Download Unit 4 Study Guide Math 6

Unit 4
Study Guide
Math 6
Overhead Version
1) Define inverse operations.
• Inverse operations are operations that “undo”
each other: addition/subtraction;
multiplication/division
2) Explain the difference between
an expression and an equation.
• An equation has a set value or a mathematical sentence
that contains an = sign;
– Example 4 + 2 = 6
• An expression will change as the value of the variable
changes OR
• An expression is a variable or combination of variables,
numbers, and symbols that represents a mathematical
relationship
• An expression is a math sentence that contains numbers,
symbols (not equals) and letters AND the value of the
variable can change.
– Example 3a + 4
3) Give the definition of variable and
constant.
• A variable is a letter or symbol that represents
a quantity that can change.
– Example: a
b
c
• A constant is a quantity that does not change.
– Example: 5 13 116
4) Solve the expression
24 ÷ 2³ - 2 + 19
24 ÷ 2³ - 2 + 19
24 ÷ 8 – 2 + 19
3 – 2 + 19
1 + 19
20
5) Solve the expression 52 + 33 – (22 ÷ 2)
52 + 33 – (22 ÷ 2)
52 + 33 - (11)
52 + 27 – (11)
79 – (11)
68
Solve the equations.
6) 8𝑥 = 96
8𝑥 = 96
8
8
1x = 12
x = 12
Solve the equations.
7) x – 47 = 83
x – 47 = 83
+47 +47
x – 0 = 130
x = 130
Solve the equations.
8) x + 34 = 55
x + 34 = 55
-34 -34
x – 0 = 21
x = 21
Solve the equations.
𝑥
9) = 12
6
6•
𝑥
6
= 12 • 6
1x = 72
x = 72
10) What is the product of 9 and 3
decreased by x if x = 15?
9•3–x
9 • 3 – 15
27 – 15
12
11) Evaluate the expression ab – c + d
if a = 9, b = 7, c = 6, and d = 5.
ab – c + d
9•7–6+5
63 - 6 + 5
57 + 5
62
12) Given the equations below, find
the product of x and y.
6x = 72
6
5 •
𝑦
5
= 10 • 5
6
1x = 12
x = 12
12 • 50
600
1y = 50
y = 50
13) Simplify: The quotient of x and 3
if x = 45.

x÷3
45 ÷ 3
15
14) Write this out as a mathematical
sentence: The difference of a number
and four is eleven.
n – 4 = 11
15) If 3 pairs of shoes cost $69, how
much would 1 pair cost? Write an
equation and solve.
69 = 3n OR 69 ÷ 3 = n
69 ÷ 3 = n
23 = n
16) What is the length of a rectangle
that has an area of 35 cm2 and a width
of 5 cm? Write an equation and solve.
area = length x width
35 = L x 5
5
5
7
=L
17) From your house, you travel 5 miles to your friend
John’s house. From John’s house you go to visit Emma.
When you get to Emma’s house you realize that you
have traveled a total of 17 miles. Write an equation to
show how far you have traveled. Solve the equation to
find how far it is from John’s house to Emma’s house.
(Draw a picture)
18) Rashad spent $117 on batteries. If n
represents the number of batteries
purchased and each battery was $9, write
an equation to represent how many
batteries he bought. (Use 117, n, and 9 in
the equation.)
117 = 9n
9
9
13=n
19) Jaime drives from Marietta to Atlanta and back
again five times a week. The approximate distance from
Marietta to Atlanta is 32 miles. How many total
numbers of miles driving is round trip for 5 days?
• (Think: How many times does Jamie drive to Atlanta from Marietta in
one day? Think about it.)
2 • 32 • 5
62 • 5
320
20) If a rectangle has an area of 48in.² and a
width of 8in., what is the length of the base?
(The in2 means that the unit is being
squared, not the number.)
area = length x width
48 = L x 8
8
8
6 = L