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On Friday, a bowling alley made $842.72 from lane rentals and $412.38 from the concession stand. On Saturday, their lane rentals were down by 1/8 but the concessions increased by 1/2. What is the total amount that the bowling alley earned in lane rentals and concessions on Friday and Saturday?

$2,611.05

Anusha brings a $20 bill to the store. She purchases 4 pairs of socks for $2.25 each and a new belt for $7.50. How much change will Anusha receive when she pays for her clothes?

$3.50

Keenan buys 6 items that each cost $4.25 and 3 items that each cost $6.75. How much does Keenan spend in total?

$45.75

Noa buys 6 items that each cost $4.25 and 3 items that each cost $6.75. How much does Noa spend in total?

$45.75

Tamir buys tickets to two concerts this season. One has a face value of $32.50, and one has a face value of $26.50. He uses a coupon and gets both tickets at 1/4 off. If he pays with a $50 bill, how much change should Tamir receive?

$5.75

Which shows two expressions that are equivalent to (-7)(-15)(-5)?

(-1)(525) and (35)(-15)

50p⁷

(-10p³)(-5p⁴)

10,000p¹²

(-10p³)⁴

-1000p¹²

(-10p⁴)³

Which product is positive?

(-2/5)(-8/9)(1/3)(2/7)

Which product is negative?

(-3/8)(-5/7)(-1/4)

-15w⁵

(-3w³)(5w²)

Which expression has a positive value?

(-5)(-9)

25

(-5)²

Which shows two expressions that are equivalent to (-8)(-12)(2)?

(-8)(-24) and (-16)(-12)

-x³y⁷

(-x²y⁴)(xy³)

10,000

(1/10)⁻⁵

-5y³/x⁷

(10xy⁵)/(-2x⁸y²)

-5x⁵y³

(10x⁹y⁵)/(-2x⁴y²)

3a²

(12a³)/(4a)

Which shows two products that both result in negative values?

(2.4)(-1.8) and (0.6)(-0.4)

b²/4a²

(2ab⁻¹)⁻²

16a⁸

(2a³)(8a⁵)

1/(16x⁴)

(2x)⁻⁴

27a⁶b³

(3a²b)³

6x⁵

(3x³)(2x²)

Laurie was scuba diving. Each time she dove 5 feet deeper, she would stop and clear her ears. Each time that this totaled 20 feet deeper, she would stop and check her instruments to make sure they were working properly. After Laurie had checked her instruments 3 times, she was at her maximum depth. Which expression best represents Laurie's maximum depth?

(4)(-5)(3)

A sign language club made $627.50 from selling popcorn at a festival. The popcorn cost the club $95.00. Which expression represents the amount of money that was raised for each member of the club?

(627.50-95)/m

2a

(6a²b)/(3ab)

30a⁹

(6a³)(5a⁶)

Associative Property of Multiplication

(7∙5)6=7(5∙6)

Which correctly applies the distributive property to show an equivalent expression to (8.6)(-2.5)?

(8.6)(-2) + (8.6)(-0.5)

Associative Property of Addition

(a+b)+c=a+(b+c)

a³b⁵c⁴

(ab²c)(a²b³c³)

a⁷b¹²c⁹

(ab²c)³ * (a²b³c³)²

ac³

(a²bc³)/(ab)

Associative Property of Multiplication

(de)f=d(ef)

-12c³

(−4c)(3c²)

-12m²

(−4m)(3m)

-x⁵

(−x⁷)(x⁻²)

-4m - 2

- (4m + 2)

Opposite of a Sum

- (a + b) = -a + -b

Opposite of a Difference

- (a - b) = -a + b or b - a

Compatible numbers for 2.4 and -0.18 are 2.5 and -0.2. What is the estimation of the product of (2.4)(-0.18) using these compatible numbers?

-0.5

Crystal lives on the twelfth floor of her apartment building. She walks down 2 flights to visit a friend named katherine, then up 3 flights to deliver a message to a neighbor. Which integer best represents the number of flights Crystal must walk to get back to her starting point?

-1

What is the quotient? 457.6 divided by -286

-1.6

Which of the following terminating decimals is equivalent to -1 3/4/

-1.75

What is the difference between -4 and 6?

-10

What is the difference of the fractions? Use the number line to help find the answer. 1 - 3 5 4

-11 20

Commutative Property of Addition

-12+20+13=-12+13+20

A submarine hovers at 66 2/3 yards below sea level. If it ascends 24 1/8 yards and then descends again 78 3/4 yards, what is the submarine's new position, in yards, below sea level?

-121 7/24

Which expression can be used to check the answer to 56/(-14)=

-14xn

Alaina has $28 in her account. She wants to purchase a pair of shoes that costs $45. If Alaina makes the purchase, which integer will represent the amount of money in Alaina's account?

-17

Use the commutative and/or associative properties to simplify −36⋅11⋅4/9.

-176

Janelle subtracts -4 from a number. The result is 2. What is the number?

-2

What is the value of the expression below? 7/2-4.5*3+8

-2

2x + 6

-2 (x+3) + 11 (2x)+12 3x + 2 - x + 4

-6m + 12

-2(3m - 6)

What is the quotient? -4/5/2

-2/5

kailey increases the temperature of a block of ice by 20º. Which integer represents the amount by which kailey must change the temperature for the block of ice to return to its starting temperature?

-20

Bobby's football team received four five-yard penalties in the first quarter, which meant his team lost yardage in their progress toward the goal line. What was the change in their progression down the field as a result of these penalties?

-20 yards ? "correct"-5 yards "incorrect"5 yards20 yards

Gemma, a scuba diver, begins a dive on the side of a boat 4 feet above sea level. She descends 28 feet. Which integer represents Gemma's position with respect to sea level?

-24

A diver dives 17 2/3 yards and then comes back to the surface. Then, she dives 9 3/8 yards deeper than her first dive. What is her depth, in yards, in relation to the surface of the water?

-27 1/4

8x - 15

-3 + 4(2x - 3)

A recipe that makes 4 servings calls for 2/3 cup of flour. uses a large container of flour to make 20 servings of the recipe. What number represents the change in the amount of flour from the large container?

-3 1/3 cups

What is the quotient of -27.375 divided by 7.5?

-3.65

What is the value of the expression? -16+12

-4

What is the sum of the fractions? Use the number line to help find the answer. 3/5+(-7/5)

-4/5

5m - 5

-5(-m + 1)

-10m - 15n

-5(2m + 3n)

Which of the following repeating decimals is equivalent to -5 1/9?

-5.1 bar on top of 1

-25

-5²

Use the dist. property: -7(e + 4)

-7e + -28 or -7e - 28

3y

-7y + 10y

Which is the best estimate of (-3/5)(17 5/6)?

-9

Simplify: -7x + 1 - (2x + 10)

-9x - 9

Yasmine finds the absolute value of -655. Which expression represents this value?

0-(-655)

Which of the following terminating decimals is equivalent to 3/8?

0.375

Evaluate the expression when b=4/5:b+0.92+(−b)

0.92

What is the difference between the absolute value of 4 and the absolute value of -3?

1

What is the difference between the absolute value of 4 and the absolute value of -3?

1 4 7 8 "incorrect"

-2x + 2

1-2(x+4)+9 simplify x+2+x -4x + 2 -x + 3x

What is the simplified value of the expression below? 1/3 divided by 2/3

1/2

What is the simplified value of the expression below? 1/3/2/3

1/2

Simplify: 3/8⋅1/5⋅8/3.

1/5

Patel squeezed oranges so that his family could have fresh-squeezed juice for breakfast. He squeezed 4/17 cups from the first orange, 3/10 cups from the second orange, 9/20 cups from the third orange, 3/11 cups from the fourth orange, and 7/15 cups from the fifth orange. Patel estimates that he needs 2 cups of orange juice for his family. About how much more orange juice does he need?

1/6 cups

x+31

10 + 3(x + 7) - 2x

A science experiment calls for mixing 4 3/4 cups of distilled water with 5 3/4 cups of vinegar and cups of liquid detergent. How much liquid in all, in cups, is needed?

10 1/2 cups

Evaluate the expression when m=11:4/7(7/4m)

11

Simplify expressions involving fractions or decimals using the commutative and associative propertiesSimplify: (4/7+1/4)+3/4.

11/7

Simplify -24 x (15) + 36 x (15)

12

Which expression has the same value as the one below?

12 + (-9

Substitution Property

12 - 10 + y = 2 + y

What is the y-value of the vertex of the function f(x) = -(x + 8)(x - 14)? The y-value of the vertex is

121

Rewrite 13 x (2.01) using distributive property

13*x*2+13*x*0.01*******

What is the best estimate of the sum of the fractions? 31 + 17 + 8 4 3 18

14 1 2

Simplify 72 x 38 + (-72) x 18

1440

(2m + x) + (12m + 2x)

14m + 3x

What is the value of the expression -225/(-15)

15

T'jay wants to bike a total of 100 miles over the course of one week in the summer. He logs how much he bikes each day in the table below. T'jay Biking Log Day Miles Completed Monday 16.3 Tuesday 14 1/2 Wednesday 18.75 Thursday 12 1/4 Friday 22 3/5

15 3/5

Simplify 16 x (-31) + 16 x 32

16

(2 x 4) x 1

2 (4 x 1)

The temperature at 9 a.m. is 2 degrees. The temperature rises 3 more degrees by noon. Which expression describes the temperature at noon?

2 + 3

(2 + y) + 3y

2 + 4y

-2x+22

2 + 5(x + 4) - 7x

4m + 10

2(2m + 5)

70 + 10a

2(35 + 5a)

6x - 2

2(3x - 1)

12x+8

2(4 + 6x)

Distributive Property

2(6-2) = 12-4

2x - 3

2(x - 3) + 3

Associative Property of Addition

2+(7+8)=(2+7)+8

A recipe shows that the yeast needed for a bread recipe is 2 1/3ounces. Which of the following decimals is equivalent to this number?

2.3 bar on top of 3

Mr. braswell is competing in a local biathlon, a race which consists of a biking and a running event. The race is a total distance of 11.42 miles. If the biking event is 8.7 miles, what is the distance of the running event?

2.72 miles

Robert used front-end estimation to estimate the product of (-24.98)(-1.29). What was his estimate?

20

Evaluate the expression when g=21:3/4(4/3g) Provide your answer below:

21

What is the simplified value of the expression below? -8*(-3)

24

5x²

25x⁴/5x²

Use the commutative and/or associative properties to simplify 5/6a+3/10a+1/6a+7/10a.

2a

28

2x - 2(x + 3) + 34 4*7 7*4

16x⁶

2x(8x⁵)

y + 4 + y

2y + 4

Liam had a container of oatmeal that contained 5 1/2 cups of oatmeal. Liam ate 4/9 cup of oatmeal every morning before school for a week. Which is the best estimate of the number of cups of oatmeal that Liam had left in the container at the end of the five-day week?

3

A recipe that makes 4 servings calls for 2/3 cup of flour. How much flour is required to make 20 servings?

3 1/3 cups

Eliza's backpack weighs 18 7/9 pounds with her math book in it. Without her math book, her backpack weighs 14 7/8 pounds. How much does Eliza's math book weigh?

3 65/72

21x+6

3(2 + 7x)

18x+9

3(6x + 3)

3m + 24

3(m+ 8)

Commutative Property of Multiplication

3+(5∙2)=3+(2∙5)

The weights of five grapefruits are 7.47 ounces, 7.23 ounces, 6.46 ounces, 7.48 ounces, and 6.81 ounces. Using the clustering estimation technique, what is the approximate total weight of the grapefruits?

35 ounces

Suppose that P partners equally share the profits from a sale of $3,600. Which algebraic expression represents this situation?

3600/p

24u¹³

3u⁷⋅8u⁶

14 + 3x

3x + 14

3x+15

3x + 5

Substitution Property

3x+4x+7 = 7x + 7

3x⁶

3x⁴(x²)

Which is the best estimate of 11 1/5/2 3/4?

4

Alexia ran three laps around her neighborhood. Each lap is 1 3/8 miles. Which is the best estimate of the number of miles that Alexia ran?

4 1/2 miles

There are 3 different cheeses at the deli. Yasuko buys 3/4 of a pound of each. There are also 4 different meats. She buys 1/2 of a pound of each. How much total food did Yasuko buy at the deli?

4 1/4 pounds

20x+4

4(5x+1)

4x+40

4(x + 10)

Katie baked three loaves of zucchini bread. Each cake needed 17/4 cups of flour. Which expression shows the best estimate of the number of cups of flour that Katie used?

4+4+4 = 12

R.J. worked 15.35 hours one week and 32.7 hours the next week. How many hours did R.J. work over the two weeks?

48.05 hours

20a⁵term-200

4a(a)(5a³)

4x(y/y)

4x

4(y + 3)

4y + 12

What is the distance between -3 and 2 on the number line?

5

What is the value of 3 - (-2)?

5

3x - 10

5 + 3(x - 5)

Dianna made several cakes yesterday. Each cake required 2 2/3cups of flour. All together, she used 13 1/3 cups of flour. How many cakes did Dianna make?

5 cakes

Rewrite using distributive property in reverse: 5( 40 - 1)

5 x 39

40x+5

5(1 + 8x)

-5m+ 30

5(m - 6)

5m - 30

5(m - 6)

5x - 13

5(x - 3) + 2 2(x-2)+(3x(-9))

Which number is rational?

5.333333........

Which number is rational? -2.1010010001... -0.8974512.. .1.2547569... 5.3333333...

5.3333333...

Alicia drove 265 miles in 5 hours. What is the average rate that she traveled?

53 miles per hour

matthew's dog weighs 34.1 pounds. james dog weighs 53.08 pounds. Which expression finds how much more Josiah's dog weighs than matthew's dog?

53.08 - 34.1

11x+18

5x + 6(x + 3)

11x

5x + 6(x+2) - 12

Use the associative properties to rewrite (5⋅4/3)⋅9=−−.

5⋅(4/3⋅9)=−− Change the grouping. (5⋅4/3)⋅9=5⋅(4/3⋅9) Notice that 4/3⋅9 is 12. The multiplication will be easier if we group as shown on the right.

The lowest recorded temperature in a town was 4ºF, without the windchill. With the wind, the temperature felt like 10ºF below zero. On a number line, what is the distance between the two temperatures?

6

A science experiment calls for mixing 3 2/3 cups of distilled water with 1 3/4 cups of vinegar and 2/3 cups of liquid detergent. How much liquid in all, in cups, is needed?

6 1/12

Distributive Property

6(8+7)=6∙8+6∙7

6m

6(m - 0)

Associative Property of Addition

6+(0+7)=(6+0)+7

Which expression is equivalent to 6 - (-8)?

6+8

Commutative Property of Addition

6+8=8+6

Which expression is equivalent to 63.56 + (-81.47)?

63.56 - 81.47

12m + 15

6m + 3(2m + 5)

x(4 + 2)

6x

6x - 12

6x - 2

6x - 24

6x - 4

y(6 + x)

6y + xy

What is the value of x in the equation below? -3 - (-8) - (-2) = x

7

Chen is baking cookies and a cake for a party. He needs 3 1/5 cups of flour to make the cookies and 3 2/3 cups of flour to make the cake. Which is the best estimate of the number of cups of flour that Chen needs to bake both recipes?

7 cups of flour

-7m + 49

7(-m + 7)

21x + 22

7(2+3x) + 8

14x+7

7(2x + 1)

7m + 14

7(m - 4 + 6)

Rewrite using distributive property: 7 x 22

7*20+7*2

Simplify: (3/4+2/3)+1/3

7/4

21x⁵

7x²(3x³)

-10x - 43

8 - 10(x + 6) + 9

Rewrite using dist property: 8 x 5.99

8 x 6 - 8 x 0.01

16 - 8x

8(2 - x)

8x-32

8(x - 4)

Use the commutative properties to rewrite 7+8=−−.

8+7 7+8=−− Use the Commutative Property of Addition to change the order.7+8=8+7

Simplify: (3/5+1/8)+7/8

8/5

Use the commutative and/or associative properties to simplify 12(4/6p).

8p

20x

8x + 9x + 3x

Use the dist. property: 8(x - 3)

8x - 24

At a farmers market, Samuel bought 3 pounds of apples for x dollars per pound and 2 bags of spinach for y dollars each. The next day he returned and bought 5 pounds of apples for x dollars per pound and 3 bags of spinach for y dollars each. Which expression represents the total amount he spent at the market on both days?

8x+5y

Evaluate the expression when n=9:2/5(5/2n)

9

20x + 29

9 + 5(4x+4)

6x - 14

9 + 6(x - 5) + 7

Commutative Property of Addition

9(a+b)=9(b+a)

Robert earns $20 per month for completing chores around the house. Each month, the amount Robert earns increases by $0.50. Which expression represents how much total money Robert earns from month 3 to month 18?

A

Beginning with Roberta's first month of high school, his father deposits $5 into Roberta's savings account. Each month after the first month, his father deposits $2 more than the previous month. The total amount deposited in Roberta's account after four years can be represented using the expression . How much total money has been deposited?

A $2,496

collene collects antique picture frames. In her first year of collecting, she collects 10 frames. Each year, she hopes to collect three more frames than the previous year. The situation is represented by the expression below. How many frames will collene have after 10 years of collecting?

A 235

Which expression is equivalent to mc007-1.jpg?

A 35(35+1)/2

Opposite of an Opposite

A negative number times a negative number equals a positive number. -(-a) = a ex.: -(-5) = 5

An isosceles triangle's altitude will bisect its base.mc026-1.jpg Which expression could be used to find the area of the isosceles triangle above?

A.

Using the quadratic formula to solve 11x2 - 4x = 1, what are the values of x?

A.

Which expression is equivalent to (4 + 6i)2?

A. -20 + 48i

A point of the form 25 +bi is 37 units from 13 - 31i. What is the value of b?

A. 4

What are the values of x in the equation x2 - 6x + 9 = 25?

A. x = -2 or x = 8

Use the number line to answer the question. Which statement about graphing rational numbers is true?

All of the points on the graph could represent rational numbers.

Multiplication by 0

Any numbers times zero equals zero. a × 0 = 0 ex.: 9 × 0 = 0

What is the value of the expression mc002-1.jpg?

B 12(3 + 4 + 5 + ... + 12 + 13) = 1,056

Which equation is an example of the commutative property of multiplication?

B. (4 + 2i)(3 - 5i) = (3 - 5i)(4 + 2i)

What is the greatest possible integer value of x for which mc006-1.jpg is an imaginary number?

B. 4

What is the sum of 12 - 5i and -3 + 4i?

B. 9 - i

If the discriminant of a quadratic equation is 4, which statement describes the roots?

B. There are two real roots.

How can the additive inverse be used to evaluate the problem below? -3 - (-6)

Because -3 + 6 is an equivalent expression, the answer is 3.

Which best describes the solution to 4 - 7?

Because 4 + (-7) is an equivalent expression, the answer is -3.

Which expression is equivalent to

C

Which of the following is one way the expression can be rewritten using summation properties?

C 1/2(64(65)/2)-1/2(17(18)/2)

What is the value of mc014-1.jpg?

C 2,635

What is the sum of the series below?

C 218,085

Which pair of complex numbers has a real-number product?

C. (1 + 3i)(1 - 3i)

Tommy is solving the equation x2 - 10x = 21. Which value must be added to both sides of the equation to make the left side a perfect-square trinomial?

C. 25

The following statements concern the modulus. Which statement is false?

C. The modulus is sometimes negative because of the computations with i.

Which function has a vertex on the y-axis?

C. f(x) = (x - 2)(x + 2)

Carlos biked 139/8 miles on Saturday and 135/7 miles on Sunday. On which day did he ride further and by how much?

Carlos rode further on Sunday by 1 51/56

Which expression is equivalent to

D

Which of the following shows one way to simplify mc009-1.jpg?

D mc009-5.jpg

Solve for mc014-1.jpg in the equation mc014-2.jpg.

D.

Crystal wants to write 2/6 as a decimal. Which method could she use?

Divide 2 by 6

The quotient of two numbers is negative. What must be true about the two numbers?

Either the dividend or the divisor is negative, but not both

Identity Property of Addition

If you add zero to a number, the sum is the same as that number.

Identity Property of Multiplication

If you multiply a number by one, the product is the same as that number.

Yuri's sister Karina is 12 years old. In the equation below, y represents Yuri's age in years. 12=3y-2

Karina is 2 years younger than triple Yuri's age.

Michael is using a number line to evaluate the expression -8 - 3. After locating -8 on the number line, which step could Michael complete to evaluate the expression?

Michael could rewrite the expression as -8 + -3 and move 3 spaces to the left.

Morena, a scuba diver, used the expression below to describe her position in relation to sea level. 0 + (-15) + 6

Morena started at sea level, dove down 15 feet, then rose up 6 feet.

Veronica wants to check her work after evaluating -108/(-6). What steps can she follow to verify her answer?

Multiply her answer by -6 and see if the result is -108

What is the first step when applying properties of operations to divide 73.85 by 4.1?

Multiply the divisor and dividend by 10.

Which expression is equivalent to mc003-1.jpg?

NOT B mc003-3.jpg

Which expression is equivalent to mc004-1.jpg?

NOT C

james starts a new career making $32,000 annually. Each year for a total of 30 years, james receives a $1,200 annual pay increase. The total amount earned over the 30 years can be determined using the expression How much money does james earn over the 30 years?

NOT C $1,518,000 NOT B $1,516,800

inverse

Reversed in position OR order

George is comparing the sizes of two different phones. The screen of phone A has a width of 5.3 cm. The width of the screen on phone B is 5 1/3 cm. Which statement explains which phone has the wider screen.

Screen B is wider, because 5.3 > 5 1/3

Rita is adding 3 + (-8) + 1. She rewrites the expression as 3 + (-1) + 8.What is Rita's error?She used the commutative property, which cannot be used with negative numbers.In the new expression, -8 and 1 should both be negative.She used the associative property which should only be used with positive numbers..She switched the negative signs for -8 and 1.

She used the commutative property, which cannot be used with negative numbers.In the new expression, -8 and 1 should both be negative. "incorrect"She used the associative property which should only be used with positive numbers..She switched the negative signs for -8 and 1. "correct"

Definition of Subtraction

Subtracting a number is like adding a negative. a - b = a + (-b) ex.: 7 - 5 = 7 + ( -5 )

Juan is rewriting the expression 12d-26c as a product. Which statements about the expression are accurate and relevant to his rewriting the expression? Check all that apply.

The GCF of the numbers in each term in the expression is 2. The factored expression is 2(6d-13c)

Aaron claims the same answer could also be found by adding either -5 + 3 or -3 + 5. What is the error in Aaron's reasoning?

The negative signs were switched

R'Jay writes an integer on a piece of paper. The absolute value of his number is less than 4. Which is true of the possible values of R'Jay number?

The possible values are less than 4. "correct" The possible values are less than -4. "not correct" The possible values are less than 4 but greater than -4. The possible values are either greater than 4 or less than -4.

What is the product of any integer and -1?

The product is the opposite of the integer. The product is the integer unchanged. The product is positive.The product is negative. "incorrect"

Multiplicative Property of Zero

The product of any number and zero is zero. a*0=0

Jalen plots two integers on a horizontal number line. The leftmost integer is negative. Which must be true of the second integer?

The second integer is greater than the first integer

A meteorologist used the expression below to describe how the temperature changed. -5 + (-4) Which statement could describe how the temperature changed?

The temperature was -5 degrees, then it decreased 4 degrees.

Vanessa and Zack are playing a game where the player with the lower score wins. At the end of the game, Vanessa has a score of -3 5/8 and Zack has a score of -3 2/3. Which statement explains who won?

Vanessa won. If you compare the decimal equivalents of their scores, -3.666 < -3.625.

Multiplication by -1

When you multiply a number by -1, it will give you the opposite (if the number is positive, it will now be negative, vice-versa) a × -1 = -a ex.: -1 × -7 = 7-1 × 5 = -5

Katie has Y pairs of skates. Her friend kailey has three more pairs of skates than Katie has. Write an expression for the number of pairs of skates that her friend has.

Y + 3

Matthew has Y pairs of shoes. His brother james has 3 fewer pairs. Write an expression for the number of shoes his brother has

Y - 3

Opposite of a Product

You can apply the negative to one value at a time. - (ab) = -a × b = a (-b) ex.: - (3×5) = -(-15) = 15

Definition of Division

You can write division as the product of the first number times the reciprocal of the second number. a ÷ b = a × ¹/b b ≠ 0 ex.: 9 ÷ 3 = 9 × ¹/₃

Distributive Property for Subtraction

a (b - c) = ab - ac

True or False: If the term outside the parentheses is negative, the sign of each term in the parentheses will change

always truely very truely the best truely the very best truely

a²

a⁷⋅a⁻⁵

Bill claims that he found the actual December temperature by adding either -5 + 3 or 3 + -5. What property did Bill use?

commutative property

c⁷

c¹³/c⁶

c¹²

c¹⁵/c³

c⁵

c⁹⋅c⁻⁴

c¹³

c⋅c¹²

Commutative Property of Multiplication

d(ef)=d(fe)

Yan is climbing down a ladder. Each time he descends four rungs on the ladder, he stops to see how much farther he has to go. Which word in the problem indicates that a negative integer should be used?

descends

R.J. made a triangular picture frame out of cardboard. The sides of the frame are 6.75 in., 6.75 in., and 8.375 in. R.J. uses the addition below to determine the amount of string she needs to decorate the edges of the frame.

he should have included the decimal in 6.75 and aligned the decimal points to add 6.750 + 6.750 + 8.375 = 21.875.

reciprocal

mutual; shared; interchangeable

Use the associative property to simplify (n+17)+33.

n+50

Which rule about the sign of the quotient of positive and negative decimals is correct?

negative divided by negative = positive

When multiplying two negative integers, what is the sign of the product?

positive

p¹⁴

p¹⁷/p³

p¹⁰

p⁷⋅p³

matthew used the calculations below to find the product of the given fractions.(3/5)(4/9)(-1/2) Step 1 (3)(4)(-1)(5)(9)(-2) Step 2 -12-90 Step 3 12 90 Step 4 2 15 In which step did his first error occur?

step 1

katie bought a shirt for $14.98. She gave the cashier a $20 bill. Which operation(s) finds the amount of change katie received?

subtracting 14.98 from 20.00

Multiplicative Inverse Property

the product of a nonzero number and its reciprocal is 1

Which situation is best represented using a negative integer?

the temperature decreasing by 18º

Simplify 2(x - y) - (x + y)

x - 3y

Simplify: 2(x - y) - x + y

x-y

Half of a number minus seven is one and five-tenths.

x/2-7=1.5

x¹⁵

x²(x¹³)

x⁸

x⁵⋅x³

x³

x⁹⋅x⁻⁶

3x + y

y + 3x