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Which of the following describes the expression 6(4-2) accurately?
a) Six and the difference of four and two.
b) The product of six and the sum of four and two.
c) The product of six and the difference of 4 and 2.
d) The quotient of six and the difference of four and two.
c) The product of six and the difference of 4 and 2.
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(4-2) --> the difference of 4 and 2
6(4-2) --> The product of 6 and the difference of 4 and 2
Use the formula V=s3 to find the volume of a cube with a side length of 2 cm.
a) 4 cm3
b) 6 cm3
c) 8 cm3
d) 9 cm3
c) 8 cm3
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V=s3
V=(2)3
V=8cm3
36x-12=108 has the same solution(2) as
a) 3(3x-12)=108
b) 12(3x-1)=108
c) 3(12x-12)=108
d) 12(x-1)=108
b) 12(3x-1)=108
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The GCF of 36 and 12 is 12. The Distributive Property states that number outside of the parentheses should be distributed to all numbers inside the parentheses.
Mr. Hall had $45.00. He spent all of the money on a shirt and a pair of shoes. He spent $19.00 on the shirt and x dollars on the shoes. Which of the following equations is true?
a) $45.00 + x = $19.00
b) $45.00 -x = $19.00
c) x - $19.00 = $45.00
d) $19.00 + $45.00 = x
b) $45.00 -x = $19.00
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Subtracting the cost of the shoes (x) from the total cost ($45.00) would leave the cost of the jeans ($19.00).
Find the value of p:
72 + p = 108
p=36
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To find the value of p, you must first isolate it. Do that by subtracting 72 from both sides.
Which of the following describes the expression (8/2)-10 accurately?
a) The quotient of eight and two subtracted from ten.
b) Ten less than the quotient of eight and two.
c) The difference of ten and the quotient of eight and two.
d) The product of eight and two minus ten.
b) Ten less than the quotient of eight and two.
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(8/2) --> The quotient of 8 and 2.
-10 --> less 10 or 10 subtracted from.
What is an equivalent expression for 3n-12?
a) 3n+1
b) 3n+4
c) 3n-4
d) 3(n-4)
d) 3(n-4)
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The expression, 3(n-4), is equivalent because it has the same value as the original. The GCF (Greatest Common Factor) of 3 has been factored out from each term.
Three times the quantity u-4 is less than 17
3(u-4)<17
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"Three times the quantity u-4" means to multiply (u-4) by 3 ---> 3(u-4)
"is less than 17" means <17
3(u-4)<17
The library has 2,500 books. The librarian wants to purchase x more books for the library. The director decides to buy twice as many as the librarian requested. How many books will the library have if the director purchases the number of books he wants?
a) 2,500 + x
b) 2,500 + 2x
c) 2,500 - x
d) 2,500 - 2x
b) 2,500 + 2x
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The director wants to buy double x books, which is 2x. Add that to the 2,500 existing books to create the expression 2,500 + 2x.
Find the value of n: 428 - n = 120
n= 308
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To find the value of n, you must isolate it.
Subtract 428 from both sides.
Then divide both sides by -1.
Which of the following accurately represents "The product of 15 and the sum of 9 and 7."
a) 15+(9x7)
b) (15+9)x7
c) 15/(9+7)
d) 15(9+7)
d) 15(9+7)
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The sum of 9 and 7 ----> (9+7)
The product of 15 and the sum of 9 and 7 ---> 15(9+7)
Simplify 2n-7n to create an equivalent expression.
a) 5n
b) -5n
c) -n(2-7)
d) n(5)
b) -5n
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Here, the variable is the common factor and can be factored out n(2-7).
Then, simplify within the parentheses: n(-5).
Finally, use the Commutative Property to rewrite the expression, coefficient first: -5n.
For which of the following values of x is this inequality true?
500-3x>18
a) x=140
b) x=150
c) x=210
d) x=120
d) x=120
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Solve to find x:
500-3x>80
First, subtract 500 from both sides
-3x>-420
Next, divide both sides by -3. (Don't forget to switch the inequality sign when dividing a negative in an inequality.)
x<140
So, x=120 would work as a solution.
To check: 500-3(120) = 500-360 = 140
Find the value of p:
13 + p = 39
p=26
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To find the value of p, you must isolate it.
Subtract 13 from both sides to isolate the variable.
Mr. Hall loves candy! He goes to the store and sees that the bulk candy is $0.84 a pound. Mr. Hall wants to buy 3 pounds of candy to share with his class. Using the equation m=0.84(p), figure out how much money (m) Mr. Hall needs.
$2.52
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m=$0.84(3)
m=$2.52
What is the value of y in the equation y=3x-13, when x=6?
5
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y=3x-13
y=3(6)-13
y=18-13
y=5
Which expression is equivalent to 5y+2z-3y+z?
a) z
b) 2y+3z
c) yz
d) 11yz
b) 2y+3z
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5y+2z-3y+z = 2y+3z
Combine the like terms to simplify: 5y+2z-3y+z = (5y-3y) + (2z+z) = 2y+3z
Riley had 117 gumballs. Zay had x less than half the amount that Roula had. Which expression shows how many gumballs Zay had?
a) 117-x/2
b) (1/2)(117)-x
c) 117-2x
d) 2x+117
b) (1/2)(117)-x
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Half of 117 can be expressed as (1/2)(117)
x less than that is expressed as -x.
Find the value of w:
6w=54
w=9
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To find the value of w, you must isolate it.
Divide each side by the coefficient, 6, to isolate the variable.
Ms. McCauley is going a road trip. She has to purchase gas so that she can make it to her first destination. Gas is $3.58 a gallon. Ms. McCauley needs to get 13 gallons. Using the expression t=g(3.58), figure out how much Ms. McCauley will spend on gas.
$46.54
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t=13 gallons ($3.58)
t=13(3.58)
t=46.54
83
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3a2-7b
3(3)2-7(-8)
3(9)-7(-8)
27-(-56)
27+56
83
Which inequality has the same solution set as 3(q+6)>11?
a) 3q+18<11
b) 3q+18>11
c) 3q+6>11
d) q+18>11
b) 3q+18>11
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The Distributive Property states that a number outside of the parentheses should be used to multiply all numbers inside the parentheses. The inequality symbol should not change.
Mrs. Hampton loves to cook. She makes a total of 23 different items. Mrs. Hampton makes 6 different desserts, 12 appetizers, and x main courses. Which equation represents the total amount of food that Clinton cooked?
a) 6-12+x=23
b) 6+12+x=23
c) 18-x=23
d) 6+12-x=23
b) 6+12+x=23
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Mrs. Hampton made a total of 23 items, so you know the expression has to equal 23. She made 6 dessert and 12 appetizers. You do not know how many main courses she made, so that is represented by x.
Find the value of h:
h - 4 = 20
h= 24
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To find the value of h, you must isolate it.
Add 4 to both sides.
The Gordons built a new house. They want to plant trees around their house. They want to plant 8 trees in the front yard and 17 in the backyard. The trees that the Gordon's want to plant cost $46 each. Could they use the equation t=c(n) where t is the total coast, c is the cost per tree, and n is the number of trees purchased, to figure out the cost to purchase trees for both the front and the back yards?
a) No, because the variables represent only two specific numbers that will never change.
b) Yes, because the variables represent only two specific numbers that will never change.
c) No, because the variables can be filled with any number.
d) Yes, because the variables can be filled with any number.
d) Yes, because the variables can be filled with any number.
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The equation t=c(n) can be used with any numbers. The equation has the number of trees and the cost of one tree as variables. Those qualities, no matter what they are, when multiplied together will always equal the total cost.