Simplifying Fractions
Variable Expressions
Order of Operations
More Variable Expressions
Evaluating with Substitution
Miscellaneous
100
Simplify. Write the final answer as a reduced proper fraction or a reduced mixed number.
-1 11/18 +3 1/2
-29/18+7/2
-29/18+63/18=34/18
17/9=1 8/9
100
Write a variable expression to represent the phrase.
The product of 15 and a number
15x
100
Simplify. Show your work (minimum steps listed).
3 steps
5+2(4+3)^2
5+2(7)^2
5+2(49)
5+98
103
100
During a canned food drive, Bob collected 6 more cans than Tom. Let t represent the number of cans that Tom collected.
Write a variable expression that represents the number of cans that Bob collected. Define the variable first.
t = number of cans Tim collected
t+6
100
EVALUATE when
a=-23, b=-36, c=19
Show your work (minimum steps listed) including the substitution step.
1 step
-c-b
-19-(-36)
-19+36
17
100
Simplify.
|-14|
14
200
Simplify. Write the final answer as a reduced proper fraction or a reduced mixed number.
-2 3/4 times -8
-11/4 times-8/1=88/4
22
200
Write a variable expression to represent the phrase.
A number less than 27
27-x
200
Simplify. Show your work (minimum steps listed).
2 steps
7+24divide4times2
7+6times2
7+12
19
200
Owen loves reading books. Before his first birthday, he had 50 books. For his first birthday, he got x books.
Write a variable expression for the number of books Owen now has. Define the variable first.
x = number of books Own received for his first birthday
50 + x
200
EVALUATE when
a=-23, b=-36, c=19
Show your work (minimum steps listed) including the substitution step.
2 steps
|a|-b
|-23|-(-36)
23+36
59
200
Simplify.
Opposite of 23
-23
300
Simplify. Write the final answer as a reduced proper fraction or a reduced mixed number.
10/21divide-5 1/3
10/21 divide -16/3
10/21 times -3/16=-30/336
-5/56
300
Write a variable expression to represent the phrase.
20 divided into x
xdivide20
300
Simplify. Show your work (minimum steps listed).
1 step
-24-(-8)-5-(-2)
-24+(+8)+(-5)+(+2)
-16+(-5)+2
-21+2
-19
300
Sam is having a bonfire, and he needs to buy S’mores supplies. Marshmallow sticks cost $1.99 each, a bag of marshmallows costs $1.30, a box of graham crackers costs $2.50, and a package of chocolate bars costs $3.75. Sam decides to buy twelve marshmallow sticks, three bags of marshmallows, two boxes of graham crackers, and two packages of chocolate bars.
Write a numerical expression for the total cost of the S’mores supplies. Then simplify the expression. Do not forget to label the final answer.
12(1.99)+3(1.30)+2(2.50)+2(3.75)
23.88+3.90+7.50
$40.28
300
EVALUATE when
a=-23, b=-36, c=19
Show your work (minimum steps listed) including the substitution step.
1 step
14-c+a
14-19+(-23)
14+(-19)+(-23)
-5+(-23)
-28
300
Bob has 250 pieces of candy. He wants to give each of his friends the same amount of candy.
Write a variable expression for the number of pieces of candy Bob gives each of his friends. Define the variable first.
x = number of friends Bob has
250 divide x
400
Simplify. Write the final answer as a reduced proper fraction or a reduced mixed number.
4 1/2 divide 7
9/2 divide 7
9/2 times 1/7
9/14
400
Write a variable expression to represent the phrase.
The sum of 10 and a number
x+10
400
Simplify. Show your work (minimum steps listed).
3 steps
(6(2+5))/((1+9)divide2times 8)
(6(7))/(10divide2times8)
(42)/(5times8)
42/40
21/20
400
Mrs. Willats tapes five 11 inch long pieces of paper together to make a banner. She tries to hang it on her wall but it is too long. After cutting off 3 inches, it is perfect.
Write a numerical expression for the length of the poster. Then simplify the expression. Do not forget to label the final answer.
5 times 11 -3
55-3
52 inches
400
EVALUATE when
a=-23, b=-36, c=19
Show your work (minimum steps listed) including the substitution step.
2 steps
-b+|c|
--36+|19|
36+19
55
400
Write a variable expression to represent the phrase.
7 increased by a number
7+x
500
Simplify. Write the final answer as a reduced proper fraction or a reduced mixed number.
1 3/8 times 2 2/3
11/8 times 8/3=88/24
11/3=3 2/3
500
Write a variable expression to represent the phrase.
The quotient of 16 and a number
16dividex
500
Simplify. Show your work (minimum steps listed).
4 steps
[3(7-5)^3-19]^2
[3(2)^3-19]^2
[3(8)-19]^2
[24-19]^2
[5]^2
25
500
You are purchasing supplies for an art project. You need 3 containers of paint, 2 brushes, and 1 case of paper. Each container of paint is $4, each brush is $5, and each case of paper is $16. You have a $3 coupon.
Write a numerical expression for the total cost of the art supplies. Then simplify the expression. Do not forget to label the final answer.
3(4)+2(5)+16-3
12+10+16-3
$35
500
EVALUATE when
x=2 and y=8
Show your work (at least 3 steps) including the substitution step.
(5y-xy)/(y-4)^2
(5times8-2times8)/(8-4)^2
(40-16)/(4)^2
24/16
3/2
500
Five friends are dining together and want to buy 3 salads, 5 sandwiches, 2 bowls of soup, 1 large drink, and 4 medium drinks. They plan on dividing the cost evenly among themselves.
Write and simplify a numerical expression to find the total bill. Do not forget to label the final answer.
3(1.50)+5(3.50)+2(2.25)+1.05+4(0.95)
$31.35