms, 3x and -9x are like terms, and -1 and 8 are like terms

The quotient of three and a number =

3 / x

Multiply using the Distributive Property... 3(52) =

3(50) + 3(2) = 150 + 6 = 156

Evaluate: 3(x + 5y) for x = 6 and y = 3

3(6 + 5(3)) = 3(6 + 15) = 3(21) = 63

Multiply using the Distributive Property... 3(p + 3 + 6q) =

3(p) + 3(3) + 3(6q) = 3p + 9 + 18q

Evaluate: 3/5y - 5 for y = -20

3/5 (-20) - 5 = 3/5 x -20/1 = -60/5 = -12 - (-5) = -12 + 5 = 17

-6/35 / (-2/5) = -6/35 x -5/2 = 3/7 x 1/1 =

3/7

20(1.5) =

30

Combine like terms: 17x + 8y + 20 + 14x -2y -12 =

31x + 6y + 8

Multiply using the Distributive Property... 3(n - 6) =

3n - 18 = 3n + (-18)

3x + 4y - 7x + 5z

3x and -7x are like terms

For the algebraic expression -5y2 + 6x -3xy2 + 2, which is NOT a term in the expression? a. 6x b. 3xy c. -5y2 d. -3xy

3xy

Evaluate (-1/2)1/-2/9 + 10(1/4) = -1/2 / -2/9 + 10(1/4) = 2 1/4 + 2 1/2 =

4 3/4

Multiply using the Distributive Property... 4(102) =

4(100) + 4(2) = 400 + 8 = 408

Evaluate: 4a + 6b for a = 7 and b = 5

4(7) + 6(5) = 28 + 30 = 58

Multiply using the Distributive Property... 4(x + 5y) =

4(x) + 4(5y) = 4x + 20y

18.56 / 4 =

4.64

4 3/5 = 23/5 =

5/23

Which of the following are like terms? a. 2x2y and 2xy2 b. 4x, 7x, and -9x c. 8b and -8b2 d. 3x and 9y

4x, 7x, and -9x

Combine like terms: 5x2 -3x -4 -7x + 6 -1x2 =

4x2 -10x + 2

For the expression -54, identify the base a. -5 b. 5 c. -1 d. 4

5

Simplify the expression. 5 + 6 (w + 4) + w =

5 + (6)(1w) + (6)(4) + 1w = 5 + 6w + 24 + 1w = 7w + 29

The sum of five and three times a number =

5 + 3x

Five-sevenths of a number decreased by three =

5/7x + 16

-32 / -4/7 = -32/1 x -7/4 = 224/4 =

56

For the algebraic expression 5x2 + 3x -6x2 + 7x -2, identify the like terms. a. 3x and 7x are the only like terms b. 5x2 and -6x2 are the only like terms c. 5x2 and -6x2 are like terms, as well as 3x and 7x d. There are no like terms

5x2 and -6x2 are like terms, as well as 3x and 7x

List the terms of the expression 5x2y -5y2 -7z3

5x2y, -5y2, and -7z3

Combine like terms: 7xy + 5yz -6xz -7xy =

5yz - 6xz

-12 / (-2) =

6

Use the Commutative Property to rewrite the following expression. 6 x 16

6(16) = (16)6

Which example does NOT apply the Distributive Property correctly? a. 12(x - 2) = 12x - 24 b. (2 + x)3 = 6 + 3x c. -4(a + b - c) = -4a -4b + 4c d. 6(x - 3) = 6x - 3

6(x - 3) = 6x - 3

Evaluate -(-4/5)3 = -(-64/125) =

64/125

Evaluate (-3/4)4 = (-3/4)(-3/4)(-3/4)(-3/4) =

81/256

-25.2 / -3.6 =

7

6/7 =

7/6

List the terms of the expression 7a + 3b -8c

7a, 3b, and -8c

Evaluate 5 - 3(2)3 / (-8) = 5 - 3(8) / (-8) = 5 - 24 / (-8) = 5 - (-3) =

8

Evaluate [32 + 3(-19)]/[-1 + (-5)] = [9 + (-57)] /[-1 + (-5)] = -48 / -6 =

8

the Distributive Property to rewrite the expression, then simplify... 8(5 + 8) =

8(5) + 8(8) = 40 + 64 = 104

Evaluate: 8x -2y for x = 5 and y = 4

8(5) - 2(4) = 40 - 8 = 32

Simplify the expression. 9 + 5 (2c - 1) =

9 + (5)(2c) + (5)(-1) = 9 + 10c + (-5) = 9 + 10c - 5 = 4 + 10c

Identify the like terms. 5d, 9, 2b, -4

9 and -4

Which of the following statements is TRUE? a. The expression (-2)3 means -(2)(2)(2) b. A negative base raised to an even power will be negative c. The expression -34 is read "negative three raised to the forth power" d. A negative base raised to an even exponent will be positive

A negative base raised to an even exponent will be positive

A negative base raised to an even power is positive

A negative base raised to an odd power is negative

Which of the following statements about exponents is FALSE? a. A negative number raised to an even power is positive b. Any number raised to the first power is itself c. A negative number raised to an odd power is positive d. Any non-zero number raised to the zero power is 1

A negative number raised to an odd power is positive

Which of the following statements about exponents are TRUE? Select all that apply. a. An exponent is used as a shortcut for repeated multiplication b. An exponent is the number of times the base is used as a factor c. An exponent is written as a smaller number to the right and slightly above the base (superscript) d. An exponent is the number that is being multiplied

An exponent is used as a shortcut for repeated multiplication An exponent is the number of times the base is used as a factor An exponent is written as a smaller number to the right and slightly above the base (superscript)

Special Cases with Exponents

Any non-zero number raised to the zero power is equal to 1 b0 = 1 (b ≠ 0) Any number raised to the power of 1 is equal to itself b1 = b

Associative Property of Multiplication

Changing the grouping when multiplying numbers does not change the product. a x (b x c) = (a x b) x c

Commutative Property of Multiplication

Changing the order when multiplying numbers does not change the result. The product is the same no matter which number is written first. a x b = b x a

Which property identifies the following statement? 4 x 7 = 7 x 4 =

Commutative Property

Which property of multiplication discusses changing order? a. Identity Property b. Associative Property c. Distributive Property d. Commutative Property

Commutative Property

The Distributive Property

For all real numbers a, b, and c, a(b + c) = ab + ac

The highest temperature ever recorded in a continent was 40˚C, and the lowest temp was -50˚C. What was the temperatures in degrees Fahrenheit?

Highest = 9/5(40) + 32 = (9/1 x 8/1) + 32 = 72 + 32 = 104˚F Lowest = 9/5 (-50) + 32 = (9/1 x -10/1) + 32 = -90 + 32 = -58˚F

Which property justifies the following statement? (-4/3)(2/2) = -4/3 =

Identity Property

Which property justifies the following statement? 9 x 1 = 9 =

Identity Property

Combining like terms

If an expression has several terms, you might find it helpful to rearrange the terms so that like terms are together.

When dividing real numbers, how do you determine the sign of the quotient? a. The answer will have the same sign as the divisor. b. If both numbers have the same sign, the answer will be positive, and if both numbers have different signs, the answer will be negative. c. If both numbers have the same sign, the answer will be negative, and if both numbers have different signs, the answer will be positive. d. The answer will have the same sign as the dividend.

If both numbers have the same sign, the answer will be positive, and if both numbers have different signs, the answer will be negative.

Identity Property of Multiplication

Multiplying a number by 1 gives us the same number. 1 x a = a a x 1 = a

The base is the number being multiplied

The exponent is the number of times the base is used as a factor

Two numbers are reciprocals of each other if their product is 1. b/a is the reciprocal of a/b

The reciprocal is also called the "multiplicative inverse" of a number

Which of the following statements is FALSE? a. The rules for determining the sign when multiplying and dividing real numbers work the same way. b. To divide two numbers with different signs, divide the numerical parts and the answer will be negative. c. To divide two numbers with the same sign, divide the numerical parts and the answer will be positive. d. To divide two numbers with different signs, divide the numerical parts and the answer will have the sign of the larger number.

To divide two numbers with different signs, divide the numerical parts and the answer will have the sign of the larger number.

In which of the following situations is it appropriate to use the Distributive Property? a. To subtract a negative number b. To multiply fractions with different denominators c. To multiply three numbers together d. To rewrite an expression without parentheses

To rewrite an expression without parentheses

Which phrase best represents 2 (n - 3)? a. The difference between twice a number and 3 b. Twice the difference between a number and 3 c. The product of 2 and a number subtracted from 3 d. Twice the difference between 3 and a number

Twice the difference between a number and 3

Many expressions in algebra use grouping symbols such as (parentheses), {braces}, or [brackets].

Use the Distributive Property to remove the parentheses.

When multiplying and even number of negative factors, the product is positive.

When multiplying an odd number of negative factors, the product is negative.

Sign Rule for Exponents

When the base is negative, be especially careful in determining the sign of the answer.

(-2)4 means (-2)(-2)(-2)(-2) = 16

When the negative sign is inside the parentheses, the negative applies to all the bases

-2(4) means (-2)(2)(2)(2) = -16

When there are no parentheses, the negative only applies to the first base

X2 = squared

X3 = cubed

Find the product and determine which property of multiplication is used. 0(-76) = 0 =

Zero-Product Property

Which of the following is FALSE about a reciprocal? a. a number and its reciprocal have opposite signs b. two numbers are reciprocals of each other if their product is 1 c. the reciprocal is also called the "multiplicative inverse" of a number d. to find the reciprocal of a fraction, invert (or flip) the fraction

a number and its reciprocal have opposite signs

Which of the basic operations is Commutative? a. addition and multiplication b. subtraction and division c. addition and subtraction d. only addition

addition and multiplication

Which choice CORRECTLY finishes the statement? A combination of numbers and variables, operation symbols and grouping symbols is called a(n) _____. a. variable b. term c. like term d. algebraic expression

algebraic expression

2. How are parentheses removed from an algebraic expression? a. multiplying everything in parentheses by -1 b. remove the parentheses c. using the Distributive Property d. combine like terms inside the parentheses

using the Distributive Property

To Divide Signed Numbers

divide the absolute values or numerical parts, and determine the sign of the quotient.

To divide by a fraction

find the reciprocal of the divisor, find the any common factors, and multiply.

Which answer choice CORRECTLY finishes the statement? To find the reciprocal of an integer, _____. a. first write it as a fraction by putting it over 1, and then change the sign of the fraction b. multiply the integer by 1 c. first write it as a fraction by putting it over 1, and then invert the fraction d. none of the above, it is not possible to find the reciprocal of an integer

first write it as a fraction by putting it over 1, and then invert the fraction

Which of the following phrase(s) translate(s) to addition? a. four more than a number b. 2 of a number c. 8 is increased by some number d. The sum of a number and -5

four more than a number, 8 is increased by some number, and The sum of a number and -5

List the terms of the expression mn -7n + 4

mn, -7n, and 4

When evaluating the expression 2a-b/3 for a = 9 and b = 12, what is the first operation that would be done? a. divide 12/3 b. subtract 9-12 c. divide 9/3 d. multiply 2(9)

multiply 2(9)

What will be the sign of the product below? (+)(-)(-)(+)(+)(-) a. positive b. cannot be determined from the information given c. negative d. could be positive or negative

negative

3. Which of the following would NOT be helpful in combining like terms? a. rearrange terms to group like terms together b. circle or underline like terms c. place the numbers in order from smallest to largest d. identify like terms

place the numbers in order from smallest to largest

To divide by a mixed number

rewrite as an improper fraction, find the reciprocal of the divisor and multiply.

4. For the expression -(5 -x), which of the following is FALSE? a. the - sign in front of (5 -x) should be distributed as a negative 1 in order to simplify the expression b. the simplified expression, without parentheses is -5 + x c. this expression should be considered the opposite of the expression -5 + x d. the Distributive Property can be used to remove parentheses and result in the expression -5 -x

the Distributive Property can be used to remove parentheses and result in the expression -5 -x

When multiplying two numbers with different signs, _____. a. the answer will have the sign of the larger number b. the answer will always be positive c. the answer will always be negative d. the answer could be negative or positive

the answer will always be negative

Which of the following statements is NOT correct? a. the equality -7y = y(-7) is an example of the Commutative Property of Multiplication b. the equality 6(-4 x 5) = (6 x -4) x 5 is an example of the Associate Property of Multiplication c. the equality -9(1) = -9 is an example of the Identity Property of Multiplication d. the equality -3a = a(-3) is an example of the Associate Property of Multiplication

the equality -3a = a(-3) is an example of the Associate Property of Multiplication

A negative sign in front of the parentheses means

the opposite of what is inside the parentheses.

George's multiplication problem has an even number of negative factors. Which of the following is TRUE about his answer? a. the sum will always be positive b. the product will always be negative c. the product will always be positive d. the product could be negative or positive

the product will always be positive

If the dividend and the divisor have different signs

the quotient is negative.

If the dividend and the divisor have the same sign

the quotient is positive.

Which of the following statements is FALSE? a. the reciprocal of 1 is 1 b. the reciprocal of 2 is 1/2 c. the reciprocal of -3/4 is 4/3 d. 0 does not have a reciprocal

the reciprocal of -3/4 is 4/3

When evaluating an algebraic expression, the value of the expression depends on _____. a. the order of the terms in the expression b. the number of variables in the expression c. the value of the variable d. the number of terms in the expression

the value of the variable

Combine like terms: 8a5 -5a3 + 2a4 =

this expression cannot be simplified

2. What does it mean to combine like terms? a. to use the order of operation to simplify the expression b. to add or subtract all terms, regardless of the variables c. to multiply any terms that are "like" d. to add or subtract any terms that are "like"

to add or subtract any terms that are "like"