7th Grade Accelerated Math: Benchmark Assessment #1 Review (Chapters 1-5)
0.5b + 7
(4 - 3.7b) - (-5.4b - 4) - (1.2b + 1)
56
(7)(8)
9
(−3) + 5 + (−5) + 12
−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
- 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)
-3.68
-0.7 + 0.02 + (-3)
x > -4
-1 - 6x - 6 > -11 - 7x
-182.608
-1.808 + (-180.8)
1/18
-1/2 - (-5/9)
56
-10 2/3(-5 1/4)
x = 5
-10(-4x + 7) = 130
-432.558
-102.99 x 4.2
x = 13
-10x + 4 = -126
x = 19
-10x - 10 = -200
x = 11
-10x - 5 = -115
x = -10
-10x - 7 = 93
-5
-12 - (-7)
x = 1
-12x + 7 = -5
x = -17
-12x - 1= 203
- 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)
x = 10
-210 = -7(9x - 60)
11
-22.44/-2.04
-9
-26 - (-17)
x = 6
-2x + 16 = 4
21x + 18
-3 (-7x - 6)
x < 3
-3 - 6(4x + 6) > -111
21/22
-3 1/2 ÷ -3 2/3
12
-3 Times -4
21x + 18
-3(-7x - 6)
x < -10
-3(x + 2) > 24
-3.45
-3.1 + (-0.35)
x = -1
-3x + 5 = 8
x = -5
-3x + 7 = 22
x = -3
-3x - 11 = -2
x > -3
-3x - 4 < 5
x ≥ -9
-3x ≤27
-1 2/5
-4 1/5 x 1/3
-12 3/5
-4 1/5 ÷ 1/3
8.1
-4.86 ÷ (-0.6)
x = 6
-4x + 8 = -16
x = -4
-4x + 9 = 25
x = 16
-4x - 10 = -74
x = -15
-4x - 8 = 52
x = 14
-4x - 9 = -65
-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
x = 3
-5x - 2 = -17
x = -11
-5x - 4 = 51
-1 9/20
-6 1/5 - (-4 3/4)
-12x + 30
-6(2x - 5)
-6.505
-6.98 + 0.475
-152
-65-87
x = -3
-6x - 8 = 10
161.28
-7.2(-22.4)
-1.83
-7.34 - (-5.51)
x = -6
-7x + 1= 43
0
-8 + 8
-18 13/24
-8 3/8 - 10 1/6
3.21
-8.49 + 11.7
x > -2
-8x + 2x - 16 < -5x + 7x
x = 20
-8x + 5 = -155
-11
-9 + -2
-6
-9 + 3
-5/14
-9/14 + 2/7
x = 15
-9x - 4 = -139
x ≤ -6
6 - 4(6x + 7) ≥ 122
36
6 posters cost $48. At that rate, how many posters can you buy for $288?
$120
6 t-shirts are $24. How much are 30?
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
5
6/15 = 2/x
36
6/x = 2/12
All Real Numbers
6x + 2 - 6x < 14
x = 1/3
6x - 4 = -2
x = 10
6x - 8 = 52
17
100 students went on a field trip. 6 buses were filled and 10 students traveled to the destination in cars with their parents. How many students were on each bus?
x = 11
10x + 2 = 112
x = -13
10x + 7 = -123
16 + (-5)
11
- 3.52 + 14.7
11.18
-1/3
11/12 + (-7/12)
0.55
11/20
x = 17
11x + 10 = 197
x = -5
11x + 3 = -52
x = 7
11x + 6 = 83
11
7 + (−1) + 12 − 7
11
7 - (-4)
x = 10
7 - x = -3
4.2
7 − 2.8
x = -3
7(2 - x) - 5= 30
14x + 21
7(2x + 3)
5x + 14
7(x + 2) - 2x
2.3
3.1 + -0.8
0.096
3.2 × 0.3
15.5
3.4 − (−12.1)
0.15
3/20
1 1/2
3/4 + 3/4
x = 16
3/4 x - 2 = 10
0.6
3/5
31
3/x = 6/62
7x - 14
7(x - 2)
x = -2
4x + 12 = 4
x = -1
4x + 16 = 12
x = 0
4x - 13 = -13
x < 1/2
4x - 2 < 0
x = -1/2
4x - 3 = -5
x = 12
4x - 4 = 44
x = -16
4x - 9 = -73
-20x + 5
5 (-4x + 1)
x ≥ 1
5 + 2x - 3x(2 + 4) ≤ -x(3 + 5) -3
x = 5
5 - 3x = -10
$1.80
5 apples cost $1. How much are 9?
-42
5 x (-8 2/5)
-20x + 5
5(-4x + 1)
10x + 15
5(2x + 3)
x = 6
5(5 - x) = -5
x ≥ 6
5(6 + 3x) + 7 ≥ 127
x = 1
5(7x - 13) = -30
x = -5
5(n + 2) = 3n
x = 6
5(x + 2) = 40
5x - 25
5(x - 5)
x = -35
5(x - 6) = 3 + 8 (x + 9)
4.002
5.001 + (-0.999)
−4.3
5.4 + (−9.7)
3.3
5.8 + (−2.5)
7x - 28
7(x - 4 )
26
5/13 = 10/x
38
5/19 = 10/x
4 1/3 + (- 3 1/2)
5/6
0.625
5/8
-1/4
5/8 - (7/8)
19
5/x = 10/38
x = 2
5x + 1 = 11
x = 3
5x + 3 = 18
x = 4
5x - 7 = 13
x = -12
5x - 8 = -68
x < 1
5x < 5
x = 3
7(x - 4) = - 7
0.35
7/20
1.75
7/4
28
7/x = 2/8
x = 2
9x - 10 = 8
x = -9
9x - 4 = -85
27
A baseball player has hit 9 home runs in 54 games. At that rate, how many home runs will he hit during a 162-game season?
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?
30
A boat travels 450 miles in 15 hours. What is the boat's speed in miles per hour?
160
A car can travel 480 miles on 15 gallons of gasoline. How far can it travel on 5 gallons?
300
A car can travel 80 miles on 4 gallons of gasoline. If the gas tank, which can hold about 15 gallons. How many miles can the car travel before it runs out gas?
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?
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?
L = A/W
Area of a rectangle A = LW Solve for L
h = 2A/b
Area of a triangle. A= (1/2)bh Solve for h
5 + (-3)
Create an expression to represent the number line.
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?
y ÷ x
How do you calculate the constant of proportionality?
7
How many days are in a week?
12
How many months are in a year?
Infinitely Many Solutions
How many solutions? 10 + x = x + 10
Infinitely Many Solutions
How many solutions? 2(3x + 3) = 3(2x + 2)
Infinitely Many Solutions
How many solutions? 3x + 1 = 1 + 3x
No Solution
How many solutions? 3x + 7x + 7 = 2(5x + 1)
No Solution
How many solutions? 3x - 2(3x + 5) = -5 - 3x + 15
No Solution
How many solutions? 4(2x + 1) = 5x + 3x + 9
One Solution
How many solutions? 4(x + 1) = x - 2
Infinitely Many Solutions
How many solutions? 4(x + 3) = 4x + 12
No Solution
How many solutions? 4x + 1 = 2(2x + 3)
One Solution
How many solutions? 4x + 2x - 5 = 7x - 1
Infinitely Many Solutions
How many solutions? 5(x + 2) - 3x = 2(x + 5)
Infinitely Many Solutions
How many solutions? 6(x + 1) + 5 = 13 - 2 + 6x
One Solution
How many solutions? 8(x + 2) = 2x + 16
No Solution
How many solutions? x + 5x + 4 = 3(2x - 1)
No Solution
How many solutions? -2(x + 1) = -2x + 5
Infinitely Many Solutions
How many solutions? 2x + 8 = 2(x + 4)
Infinitely Many Solutions
How many solutions? 2x - x + 7 = x + 3 + 4
One Solution
How many solutions? 3(x - 1) = 2x + 9
One Solution
How many solutions? 4x + 2x + 2 = 3x - 7
No Solution
How many solutions? x + 2x + 7 = 3x - 7
No Solution
How many solutions? x + 2x + 7 = 3x - 9
52
How many weeks are in a year?
500-3x=26
How old am I if 500 reduced by 3 times my age is 206?
33
The money used in Jordan is called the Dinar. The exchange rate is $3 to 2 Dinars. Find how many dollars you would receive if you exchanged 22 Dinars.
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?
the independent variables
In a table or a graph, what do the "x" values represent?
the dependent variables
In a table or a graph, what do the "y" values represent?
KIND
In a world where you can be anything, be....
straight (linear)
In order for a graph to represent a proportional relationship, the line of the graph must be _________.
origin (0,0)
In order for a graph to represent a proportional relationship, the line of the graph must pass through the _________.
terms
The parts of an algebraic expression.
0.18x + 36 = 60
Pete rents a car for one day. The charge is $36 plus $0.18 per mile. His total charge for the car was $60.
372
Portia travels 248 miles in 4 hours. At this rate, how far can she travel in 6 hours?
−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
−9w − 55.8
Simplify the expression: 9(−3w − 6.2 + 2w)
−x − 9
Simplify the expression: −1(x + 9)
1.5n − 3.2
Simplify the expression: −1.5(4 − n) + 2.8
−2z − 4
Simplify the expression: −1.5(8m − n)
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)
16
Six tons of ore can be processed in 3 hours. At that rate, how many tons of ore can be processed in 8 hours?
m = (y - b)/x
Slope Intercept Form y = mx + b Solve for m
b = -a/m
Slope of a line in standard form is: m= -a/b Solve for b
p-2L/2=w
Solve P = 2L + 2w for w
d/r=t
Solve d = rt for r
b₁ = 2A/h - b₂
Solve for b A = ½(b₁ + b₂)h
b = 2A/h
Solve for b A = ½bh
h = 2A/(b₁ + b₂)
Solve for h A = ½(b₁ + b₂)h
h = 2A/b
Solve for h A = ½bh
r = C/2π
Solve for r C = 2πr
x = 3/2y + 3
Solve for x 2x - 3y = 6
x = 2/3y + 2
Solve for x 3x - 2y = 6
x = 7/2 - y
Solve for x 7 = 2(x + y)
x=c-b/a
Solve for x ax + b = c
x = ½y + 8
Solve for x y = 2(x - 8)
y = 2/3 x - 2
Solve for y 2x - 3y = 6
y = 3/2x - 3
Solve for y 3x - 2y = 6
y = (x + 4)/x
Solve for y x = xy -4
π = A/r²
Solve for π A = πr²
k = 0.75
Solve the proportion.
x = (C - By)/A
Standard Form Ax + By = C Solve for x
inverse of addition
Subtraction
π = SA/(4r³)
Surface Area of a Sphere SA= 4πr³ Solve for π
like terms
Terms that have the same variables raised to the same exponents (terms that look alike).
reciprocal
The "flip" of a fraction
Constant Of Proportionality
The constant ratio between two proportional quantities (usually simplified to whole numbers).
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.
715.36
The tickets to a LegoLand park cost $89.42 each. How much will 8 tickets cost?
k = 1/10
What is the constant of proportionality? 10y = x
k = 1/12
What is the constant of proportionality? 12y = x
k = 1/23
What is the constant of proportionality? 23y = x
k = 1/2
What is the constant of proportionality? 2y = x
k = 1/3
What is the constant of proportionality? 3y = x
k = 1/4
What is the constant of proportionality? 4y = x
k = 1/6
What is the constant of proportionality? 6y = x
k = 1/7
What is the constant of proportionality? 7y = x
x < -5
What is the inequality for the graph?
x < 5
What is the inequality for the graph?
x > 2
What is the inequality for the graph?
x > 5
What is the inequality for the graph?
x ≤ 5
What is the inequality for the graph?
x ≥ -3
What is the inequality for the graph?
x ≥ 2
What is the inequality for the graph?
30
What is the length of the missing side?
4.8
What is the length of the missing side?
5
What is the length of the missing side?
8
What is the length of the missing side?
Simon
What is the name of Ms. Bixby's cat?
The Chum Bucket
What is the name of Plankton's restaurant?
The Krusty Krab
What is the name of the restaurant that Spongebob and Squidward work at?
45
What is the opposite of -45?
50
What is the opposite of -50?
64
What is the opposite of -64?
-19
What is the opposite of 19?
-1
What is the opposite of 1?
-81
What is the opposite of 81?
-3
What is the opposite of the opposite of -3?
$0.24
What is the unit price of a pack of 12 water bottles that cost $2.88?
$10 for 1 hour
What is the unit rate if it costs $20 for 2 hours?
$5 for 1 hour
What is the unit rate of if it costs $45 for 9 hours?
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 ?
23
What is the value of I 23 I ?
1
What is the value of the expression when q = -2, r = -12 and s = 8
-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 | ?
December
What month comes after November and before January?
WMS
What school do you attend?
The Greeks
When Ms. Bixby taught sixth grade, what team was she on?
Ms. Harrington and Mrs. Malloy
When Ms. Bixby taught sixth grade, who was she on a team with?
April 1st
When is Ms. Bixby's birthday?
Tomorrow
When is your math test?
Lesley University
Where did Ms. Bixby go to GRADUATE school?
Roger Willams University
Where did Ms. Bixby go to UNDERGRAD college?
-20
Which integer describes 20 years ago?
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?
207
Which room is Mr. Brennan's?
206
Which room is Mr. Dumont's?
211
Which room is Mrs. Doyle's?
208
Which room is Ms. Bixby's?
Roger Williams University
Which school did Ms. Bixby attend for her UNDERGRADUATE degree?
Responsibility
Which team are you on this year?
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?
Mrs. Doyle
Who is your language and literacy teacher this year?
Ms. Bixby
Who is your math teacher this year?
Mr. Brennan
Who is your science teacher this year?
Mr. Dumont
Who is your social studies teacher this year?
Mrs. D'Agostino
Who is your vice principal?
SpongeBob SquarePants
Who lives in a pineapple under the sea?
Spongebob Squarepants
Who lives in a pineapple under the sea?
28
William sold half of his comic book collection then purchased 10 more. He now has 24 comic books. How many books did William begin with?
0.85
Write 17/20 as a decimal.
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
x > -1
Write and solve this inequality: Negative twelve times a number is less than twelve.
x ≥ 37
Write and solve this inequality: Two more than twice a number is greater than or equal to seventy six.
-8 - x = -4x +1
x = 3
4x - 40 = 7(-2x + 2)
x = 3
13 - 4x = 1 - x
x = 4
-10x + 2 = -8x - 8
x = 5
x + 2 = 14 - x
x = 6
-13 + 4x = 1 + 2x
x = 7
8x = 3x + 35
x = 7
2x = 4x - 16
x = 8
2x - 5 = x + 4
x = 9
4
x/10 = 6/15
11
x/12 = 22/24
22
x/20 = 33/ 30
x = 14
x/7 - 4 = -2
1
x/7 = 3/21
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
x < -4
10 + 4x < -6
x ≥ -2
4(-3x + 2) + 5 ≤ 37
12x - 4
4(3x - 1)
16x - 20
4(4x - 5)
4x - 12
4(x - 3)
4x - 32
4(x - 8)
-1.8
4.5 × (- 0.4)
6
9/12 = x/8
0.45
9/20
12
9/x = 6/8
k = 40
What is the constant of proportionality?
k = 45
What is the constant of proportionality?
k = 46
What is the constant of proportionality?
k = 47
What is the constant of proportionality?
k = 6
What is the constant of proportionality?
k = 60
What is the constant of proportionality?
k = 750
What is the constant of proportionality?
Patrick
"Is this the Krusty Krab?" "No, this is..."
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)
x = -13
-x + 4 = 17
x < 2
-x - 4x > -10
x ≤ -13
-x - 5 ≥ 8
x ≤ -3
-x - 8 ≥ -5
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
2/4
0.5
59/100
0.59
6/10
0.6
-0.18
0.63 ÷ (-3.5)
18/25
0.72
x+x+2=-88
1) Find two consecutive odd integers whose sum is -88.
x = 0
1+ 4(2x + 1) = 5
-2.6 + 4.1
1.5
6.513
1.7 − (−0.8) + 4.013
5.5
1.8 − (−3.7)
0.1
1/10
x = 27
1/3 x + 2 = 11
x = 39
1/3 x - 2 = 11
0.2
1/5
2/17
1/5 times 10/17
0.125
1/8
1/4
1/8 divided by 1/2
17
1/x = 2/34
29
1/x = 2/58
3.124
12 + (-0.076) + (-8.8)
$15
12 footballs cost $36. How much are 5?
x = -4
12(-2x - 9) = -12
x = -7
12(-x + 5) = 144
36x - 48
12(3x - 4)
x = 2
12x - 9 = 2x + 11
15
14/10 = 21/x
42
14/x = 3/9
$1.20
15 pears cost $3. How much are 6?
-7/12
15/4 + (-4 1/3)
45
15/x = 4/12
x < -3
167 < 6 + 7(2 - 7x)
x = -6
17(3x + 2) = -272
34
17/x = 1/2
0.17
18 eggs cost $3.06. What is the cost per egg?
x ≤ 2
18 ≥ 5x + 4x
0.955
191/200
-6x + 16
2 (-3x + 8)
$126.50
2 pizzas cost $23. How much would 11 cost?
-2x - 14
2(-x - 7)
4x - 2
2(2x - 1)
x = 7
2(3x + 1) = 7x - 5
8x + 14
2(4x + 7)
10x - 18
2(5x - 9)
14x + 30
2(7x + 15)
14x - 6
2(7x - 3)
x = 12
2(x + 1) = 6x - 46
x = -1
2(x + 2) = 2
7
2.1 ÷ 0.3
0.4
2/5
50
20/x = 6/15
x = -8
245 = -5(4x - 17)
35
25/x = 10/14
x = 5
2x + 10 = 20
x = -8
2x + 15 = -1
x≥ -7
2x + 6≥ -8
x = -13
2x + 9 = x - 4
x = -4
2x - 3 = -11
x = 4
2x - 4 = -4(x - 5)
x ≤ -2
2x - 4 ≤ -8
x = -5
2x - 7 = -17
x < -1
3 < -5x + 2x
$3.50
3 bananas cost $1.50. How much do 7 cost?
$180
3 pairs of shorts are $30. How much are 18?
6x - 9
3(2x - 3)
12x + 21
3(4x + 7 )
x = 2
3(5x - 2) + 2 = 26
3x + 21
3(x + 7)
44
33/x = 6/8
x = -5
3x + 12 = -3
x = 1
3x + 12 = 15
x = -1
3x + 2 = -1
x = 5
3x + 2 = 17
x = 4
3x + 3 = 15
x = 6
3x + 8 = 26
x = 10
3x - 30 = 0
x = -14
3x - 6 = -48
x = 1
3x - 7 = 5x - 9
x = -2
3x = 2(7 + 5x)
x ≥ -4
3x ≥ -12
-12x + 32
4 (-3x + 8)
3.992
4 + (-0.008)
x = -6
4 = -2x + 16
x ≥ 9
4 ≤ y + (-5)
x = 0
7x + 2 = 2
x = 4
7x + 8 = 36
x = 5
7x - 2 = 33
$360
8 hockey sticks are $240. How much are 12?
-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 )
10
8/x = 12/15
40
8/x = 3/ 15
x = 3
8x + 3 = 27
x = -8
8x - 3 = -67
x = -20
8x - 7 = -167
$1.60
9 oranges cost $3.60. How much are 4?
x = -10
9(-4x - 29) = 99
2.7
9.8 − 7.1
Complex Fraction
A fraction where the numerator, denominator or both contain a fraction (a fraction within a fraction).
64.5
A gallon of milk weighs 8.6 pounds. How much would 7.5 gallons of milk weigh?
7
A lawyer charges $100 per month to be put on retainer for a client. The lawyer also charges an hourly rate of $75 for work done. How many hours does the lawyer have to work for a client, in one month, to charge $625?
160=28+12x
A new one-year membership at RecPlex costs $160. A registration fee of $28 is paid upfront, and the rest is paid monthly. How much do new members pay each month?
coefficient
A number multiplied by a variable (the number that comes before the variable).
constant
A number that is on its own.
$1.25
A pack of 4 t-shirt costs $5. What is the unit price for a t-shirt?
$0.58
A pack of 6 Dr. Peppers cost $3.48. What is the unit price for 1 Dr. Pepper?
1.5x + 7 = 11.50
A pizza shop charges $7.00 for a pizza and $1.50 per topping. The total charge for Noah's pizza is $11.50.
35x + 55 = 160
A plumber charges $55 for a service call plus $35 per hour. The plumber's total bill was $160.
Rate
A ratio that compares two quantities with different kinds of units(include labels).
3
A recipe for making 12 cupcakes requires 2 cups of flour. How many cups of flour would be needed to make 18 cupcakes?
8
A rectangular pool is twice as long as it is wide. What is the width of the pool if the perimeter is 48 yd?
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?
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?
22
A shop produces 39 wetsuits every 2 weeks. How many weeks will it take the shop to produce 429 wetsuits?
50
A shopper's discount club charges a monthly fee of $15 and sells gasoline for $2.05 per gallon. The gas station across the street sells gasoline for $2.35 per gallon and charges no fee. How many gallons of gasoline would you have to buy in one month to spend the same amount at either store?
Unit Rate
A simplified ratio where the first quantity is being compared to one unit of the second quantity.
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.
14
A snail traveled 2 feet in 100 minutes. How far will it travel in 700 minutes?
3x + 2.5 = 5.05
A student bought a juice pouch for $2.50 and 3 bags of chips. The total cost was $5.05.
variable
A symbol or letter that represents an unknown value.
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.
4
A twelve inch candle and an 18 inch candle are lit at 6pm. The 12-in. candle burns 0.5 inches every hour. The 18 inch candle burns two inches every hour. After how many hours will the two candles be the same height?
10x + 50 = 128
A waitress makes $10 an hour plus $50 in tips. Her total earning for one day was $128.
x/2+7=12
Abhasra spent half of her weekly allowance at the movies. To earn more money her parents let her clean the windows in the house for $7. What is her weekly allowance if she ended with $12?
Inverse of subtraction.
Addition
linear expression
An algebraic expression in which the exponent of each variable is 1.
187.5
An amusement park line is moving about 4 feet every 15 minutes. At this rate, approximately how long will it take for a person at the back of the 50- foot line to reach the front of the line?
150
An assistant cook peeled 18 potatoes in 6 minutes. At this rate, how many potatoes can he peel in 50 minutes?
Proportion
An equation that shows that two ratios are equivalent.
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.
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.
no
Are the two expressions equivalent? 3 − 5x AND 4.25 − 5x − 4.25
yes
Are the two expressions equivalent? 1.25x + 4 + 0.75x − 3 AND 2x + 1
3.08
At Discount Copy, 12 copies cost $0.66. Melissa needs 56 copies. How much should they cost?
16
At one store a trophy costs $12.50. Engraving costs $0.40 per letter. At another store, the same trophy costs $14.95. Engraving costs $0.25. How many letters, e, must be engraved for the costs to be the same?
2.40
At the Copy Shoppe, 18 copies cost $1.08. At that rate, how much will 40 copies cost?
50x + 10 = 128
Ben bought some $50 video games and one $10 movie. He spent $128.
57
Bill sold 38 papers in 2 hours. At this rate, how many papers would he sell in 3 hours?
5
Bill weighs 120 pounds and is gaining ten pounds each month. Phil weighs 150 pounds and is gaining 4 pounds each month. How many months will it take for Bill to weigh the same as Phil?
352
Bobby drove 110 miles, and his car used up 5 gallons of gas. How many miles can he drive with 16 gallons of gas?
The Red Sox
Boston's baseball team.
The Celtics
Boston's basketball team.
The Bruins
Boston's hockey team.
0.6x + 18 = 36
Brady rents a paddle board. It costs $36 in total. There was an $18 rental fee and a $0.60 charger per hour.
55x + 35 = 160
Brooke spends $55 on each shirt she purchased and bought a pair of jeans for $35. Her total purchase was $160.
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?
12.5
Container A and container B have leaks. Container A has 800 ml of water, and is leaking 6 ml per minute. Container B has 1000 ml, and is leaking 10 ml per minute. How many minutes, m, will it take for the two containers to have the same amount of water?
Unit Price
Cost per one unit/item.
-3 + (-2)
Create an expression to represent the number line.
-3 + 2
Create an expression to represent the number line.
63
Darrell drove 189 miles in 3 hours. What was Darrell's average rate of speed in miles per hour?
Inverse of multiplication
Division
24=3x+18
Eugene had $24 to spend on three pencils. After buying them he had $18. How much did each pencil cost?
-9
Evaluate (-10) + (-2) + 3
3
Evaluate 10 + (-10) + 3
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.
-1.25(x + 4)
Factor out the coefficient. -1.25x - 5
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
12(3c + 2d)
Factor the expression: 36c + 24d
3.5(12 + h)
Factor the expression: 42 + 3.5h
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
3(3 − 5x)
Factor the expression: 9 − 15x
−4(x − 9)
Factor the expression: −4x + 36
−5(p − 4)
Factor the expression: −5p + 20
−12(2k − 10)
Factor −12 out of −24k + 120
−4(2k + 3)
Factor −4 out of −8k − 12
−5(d − 6)
Factor −5 out of −5d + 30
−8(4d − 7)
Factor −8 out of −32d + 56
x+x+2+x+4+x+6=56
Find four consecutive odd integers whose sum is 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)
2m − 15
Find the difference: (m − 3) − (−m + 12)
−2x − 3
Find the difference: (x − 1) − (3x + 2)
−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)
3x + 2
Find the sum: (x + 3) + (2x − 1)
0.9m − 12
Find the sum: (−2.1m − 5) + (3m − 7)
−3
Find the sum: (−8z + 4) + (8z − 7)
x+x+2+x+4=72
Find three consecutive even integers whose sum is 72
25x+612=912
Friendship's soccer team purchased uniforms and equipment for a total cost of $912. The equipment cost $612, and the uniforms cost $25 each. What equation can be used to represent the situation?
96
Gary can hike 2.5 miles in 30 minutes. At this rate, how long will it take him to hike 8 miles?
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
2.5x + 3 = 5.05
Hadlee bought scrunchies for $2.50 each and paid $3 in tax for her purchase. Her total was $5.05.
Worries
Hakuna Matata. It means no ___.
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
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
5
If 3 twinkies cost $1, how much is it for 15 twinkies?
60
If 5 pencils cost 20 cents, how much would 15 pencils cost?
25.80
If 8 bags of chips costs $10.32, how much will you pay for 20 bags?
6 and 2/3 miles
If Jim runs 5 miles in 3/4 of an hour, how many miles can he run in 1 hour?
325
If John can travel 130 miles in 2 hours, how far can he travel in 5 hours if he travels at the same rate of speed?
8 miles
If Sally swims 2 miles in 1/4 of an hour, how many miles can she swim in an hour?
additive inverses
Integers that are opposites are also called _________.
opposites
Integers that have the same absolute value but are located on opposite sides of zero are called _________.
r = I/(pt)
Interest formula I = prt solve for r
The goal when solving an equation
Isolate the variable
12
It takes 20 minutes to cut a log into 5 equal-size pieces. How long will it take to cut a similar log into 3 equal-size pieces?
20
Jenny can send texts on her phone at the rate of 32 words per minute. If she sends 8 texts that average 80 words each, about how long would it take her?
$0.99
John bought 8 Kit-Kats for $7.92. What is the unit price for the Kit-Kats?
45
Jonathan purchased 120 pieces of candy for Valentine's Day. He gives 2 pieces to each of his friends. When he finishes handing out candy, he has 30 pieces left. How many friends did he give candy to?
35+0.50x=52
Juan's cell phone company charges $35 a month for phone service plus $0.50 for each text message. How many text messages does Juan send in a month if his bill was $52?
3
Mark walked three-quarters of a mile in fifteen minutes. How many miles can he walk in an hour?
−7s + 7t
Simplify the expression: 2s − 9s + 8t − t
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.
115
Mary ran 2 miles in about 23 minutes. If she continues at the same pace, how long will it take her to run 10 miles?
2
Michael and Kevin are running. Kevin gets a 3-mile head start and runs at a rate of 5.5 mi/h. Michael runs at a rate of 7 mi/h. How many hours will it take Michael to catch up with Kevin?
121-4x=9
Ming won 121 lollipops playing basketball at her school's game night. Later, she gave four to each of her friends. She only has 9 remaining. How many friends does she have?
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?
inverse of division
Multiplication
3
Netflix charges David $15 per month for a membership, plus a $5 one-time fee for streaming on his phone. How many months will David have his membership for if Netflix charges him $50?
The Patriots
New England's football team.
21
Nine items can be produced in 15 minutes. How many items can be produced in 35 minutes?
2,100
Of the 50 fish that Jim caught from the lake, 14 were trout. The estimated population of the lake is 7,500 fish. About how many trout would you expect to be in the lake?
9
On Saturday, you bowl at Mar Vista Bowl, where renting shoes costs $2 and each game bowled is $3.50. On Sunday, you bowl at Pinz where the shoe rental is $5 and each game bowled is $3.25. If you spent the same amount each day, how many games, g, were bowled?
15
One scooter and two identical bikes are for sale. Each bike is $7 more than the scooter. If the total value of the items is $59, then find the value of the scooter.
280
Pep Club members are making spirit buttons. They make 490 spirit buttons in 3.5 hours. How many buttons can they make in 2 hours?
L = (P - 2W)/2
Perimeter of a rectangle. P= 2L + 2W Solve for L
S = P/4
Perimeter of a square. P=4S Solve for S
9
Rosemary had $37 to spend on school supplies. She buys some packages of mechanical pencils for $4 each. After her trip to the store, she only has $1 left. How many packs of pencils did she buy?
200
Ruby weighs 88 lbs. Her weight is 12 lbs. less than half her father's weight. How much does her father weigh?
25
Ryan goes to the mall with his friends after school. At the mall, he purchases 4 pairs of basketball shorts and a pair of sneakers for $100. If he spends a total of $200, how much money did he spend on each pair of basketball shorts?
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?
4+3x=19
Sandra scores 4 baskets in his first basketball game. She then scored the same number of baskets in each of her next 3 games. If Sandra made 19 baskets total, how many baskets did she score in each of the three games?
7x + 1.5 = 11.50
Seven friends go to the movies. They each get a ticket and share one bucket of popcorn for $1.50. Their total cost is $11.50.
350
Seven out of every twelve people have brown eyes. If 490 people have brown eyes, how many do not?
8r − 17
Simplify the expression: (2r − 13) − (−6r + 4)
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
400
The ratio of athletes to non-athletes at Taylor middle school is 3 to 4. If there are 300 athletes, how many non-athletes are there?
24
The ratio of seventh graders to eighth graders participating in the science fair is 4:3. There are 18 eighth graders participating in the science fair. How many 7th graders are there?
4
The ratio of teachers to students needs to be 1:30. If there were 120 students, how many teachers would be needed?
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.
67.5
The scale of a model train Is 1 inch to 13.5 feet. One of the cars of the model trains is 5 inches long. What is the length in feet of the actual train car?
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 _________.
x+x+2+x+4=39
The sum of three consecutive odd numbers is 39. What is the smallest of these numbers?
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?
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?
6x + 24 = 276
There are 276 seventh graders going on a field trip. The school ordered seven buses to transport students. The last bus has 24 students on it, and the rest of the buses all have the same number of students. Write an equation that represents this situation. Let "x" represent the number of students on the buses other than the last bus.
8
There was a blizzard. Snow was falling at a rate of 4 ½ inches per hour. If the snow kept accumulating at the same rate, how long would it take for 3 feet of snow to accumulate?
72
Tia is painting her house. She paints 45 square feet in 2.5 hours. At this rate, how many square feet can she paint in 4 hours?
18
To make lemonade, you need 6 lemons and 8 cups of water. How many lemons do you need if you have 24 cups of water?
add the opposite of the second/third/fourth... rational number.
To subtract rational numbers you must...
340
Two friends rent an apartment together. They agree that Joe will pay 1.5 times what Mike pays. If the rent is $850, how much will Mike pay?
20
UPS charges $7 for the first pound, and $0.20 for each additional pound. FedEx charges $5 for the first pound and $0.30 for each additional pound. How many additional pounds, p, will it take for UPS and FedEx to cost the same?
k = 3/2
What is the constant of proportionality?
Today
What do we call the day after yesterday but the day before tomorrow?
Common denominators
What do you need to add or subtract fractions?
y = kx
What equation can be used to represent the relationship in a table or graph that displays proportional relationships?
7th
What grade are you in?
-9/50
What is -0.18 as a fraction in simplest form?
-5.888...
What is -5 8/9 as a decimal?
-5 24/50
What is -5.96 as a fraction in simplest form?
Wildcat
What is Wilson's mascot?
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?
K = 1/2
What is the constant of proportionality?
K = 2
What is the constant of proportionality?
K = 3
What is the constant of proportionality?
K = 4
What is the constant of proportionality?
K = 5/4
What is the constant of proportionality?
k = 10
What is the constant of proportionality?
k = 16
What is the constant of proportionality?
k = 20
What is the constant of proportionality?
k = 200
What is the constant of proportionality?
$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?
4x+20=100
You and three friends go to the town carnival. You have a coupon for $20 off that will save your group money! If the total bill to get into the carnival was $100, how much does one regular price ticket cost?
2x+3=19
You bought a magazine for $3 and some candy bars for $2 each. You spent a total of $19. How many candy bars did you buy?
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.
6
You can buy 2 hot dogs for $3. How much would it be for 4 hot dogs?
75
You estimate that you can do 12 math problems in 45 min. How long should it take you to do 20 math problems?
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.
4x+11=23
You had $23 to spend on four avocados. After buying them you had $11. How much did each avocado cost?
$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.
improper fraction
when multiplying fractions I must change a mixed number to a/an
x ≤ 1
x + (-4) ≤ -3
x = 3
x + 3 = 3(11 - 3x)
x ≤ -90
x + 45 ≤ -45
x = 4
x + 9 = 13
x > -6
x - 3 > -9
x = 32
x - 7 = 25
-6x + 20 = -2x + 28
x = -2
3x + 8 = 2x - 17
x = -25
6x - 8 = 9x + 1
x = -3
-3x - 15 = -6x - 27
x = -4
-5x + 2 = 4x + 47
x = -5
6x + 7= 13 + 7x
x = -6
2x + 7 = 4x + 23
x = -8
75 + 14x = 4x - 15
x = -9
5 + 3x = 2x + 6
x = 1
8x + 4 = 10 + 2x
x = 1
15x - 10 = -9x + 2
x = 1/2
42 + 7x = 8(x + 4)
x = 10
-14 - 3x = -5x + 8
x = 11
2x - 1 = x + 11
x = 12
8x - 16 = 4x + 40
x = 14
7x - 12 = 3 + 6x
x = 15
