Name:_________________________________________________________Date:_________________Period:________
Quarter One
Final Exam Study Guide
MGSE6.NS.2 Fluently divide multi-digit numbers using the standard algorithm.
Ex.
1.) 3560 ÷ 8 =
2.) 18,973 ÷ 4 =
3.) Carver Middle
School spent $4500 on 60
math books. How much
did each book cost?
MGSE6.NS.3 Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm
for each.
-Adding/Subtracting Decimals: Always line up the ____________________.
Ex.
4.)
9.78 + 23 =
5.) 13.4 – 7.034
=
6.) Desiree went to the
store and bought a purse
for $39.65, a necklace for
$19.88, and a wallet for
$14.75. How much did
she spend in all? If she
brought $100 to spend,
how much does she have
left over?
-Multiplying Decimals: Step 1 – Multiply like ______________ numbers.
Step 2 – Add the number of ______________.
Step3 – Move the decimal that amount to the ___________.
Ex.
7.) 12.34 x 1.3
8.) 7.8 x 0.34
9.) Javious makes $15.75
an hour. How much did
he make if he worked
25.5 hours?
-Dividing Decimals: When the ________________shows a decimal move the decimal to the ________ to make
it a whole number. What you do to one side, ________________________.
Ex.
10.)
531.483 ÷ 1.23 =
11.)
19.83 ÷ 0.75
12.) Mya earns
$7.50/hour. Last week
she earned $352.50. How
many hours did she
work?
MGSE6.NS.4 Find the greatest common factor, the least common multiple and use the distributive property.
-GCF: Find the ________________ of each number. (Think of factor pairs!)
Ex. 8 and 10
13.) 24 and 36
14.) 52 and 91
15.) 42 and 16
MGSE6.EE.1 Write and evaluate expressions involving whole-number exponents.
a) Identify the base in the expression
8x8x8
The base or repeated factor is 8.
b) Identify the exponent
8x8x8
There are three 8’s, so the exponent is
three.
c) Write the expression using an exponent
8³
Base
16.)
17.)
18.)
19.)
Exponent
4
Expanded Form
Exponential Form
Standard Form
5
36
4*4*4*4*4
3
4
MGSE6.EE.2a Write expressions that record operations with numbers and with letters standing for
numbers.
*Write an expression from a written expression, ex. “8 less than four times a number.” In order to do this, you
need to understand the written forms in which the operations can be written.
a) Let n = the unknown number
Four times n is 4 x n or 4n. The coefficient of 4n is 4. The coefficient tells you to multiply the number by 4.
b) Next, Identify the operation. The phrase less than means to subtract. 8 less than means to subtract 8 from
4n.
c) Finally, write the expression. An algebraic expression to represent “8 less than four times a number” is:
4n – 8
20.) The product of
four and the third
power of a number.
21.) The quotient of
a number and 3.
23.) Fifty-six less
than x cubed.
24.) The sum of a
number and six
divided by two.
25.) A number
decreased by
twelve.
*Evaluating Algebraic Expressions: Also referred to as substitution questions. Replace the variable with the
value given in the expression. Then, use order of operations to solve.
Ex. 42 ÷ 6 + 8x when x=9
42 ÷ 6 + 8(9)
Divide (since multiplication and division are done at the same time from L to R).
7 + 8(9) Multiply
7 + 72
Add
79
26.)
20 + x² when x =4
27.)
7.8 + 3.5w when w=1.5
28.)
15z - 7 • 4 + 4 when z=2.4
29.)
2c – 2b when c = 10,b = 8
MGSE6.EE.2b Identify parts of an expression using mathematical terms; view one or more parts of an
expression as a single quantity.
3x + 5y + 7
Terms: Each of the three terms are underlined: 3x , 5y , and 7
Variable: There are two variables in this expression: x and y
Coefficient: 3 is the coefficient that means 3 times x and 5 is the coefficient that means 5 times y.
Constant: The constant is the number seven that does not represent an unknown number.
Expression: The entire mathematical phrase, including numbers, operational symbols, and variables.
30.) Identify the parts of the
31.) Identify the parts of the
32.) Identify the parts of the
following expression:
following expression:
following expression:
12j + 6p + 34 – 5j
64y + 5t – 13
34 + 18k – 54 + 2x – 8k
Constant(s): _____
Variable(s): ______
Coefficient(s):______
How many terms? ______
Constant(s): _____
Variable(s): ______
Coefficient(s):______
How many terms? ______
Constant(s): _____
Variable(s): ______
Coefficient(s):______
How many terms? ______
MGSE6.EE.2c Evaluate expressions at specific values of their variables. Include expressions that arise from
formulas used in real-world problems. Perform arithmetic operations, including those involving wholenumber exponents, in the conventional order when there are no parentheses to specify a particular order
(Order of Operations).
Ex. 19 + (6-3)² - 18 ÷ 2
Step 1: Work inside the parentheses
19 + (6-3)² - 18 ÷ 2
Parentheses
first (using order of operations).
19 + 3² - 18 ÷ 2
Step 2: Next, solve your exponents
19 + 3² - 18 ÷ 2
3² = 9
Exponents
19 + 9 - 18 ÷ 2 18 ÷ 2 = 9
Multiplication Step 3: Work out all the multiplication
and division from left to
&
right at the same time.
Division
Step 4: Work out all the addition
19 + 9 - 9
Addition
and subtraction at the same
28 - 9
&
from
left
to
right.
19
Subtraction
33.)
(19 − 9)2 ÷ 2 + 27 – 8
34.)
16 ÷ 23 + (45 – 10) - 19
35.)
62 – 3 • 8 + 2
36.)
53 - 92 - 32 + 2(12 + 5)
MGSE6.EE.3 Apply the properties of operations to generate equivalent expressions.
For these examples, think back to distributive property in unit one. The number outside the parentheses is
distributed to both terms inside the parentheses.
Ex. 3 (2 + x) = 6 + 3x
Ex. 24 x + 18y = 6 (4x +3y)
Associative Property of Addition
Commutative Property of Addition
Ex. (3 + 4) +5 = 3 + (4 + 5)
Ex. 4 + 5 = 5 + 4
Associative Property of Multiplication
Commutative Property of Multiplication
Ex. (5 x 6) x 7 = 5 + (6 + 7)
Ex. 4 x 8 = 8 x 4
Remember, for multiplication and addition it does not matter which order they are in or if they are separated
differently. You will still get the same answer.
MGSE6.EE.4 Identify when two expressions are equivalent (i.e. when the two expressions name the same
number regardless of which value is substituted into them.)
You can combine the terms that have the same variable to have a coefficient in order to represent multiple
occurrences of the same variable.
Ex. y + y + y = 3y
37.) 23x + 6y - 14x
38.) 2a + 9a
39.) 4c + 2d + 8c
40.) 5k + 3(k + 4)