7th Grade Math: Benchmark Assessment #1 Review 20-21

9.475

A container has 113.7 ounces of juice. The juice is divided into 12 equal servings. How much juice is in each serving?

64.5

A gallon of milk weighs 8.6 pounds. How much would 7.5 gallons of milk weigh?

coefficient

A number multiplied by a variable (the number that comes before the variable).

constant

A number that is on its own.

9.908

A scientist is mixing soil for his plants. He combines 4.815 kilograms of sand, 0.173 kilogram of peat moss, and 4.92 kilograms of topsoil. What is the total weight of this mixture?

8.6w

An exercise mat is 3.3 times as long as it is wide. Write an expression in simplest form that represents the perimeter of the exercise mat.

algebraic expression

An expression that contains numbers, variables, operations and one or more symbols.

14(3a + b)

Factor the expression: 42a + 14b

4(y − 5)

Factor the expression: 4y − 20

2.5(2 + q)

Factor the expression: 5 + 2.5q

6(n − 4)

Factor the expression: 6n − 24

12(6m − 5)

Factor the expression: 72m − 60

−4(x − 9)

Factor the expression: −4x + 36

−4(2k + 3)

Factor −4 out of −8k − 12

−8(4d − 7)

Factor −8 out of −32d + 56

0.5b + 7

Find the difference: (4 − 3.7b) − (−5.4b − 4) − (1.2b + 1)

2y + 12

Find the difference: (4y + 3) − (2y − 9)

−8.3c − 15

Find the difference: (−2c + 5) − (6.3c + 20)

1/20

Find the product of -2/11 and -11/40

−11n + 11

Find the sum: (4.5 − n) + (−10n + 6.5)

8z − 2

Find the sum: (5z + 4) + (3z − 6)

4c + 5

Find the sum: (c − 4) + (3c + 9)

0.9m − 12

Find the sum: (−2.1m − 5) + (3m − 7)

−3

Find the sum: (−8z + 4) + (8z − 7)

59/100

0.59

6/10

0.6

-0.18

0.63 ÷ (-3.5)

18/25

0.72

39/50

0.78

4/5

0.8

17/20

0.85

19/20

0.95

48/100

0.96

- 2 1/2 + ( 4 1/4)

1 3/4

6.513

1.7 − (−0.8) + 4.013

5.5

1.8 − (−3.7)

0.1

1/10

2.5w and 4w

Identify the like terms in the expression: 2.5w − 3y + 4w

3n and -n, 7 and -3

Identify the like terms in the expression: 3n + 7 − n − 3

3z and 4z, 4 and 2

Identify the like terms in the expression: 3z + 4 + 2 + 4z

4p and p, 7 and -5

Identify the like terms in the expression: 7 + 4p − 5 + p + 2q

1/4

1/8 divided by 1/2

16 + (-5)

11

- 3.52 + 14.7

11.18

-1/3

11/12 + (-7/12)

0.55

11/20

3.124

12 + (-0.076) + (-8.8)

36x - 48

12(3x - 4)

-7/12

15/4 + (-4 1/3)

0.17

18 eggs cost $3.06. What is the cost per egg?

0.955

191/200

-6x + 16

2 (-3x + 8)

-2x - 14

2(-x - 7)

4x - 2

2(2x - 1)

8x + 14

2(4x + 7)

10x - 18

2(5x - 9)

14x + 30

2(7x + 15)

14x - 6

2(7x - 3)

7

2.1 ÷ 0.3

0.4

2/5

6x - 9

3(2x - 3)

12x + 21

3(4x + 7 )

0.15

3/20

1 1/2

3/4 + 3/4

0.6

3/5

-12x + 32

4 (-3x + 8)

3.992

4 + (-0.008)

4x - 12

4(x - 3)

4x - 32

4(x - 8)

-1.8

4.5 × (- 0.4)

-42

5 x (-8 2/5)

4 1/3 + (- 3 1/2)

5/6

0.625

5/8

-1/4

5/8 - (7/8)

2.02

6 − 3.98

12x + 18

6(2x + 3)

18x - 12

6(3x - 2)

-1.6

6.4 ÷ (-4)

1.425

6.84 ÷ 4.8

11

7 + (−1) + 12 − 7

4.2

7 − 2.8

14x + 21

7(2x + 3)

5x + 14

7(x + 2) - 2x

7x - 14

7(x - 2)

7x - 28

7(x - 4 )

0.35

7/20

1.75

7/4

-80

8 multiplied by -10

80

8 multiplied by 10

-24x + 40

8(-3x + 5)

72x - 8

8(9x - 1)

8x - 64

8(x - 8 )

2.7

9.8 − 7.1

3n + 1

A basket holds n apples. You pick (2n − 3) apples, and your friend picks (n + 4) apples. How many apples do you and your friend pick together? How many baskets do you need to carry all the apples?

4

A basket holds n apples. You pick (2n − 3) apples, and your friend picks (n + 4) apples. How many baskets do you need to carry all the apples?

13

A bird's nest is 12 feet above the ground. A mole's den is 12 inches below the ground. What is the difference, in feet, between the height of these two positions?

Kind

In a world where you can be anything, be _____.

additive inverses

Integers that are opposites are also called _________.

−x − 9

Simplify the expression: −1(x + 9)

5y

Simplify the expression: −10y + 15y

−8 + 6n

Simplify the expression: −2(4 − 3n)

−18.5s + 28.1

Simplify the expression: −2.5(2s − 5) − 3(4.5s − 5.2)

-20 + 2.5b

Simplify the expression: −2.5(8 − b)

−12x + 30

Simplify the expression: −3(4x − 10)

28 + 21d

Simplify the expression: −7(1 − 3d − 5)

like terms

Terms that have the same variables raised to the same exponents (terms that look alike).

reciprocal

The "flip" of a fraction

52.5n + 449.85

The cost (in dollars) of a custom-made sweatshirt is represented by 3.5n + 29.99, where n is the number of different colors in the design. Write a simplified expression that represents the cost of 15 sweatshirts.

terms

The parts of an algebraic expression.

4.8

The total weight of 32 math books is 153.6 pounds. If each book is the same weight, what is the weight of 1 math book?

-5.888...

What is -5 8/9 as a decimal?

-5 24/50

What is -5.96 as a fraction in simplest form?

14

What is the absolute value of -14?

7

What is the absolute value of -7?

13

What is the absolute value of 13?

9

What is the absolute value of 9?

-19

What is the opposite of 19?

18

What is the value of I -18 I ?

76

What is the value of I -76 I ?

8

What is the value of I -8 I ?

-20

Which integer describes 20 years ago?

7m + 19

While catching fireflies, you and a friend decide to have a competition. After m minutes, you have (3m + 13) fireflies and your friend has (4m + 6) fireflies. How many total fireflies do you and your friend catch?

You

While catching fireflies, you and a friend decide to have a competition. After m minutes, you have (3m + 13) fireflies and your friend has (4m + 6) fireflies. The competition lasts 3 minutes. Who has more fireflies?

Mr. Gray

Who is your guidance counselor this year?

Mr. Hausermann

Who is your language and literacy teacher this year?

4 3/50

Write 4.06 as a fraction.

53/8

Write 6 5/8 as an improper fraction.

8 17/50

Write 8.34 as a mixed number in simplest terms.

0.36

Write 9/25 as a decimal

improper fraction

when multiplying fractions I must change a mixed number to a/an

56

(7)(8)

−5.19

(−4.79) + (−0.4)

0.8

(−8.1) − (−8.9)

-5.6

(−9.1) + 3.5

5x - 4

- (-5x + 4)

-3x + 2

- (3x - 2)

- 1/3 + (- 1/8)

- 11/24

2/3 + (-8/3)

- 2

- 2/3 + 2/9

- 4/9

1/4 + - 2/3

- 5/12

- 45.2 + (-9.3)

- 54.5

-3.68

-0.7 + 0.02 + (-3)

-182.608

-1.808 + (-180.8)

1/18

-1/2 - (-5/9)

56

-10 2/3(-5 1/4)

-432.558

-102.99 x 4.2

-5

-12 - (-7)

- 2/25 + (- 15/25)

-17/25

6x + 16

-2 (-3x - 8)

-14x + 6

-2 (7x - 3)

-2x + 14

-2 (x - 7)

6x + 16

-2(-3x - 8)

11

-22.44/-2.04

-9

-26 - (-17)

11

7 - (-4)

2.3

3.1 + -0.8

0.096

3.2 × 0.3

15.5

3.4 − (−12.1)

-20x + 5

5 (-4x + 1)

-20x + 5

5(-4x + 1)

10x + 15

5(2x + 3)

5x - 25

5(x - 5)

4.002

5.001 + (-0.999)

−4.3

5.4 + (−9.7)

3.3

5.8 + (−2.5)

119.66

A chain link fence is 19.3 meters long. Mr. Potter wants to make the fence 6.2 times longer. What will be the length of the new fence?

no

Are the two expressions equivalent? 3 − 5x AND 4.25 − 5x − 4.25

5 + (-3)

Create an expression to represent the number line.

m + 1

In a basketball game, the home team scores (2m + 39) points and the away team scores (3m + 40) points, where "m" is the number of minutes since halftime. What is the difference in the scores "m" minutes after halftime?

−5w + 2g

Simplify the expression: 2w − g − 7w + 3g

3q + 21

Simplify the expression: 3(2 + q) + 15

15 + 3n

Simplify the expression: 3(5 − 2n) + 9n

2m + 15

Simplify the expression: 3.5m − 1.5(m − 10)

1.4x − 5

Simplify the expression: 3.7x − 5 − 2.3x

-4h

Simplify the expression: 4h − 8h

−12s − 15

Simplify the expression: 6(3s − 2.5 − 5s)

3.5r − 7

Simplify the expression: 6.4r − 7 − 2.9r

9y + 2

Simplify the expression: 6y + 9 + 3y − 7

13p

Simplify the expression: 7p + 6p

x − 12

Simplify the expression: 7x − 2(3x + 6)

10x − 5

Simplify the expression: 8x − 5 + 2x

1.5n − 3.2

Simplify the expression: −1.5(4 − n) + 2.8

−2z − 4

Simplify the expression: −1.5(8m − n)

715.36

The tickets to a LegoLand park cost $89.42 each. How much will 8 tickets cost?

45

What is the opposite of -45?

50

What is the opposite of -50?

64

What is the opposite of -64?

-1

What is the opposite of 1?

-81

What is the opposite of 81?

-3

What is the opposite of the opposite of -3?

23

What is the value of I 23 I ?

-24

What is the value of the expression? 38 − (− 14)

4

What is the value of the expression? −0.28 ÷ (−0.07)

20

What is the value of | -20 | ?

1,500

Which integer describes ascending 1,500 feet?

-5

Which integer describes spending 5 dollars?

-3

Which integer is the same distance from 0 as 3?

Integrity

Which team are you on in seventh grade?

Ms. Trischitta

Who is your math teacher this year?

Ms. Trischitta

Who is your science teacher this year?

Mrs. Waldron

Who is your world geography teacher this year?

SpongeBob SquarePants

Who lives in a pineapple under the sea?

0.85

Write 17/20 as a decimal.

2/4

0.5

- 2 1/2 + (- 4 1/4)

- 6 3/4

- 3/4 + (- 1/8)

- 7/8

-33.3 + 25.25

- 8.05

-7.003

-0.003 + (-7)

1.09

-0.01 + 1.1

-6.66

-0.6 + (-6) + (-0.06)

21x + 18

-3 (-7x - 6)

21/22

-3 1/2 ÷ -3 2/3

12

-3 Times -4

21x + 18

-3(-7x - 6)

-3.45

-3.1 + (-0.35)

-1 2/5

-4 1/5 x 1/3

-12 3/5

-4 1/5 ÷ 1/3

8.1

-4.86 ÷ (-0.6)

-13

-5 + (-8)

-13

-5 + -8

-10x -35

-5(2x + 7)

-22.287

-5.7(3.91)

10.20

-55.08 divided by -5.4

-1 9/20

-6 1/5 - (-4 3/4)

-12x + 30

-6(2x - 5)

-6.505

-6.98 + 0.475

-152

-65-87

161.28

-7.2(-22.4)

-1.83

-7.34 - (-5.51)

0

-8 + 8

-18 13/24

-8 3/8 - 10 1/6

3.21

-8.49 + 11.7

-11

-9 + -2

-6

-9 + 3

-5/14

-9/14 + 2/7

9

(−3) + 5 + (−5) + 12

7200 + 57d

A ski resort makes snow using a snow fan that costs $1200. The fan has an average daily operation cost of $9.50. Write a simplified expression that represents the cost to purchase and operate 6 snow fans.

variable

A symbol or letter that represents an unknown value.

linear expression

An algebraic expression in which the exponent of each variable is 1.

10.61

Connor bought 3 packages of donuts at $1.03 each and 2 gallons of orange juice at $3.42 each. If the tax on the items was $0.68, what was the total amount she spent?

12(3c + 2d)

Factor the expression: 36c + 24d

-9

Evaluate (-10) + (-2) + 3

3

Evaluate 10 + (-10) + 3

4x + 4500

Greenland has a population of "x" people. Barbados has a population of about 4500 more than 5 times the population of Greenland. Find the difference in the populations of these two countries

Worries

Hakuna Matata. It means no ___.

38

Harry ran 34.2 miles while training for a track meet. He ran 0.9 miles each day. How many days did he train for the track meet?

-9/50

What is -0.18 as a fraction in simplest form?

−9w − 55.8

Simplify the expression: 9(−3w − 6.2 + 2w)

4 11/14

Ryder rode 3 and 1/7 miles on his bicycle yesterday. He rode 1 and 9/14 miles today. How many miles did he ride during these two days?

8r − 17

Simplify the expression: (2r − 13) − (−6r + 4)

add the opposite of the second/third/fourth... rational number.

To subtract rational numbers you must...

Common denominators

What do you need to add or subtract fractions?

6w + 8

You expand a rectangular garden so the perimeter is now twice the perimeter of the old garden. The expression 12w + 16 represents the perimeter of the new garden, where w represents the width of the old garden. Write an expression that represents the perimeter of the old garden.

$228

You want to buy a bicycle with your friend. You have $43.50 saved and plan to save an additional $7.25 every week. Your friend has $24.50 saved and plans to save an additional $8.75 every week. After 10 weeks, you and your friend use all of the money and buy the bike. How much does the bike cost?

16w + 68

You want to buy a bicycle with your friend. You have $43.50 saved and plan to save an additional $7.25 every week. Your friend has $24.50 saved and plans to save an additional $8.75 every week. Simplify an expression that represents the amount of money you and your friend save after "w" weeks.

12x - 4

4(3x - 1)

16x - 20

4(4x - 5)

0.45

9/20

0.498

(- 0.2) × 8.3 × (- 0.3)

-7

(- 2.8) ÷ 0.4

-2.55

(- 5.1) × 0.5

2.22

(-11.1) × (- 0.2)

-70

(-42) ÷ (0.6)

-56

(-7)(8)

68.62

(-7.3)(-9.4)

-27

(−16) − 6 + (−5)

-13.4

(−0.8) + (−7.2) − 5.4

10

(−11) − (−14) + 7

-12

(−11) − 8 + 1 − (−6)

-5.1

(−14.8) − (−9.7)

23/100

0.23

6/25

0.24

1/4

0.25

6/20

0.3

31/100

0.31

19/50

0.38

2/5

0.4

-2.6 + 4.1

1.5

0.2

1/5

2/17

1/5 times 10/17

0.125

1/8

3x + 21

3(x + 7)

4w + 16

A rectangular room is 10 feet longer than it is wide. How many 1-foot square tiles does it take to tile along the inside walls of the room?

6 + 2x

A table is 6 feet long and 3 feet wide. You extend the length of the table by inserting two identical table leaves. The extended table is rectangular with an area of (18 + 6x) square feet. Write an expression that represents the length (in feet) of the extended table.

30 + 9.75p

A three-dimensional printing pen uses heated plastic to create three-dimensional objects. A kit comes with one 3D-printing pen and p packages of plastic. An art club purchases 6 identical kits for (180 + 58.5p) dollars. Write an expression that represents the cost of one kit.

11,500 + 180n

An organization drills 3 wells to provide access to clean drinking water. The cost (in dollars) to drill and maintain the wells for n years is represented by 34,500 + 540n. Write an expression that represents the cost to drill and maintain one well for "n" years.

yes

Are the two expressions equivalent? 1.25x + 4 + 0.75x − 3 AND 2x + 1

-3 + (-2)

Create an expression to represent the number line.

-3 + 2

Create an expression to represent the number line.

0

Evaluate 7 + (-9) + 2

- 4/5

Evaluate the complex fraction

-1 1/5

Evaluate the complex fraction

-1 7/19

Evaluate the complex fraction

1/9

Evaluate the complex fraction

17 1/2

Evaluate the complex fraction

equivalent expressions

Expressions that have the same value but that are written in different forms.

1.7( j − 2)

Factor the expression: 1.7j − 3.4

5(3x + 5)

Factor the expression: 15x + 25

8(2n − 3)

Factor the expression: 16n − 24

6(3a − 2)

Factor the expression: 18a − 12

2(b + 4)

Factor the expression: 2b + 8

3.5(12 + h)

Factor the expression: 42 + 3.5h

3(3 − 5x)

Factor the expression: 9 − 15x

−5(p − 4)

Factor the expression: −5p + 20

−12(2k − 10)

Factor −12 out of −24k + 120

−5(d − 6)

Factor −5 out of −5d + 30

2m − 15

Find the difference: (m − 3) − (−m + 12)

−2x − 3

Find the difference: (x − 1) − (3x + 2)

3x + 2

Find the sum: (x + 3) + (2x − 1)

8x and 2x

Identify the like terms in the expression: 8x − 5 + 2x

z and 4z

Identify the like terms in the expression: z + 8 − 4z

opposites

Integers that have the same absolute value but are located on opposite sides of zero are called _________.

6m + 2

Mars has "m" moons. The number of moons of Pluto is one more than twice the number of moons of Mars. The number of moons of Neptune is one less than 3 times the number of moons of Pluto. Write a simplified expression that represents the number of moons of Neptune.

0.28

Mrs. Smith paid $5.32 to buy a pen for each student in his class. Her class has 19 students. How much did each pen cost?

−7s + 7t

Simplify the expression: 2s − 9s + 8t − t

11j + 4

Simplify the expression: (3j + 11) + (8j − 7)

−2z + 22

Simplify the expression: 14 − 3z + 8 + z

2a − 6

Simplify the expression: 2(a − 3)

−6s − 8

Simplify the expression: 2(−3s + 1 − 5)

8h − 12.75

Simplify the expression: 2.25 − 2(7.5 − 4h)

−9.8g

Simplify the expression: 2.4g − 2.4g − 9.8g

6.5w − 3y

Simplify the expression: 2.5w − 3y + 4w

6.8x − 5

Simplify the expression: 2.5x + 4.3x − 5

−6m

Simplify the expression: 2m - m - 7m

2x + 20

The rectangular pupil of an octopus is estimated to be 20 millimeters long with an area of (20x − 200) square millimeters. Write an expression that represents the perimeter (in millimeters) of the octopus pupil.

7

The sum of -25 and 32

28

The sum of 16 and 12

11.71

The sum of 2.31 and 9.4

0

The sum of an integer and it's additive inverse always equals _________.

0

The sum of an integer and it's opposite always equals _________.

31

The temperature in Juneau, Alaska was 13°F, while the temperature in Fairbanks, Alaska was -18°F. How many degrees warmer was it in Juneau than in Fairbanks?

$2.50

You and 4 friends are buying tickets for a concert. The cost to buy one ticket is "c" dollars. If you buy all the tickets together, there is a discount and the cost is (5c − 12.5) dollars. How much do you save per ticket when you buy the tickets together?

7h + 9

You and a friend collect seashells on a beach. After "h" minutes, you have collected (11 + 2h) seashells and your friend has collected (5h − 2) seashells. How many total seashells have you and your friend collected?

4m + 8

You burn 265 calories running and then 7 calories per minute swimming. Your friend burns 273 calories running and then 11 calories per minute swimming. You each swim for the same number of minutes. Find the difference in the amounts of calories burned by you and your friend.