Expressions, Inequalities, and Equations
Hannah LOVES to read. She has four books on her book shelf at home the weights of the books are shown below:
2.5, 3.2, 2.7, 2.3
Which inequality represents the weight, w, of any book on Hannah's books on the shelf?
A. w > 2.3
B. w < 2.4
C. w > 3.2
D. w < 3.3
D. w < 3.3
The lightest book Hannah has is 2.3 and the heaviest book is 3.2 this means the weight, w, must be less than 3.3 or greater than 2.2.
Meredith bought a new tumbling mat in the shape of a rectangle. What is the area of Meredith's tumbling mat if it has a base of 32 inches and a height of 14 inches? Be sure to use your units!!
448 in2
A=B X H
A = 32 x 14
A =448
At Emelia's softball game she hit 3 triples and 9 doubles. What is the ratio of the number of triples to the number of doubles that Emelia hit at her game? Make your ratio basic.
A. 1:3
B. 1:4
C. 1:6
D. 3:1
A. 1:3
Your ratio needs to be in the order Triples : Doubles
Emelia hit 3 triples and 9 doubles, 3:9
Make your ratio basic by reducing (dividing) both sides, similar to fractions!
3 goes into 3, 1 time and 3 goes into 9, 3 times creating the basic ratio 1:3.
Find the area of a trapezoid whose bases are 8.6 cm and 12.9 cm and has a height of 6.4 cm.
68.8 cm
A= Base 1 + Base 2 / 2 x H
A = 8.6 + 12.9 /2 x 6.4
A = 21.5 / 2 x 6.4
A = 10.75 x 6.4
A = 68.8 cm
What operation is being used when you are finding the sum?
Addition
What value of y makes the equation below true?
y + 2.9 = 11
A. 8.1
B. 8.9
C. 9.1
D. 13.9
A. 8.1
8.1 + 2.9 = 11
Wyatt is going hunting on a plot of land that is the shape of a rectangle. The land is 30 miles long and 17 miles wide. What this the total area of the land Wyatt is hunting on? Be sure to use your units!!
510mi2
The land Wyatt is hunting is a rectangle, the area of a rectangle is Length X Width, 30 X 15 = 510
Kaitlyn paid $8.28 for 18 Pokemon cards. At this rate, how much would it cost Kaitlyn to buy 12 Pokemon cards?
A. $2.19
B. $2.28
C. $3.72
D. $5.52
D. $5.52
Set up your ratio:
? : 1
$8.28 : 18
? : 12
Which pair of expressions below are equivalent?
A. 7(2x) and 9X
B. 3x + 5x and 15x
C. 4(2x-6) and 8x-24
D. x + x + x + x and x4
C. 4(2x-6) and 8x-24
The use of the distributive property would make the first expression 4 x 2x = 8x and 4x -6= -24, creating 8x-24.
What is a variable? Give ONE example
A variable is a symbol or letter that represents a number.
Ryan works at a bookstore after school. He earns $9.25 per hour. Which equation correctly relates Ryan's total earnings, d, to the number of hours he has worked.
A. d=9.25h
B. h=9.25d
C. d=9.25/h
D. h=9.25/d
A. d=9.25h
We are looking at Ryan's total earnings, represented by the variable d, which means our equation should equal d. We then look at Ryan's hourly rate, 9.25, and multiply that by his total amount of hours in order to find his overall earnings.
Parker's Boy Scout Troop is filling a community pool with water. The pool is 25 feet long, 5 feet deep, and 10 feet wide. What is the total volume of water the troop will need in order to fill the pool? Be sure to use your units!!
1250 ft2
V=l x w x h
V= 25 x 5 x 10
V = 1250
Ellie's dog, Douglisa, eats 8oz of dog food each day. Ellie bought a 28 pound bag of dog food. How many 8oz servings are in a 28 pound bag of dog food?
A. 14
B. 56
C. 224
D. 448
B. 56
Covert your pounds into ounces, there are 16 ounces in a pound.
28 pounds would be 448 oz.
8 : 448 ; How many times can 8 go into 448?
56
Point A and Point B are placed on a number line. Point A is located at -20 and Point B is 5 less than point A. Which statement is true about Point B?
A. It is located at -25 and is to the right of Point A on the number line
B. It is located at -15 and is to the right of Point A on the number line
C. It is located at -25 and is to the left of Point A on the number line
D. It is located at -15 and is to the left of Point A on the number line
C. It is located at -25 and is to the left of Point A on the number line
Use the following terms to show what measurement you will be using in each situation:
Perimeter, Surface Area, Volume, Area
A. The amount of sand Joyce needs to fill her sandbox
B. The measurement around the ski slopes were Jack likes to go skiing.
C. The amount of paint Faye needs to paint her room
D. The yard space Sophia has inside of her fence
A. The amount of sand Joyce needs to fill her sandbox: Volume
B. The measurement around the ski slopes were Jack likes to go skiing: Perimeter
C. The amount of paint Faye needs to paint her room: Surface Area
D. The yard space Sophia has inside of her fence: Area
Luke and Dylan have been working at the baseball fields all summer. They have earned $49.00 for cleaning up the fields. They would like to calculate the hourly rate. If they work for 3.5 hours, the equation 3.5x=49 can be used to determine their hourly rate. What would Luke and Dylan's hourly rate be in dollars?
A. $1.40
B. $14.00
C. $45.50
D. $171.50
B. $14.00
Using your inverse operation, you would get X by itself by dividing both sides of the equation by 3.5 leaving you with X=14.
Mrs. Stuart is making a new coop for her chickens. The space she is using is a rectangle that she has split diagonally in order to create two spaces for her chickens. The space is 24 feet long and 18 feet wide. What is the total area of one space she has created for her chickens? Be sure to use your units!!
216ft2
When Mrs.Stuart cut her coop diagonally she created triangles. The area formula for a triangle is A=1/2 BxH. 24 X 18= 432, 1/2 of 432 is 216.
Joel and his mom are making lemonade to sell at their stand tomorrow. The recipe calls for 1 cup of sugar and 5 cups of water. How much sugar is being used per cup of water?
A. 1/6
B. 1/5
C. 1/4
D. 5
B. 1/5
Create your ratio:
1C Sugar : 5C Water
? : 1C Water
Staples sells boxes of pencils. Each box has 160 pencils, write an equation that represents the total number of pencils, y, in x boxes.
y = 160x
Which of the following is an inequality, expression, and equation?
A. x + 94 = 100
B. 24 - 12
C. x + 21 < 42
A. x + 94 = 100: Equation
B. 24 - 12: Expression
C. x + 21 < 42: Inequality
Expressions A, B, and C are shown below:
A. 202-182
B. 8(42) +24
C. 152 - 34
Which expression is equivalent to 122
C. 152 - 34
152 = 225
34 = 81
225-81= 144
122= 12x12
12x12= 144
Colton is wrapping boxes, shaped like rectangular prisms, to display his dinosaurs in. They front is an open face in order to show the dinosaur inside. Each box has the dimensions of 2 ft tall, 4 feet wide, and 3 feet long. What is the total surface area of 3 boxes? Be sure to use your units!!
138 ft2
1. 2X3 = 6 (3) 18
2. 2X4 = 8 = 16 (3) 48
2. 3X4= 12 = 24 (3) 72
18 + 48 + 72=138
Marek has been studying the migration patterns of two types of whales.
The humpback whale traveled 2,240 miles in 28 days.
The gray whale traveled 2,368 miles in 32 days.
If the humpback whale had traveled 32 days at the same rate, how many more miles would they have traveled than the gray whale?
A. 128
B. 192
C. 280
D. 408
B. 192.
First, you need to make your ratio;
2,240 miles : 28 days
Now make your ratio a basic ratio;
2,240 miles : 28 days
? : 1 Day
? = 80
Using your basic ratio, solve for 32 days;
80 miles : 1 Day
? : 32 Days
192 Miles
A park planner is designing a dog park. He wants to use a metal fence to enclose a kennel at the dog park. The vertices of the fence are shown below. The units on the coordinate plane are yards.
Point A: (4, -4)
Point B: (-4, -4)
Point C: (-4, 3)
Point D: (1, 3)
Point E: (1, -1)
Point F: (4, -1)
The park planner wants to add a gate between points A and F. He will not put metal fencing on that side. What is the total number of yards of metal fencing that will be needed for the kennel at the dog park?
27 yds
You are finding the perimeter of the fencing!
Define the following vocab:
Mean:
Median:
Mode:
Range:
Mean: Average
Median: Middle Number
Mode: The number that appears the most
Range: Biggest-Smallest number