Unit Rate
Integer Operations
Expressions
Word Problems
Challenge
100
How is unit rate represented?
a. y/x
b. x/y
a. y/x
100
Evaluate:
5(-5)
-25
100
Write an expression that would be equivalent to:
12 + 6x
Several possible answers, some examples could be:
12 + 3x + 3x 12 + 2x + 4x
11 + 2 -1 + 7x - x 9 + 3 + x + 5x
6 (2 + x) 6 + 6 + 6x
3 (4 + 2x) 2 (6 + 3x)
100
The temperature dropped 2 °F every hour for 6 hours. What was the total number of degrees the temperature changed in the 6 hours?
-2 (6) = -12
The temperature dropped 12 degrees in 6 hours.
100
What does x equal?
x ÷ 5 = 8
x = 40
200
Find the unit rate:
420 miles in 7 hours
60 miles per hour
200
-6 + (-17)
-23
200
A football team scored 5 touchdowns, 4 extra points, and 6 field goals
Write an expression that represents the amount of points the football team scored.
5t + 4e + 6f
200
The city of St. Louis is creating a welcome sign on a billboard for visitors to see as they enter the city. The following picture needs to be enlarged so that a 1/2 inch represents 5 feet on the actual billboard. If the height of this picture is 2 inches, will it fit on a billboard that measures 20 feet in height?
Yes, 2 inches = 20 feet, so the picture will fit on the billboard.
200
Combine the like terms:
5c - 4c + 2
c + 2
300
If there are 5 boys for every 3 girls, how many girls are there if there are 60 boys?
36 girls
300
Evaluate:
(-6 - 6) (-3)
36
300
While black Friday shopping, Mrs. Allee bought several items. She bought 3 presents for her husband, 3 for her sister, 1 for her mom, 1 for her dad, and 2 for her in-laws.
Write an expression that represents the cost of all the presents Mrs. Allee bought.
3h + 3s + 1m + 1d + 2i
300
Mt. Everest, the highest elevation in Asia, is 29,028 feet above sea level. The Dead Sea, the lowest elevation is 1312 feet below sea level. What is the difference between these two elevations?
29,028 - (-1,312)
30,340 feet
300
What does x equal in this situation?
5x + 5 = 20
x = 3
400
What are the characteristics of a proportional relationship when represented in a graph?
1. Straight line
2. Goes through the origin (0,0)
3. Has the same unit rate
400
(-3) ÷ (-1) + 2 + (-6)
-1
400
Kay’s mother taught her how to make handmade ornaments to sell at a craft fair. Kay rented a table at the fair for $25 and set up her work station. Each ornament that she makes costs approximately $2.25 for materials. She sells each ornament for $7.00. Which of these expressions represent this situation?
a. -25 -2.25x + 7x
b. -25 + 4.75x
c. 25 + 4.25x
a. -25 - 2.25x + 7x
b. -25 + 4.75x
400
Is the following picture a reduction, or an enlargement?
Reduction
400
Distribute:
-3 (1 - 8m - 2n)
-3 + 24m + 6n
500
If Arralyn can make 24 cookies per hour, write an equation that represents this relationship.
y = 24x
500
Evaluate:
10 + (-3 3/8 )
6 5/8
500
Which expressions are equivalent to 4b?
a. b + 2 (b + 2b)
b. 8b - 4b
c. 2(2b)
b. 8b - 4b
c. 2(2b)
500
Ryan and Peyton are paying the integer game.
Ryan has the following cards: -2, 5, 6, -4.
Peyton has the following cards: 10, -2, 2, -5
What do each of their hands equal? If both Ryan and Peyton discarded their -2, what happens to their hands? Are they equivalent? Is one hand closer to zero than the other?
Both hands equal 5
If both Ryan and Peyton discard their -2, both of their hands will equal 7, and are still equivalent
500
Distribute:
4/5 (15x - 5)
12x - 4