Study Guide
Integers and Translating Expressions
Order of Operations
Parenthesis
Exponents
Multiplication/Division (from left to right, whichever comes first)
Addition/Subtraction (from left to right, whichever comes first)
1.) Hendrick needs to simplify this expression. Which operation should he
do first?
34 – 10 ÷ 5 x (6 x 2)
A. 34 – 10
B. 10 ÷ 5
C. (6 x 2)
D. 5 x 12
2.) Solve: 3 x (4 + 2 x 3)
3.) Lionel purchased five tickets to an Astros game online. Each ticket cost
$15. There was a one-time fee of $4 for ordering online. 4 + 15 x 5
What is the total cost of the five tickets?
4.) Evaluate this expression: 32 + 5 x 2 =
Integers
Rules for Adding/Subtracting Integers
- “Same Sign – Find the Sum” - Add the numbers and keep the same
sign.
o 4 + 12 = 16
o -9 + (-5) = -14
- “Different Sign- Find the Difference” - Subtract the numbers and
keep the sign of the largest number.
o 4 + (-9) = -5
o -3 + 15 = 12
Study Guide
Integers and Translating Expressions
Rules for Multiplying/Dividing Integers
- Multiplying and Dividing TWO Integers with the SAME SIGNS, the
answer is always POSITIVE.
o 4 𝑥 20 = 80
o −8 ÷ (−2) = +4
- Multiplying and Dividing TWO Integers with DIFFERENT SIGNS, the
answer is always NEGATIVE.
o −9 𝑥 2 = -18
o 12 ÷ (−6) = 2
Mathematical Properties
The commutative property states that order does not matter.
Multiplication and Addition are commutative.
Examples:
A. 5 + 3 + 2 = 5 + 2 + 3
B. 𝑏 + 𝑎 = 𝑎 + 𝑏
C. 4 ∙ 2 = 2 ∙ 4
D. 𝑎 ∙ 𝑏 = 𝑏 ∙ 𝑎
The associative property states that you can add or multiply regardless of
how the numbers are grouped. By ‘grouped’ we mean ‘how you use
parenthesis.’ In other words, if you are adding or multiplying, it does not
matter where you put the parenthesis. Add some parenthesis any where
you like.
1.) 𝑎 + (𝑏 + 𝑐) = (𝑎 + 𝑏) + 𝑐
2.) (2 + 7) + 5 = 2 + (7 + 5)
9 + 5 = 2 + 12
14 = 14
3.) (𝑎 × 𝑏) × 𝑐 = 𝑎 × (𝑏 × 𝑐)
4.) (6 × 5) × 7 = 6 × (5 × 7)
30 × 7 = 6 × 35
210 = 210
Study Guide
Integers and Translating Expressions
The Identity property of addition states that the sum of zero and any
number or variable is the number or variable itself.
For example, 4 + 0 = 4, - 11 + 0 = - 11, y + 0 = y are few examples
illustrating the identity property of addition.
The Identity property of multiplication states that the product of 1 and
any number or variable is the number or variable itself.
For example, 4 × 1 = 4, - 11 × 1 = - 11, y × 1 = y are few examples
illustrating the identity property of multiplication.
The Distributive Property of Multiplication is the property that states that
multiplying a sum by a number is the same as multiplying each addend by
the number and then adding the products.
The Distributive Property says that if a, b, and c are real numbers, then
𝑎 × (𝑏 + 𝑐) = (𝑎 × 𝑏) + (𝑎 × 𝑐)
For example, 3 × (4 + 5) = (3 × 4) + (3 × 5)
3 × 9 = (12 + 15)
27 = 27
Algebraic Expressions
Vocabulary:
- Addition
o plus
o and
o total of
o more than
altogether
combined
sum
added to
increased by
add
together
in all
- Subtraction
o subtract
o decrease by
o shared
o difference
gave
fewer
fewer than
less
take away
minus
less than
Study Guide
Integers and Translating Expressions
- Multiplication
o times
triple
o product
multiplied by
o increased by a factor
double
of
twice
- Division
o quotient of
o divided by
o divided into
ratio of
divisor
split up
- Equals
o Is
o Will be
per
half
percent
are
yields
were
sold for
multiple
was
- Parenthesis words
o the quantity of
twice the sum of
times the sum of
o times the difference of
plus the difference of
1.) 2 𝑡𝑖𝑚𝑒𝑠 𝑦 𝑠𝑞𝑢𝑎𝑟𝑒𝑑
2 𝑥 𝑦2
2.) 𝑂𝑛𝑒 − ℎ𝑎𝑙𝑓 𝑡ℎ𝑒 𝑝𝑟𝑜𝑑𝑢𝑐𝑡 𝑜𝑓 𝑥 𝑎𝑛𝑑 𝑦
-
1
2
(𝑥𝑦)
3.) 3𝑥 − 4
3 𝑡𝑖𝑚𝑒𝑠 𝑥 𝑚𝑖𝑛𝑢𝑠 4
3
4.) (𝑎 + 𝑏)
𝑡ℎ𝑒 𝑐𝑢𝑏𝑒 𝑜𝑓 𝑎 𝑝𝑙𝑢𝑠 𝑏
5.) 𝑡ℎ𝑟𝑒𝑒 𝑡𝑖𝑚𝑒𝑠 𝑡ℎ𝑒 𝑠𝑢𝑚 𝑜𝑓 𝑎 𝑎𝑛𝑑 𝑏
3(𝑎 + 𝑏)
6.) 𝑡ℎ𝑒 𝑞𝑢𝑜𝑡𝑖𝑒𝑛𝑡 𝑜𝑓 𝑚 𝑎𝑛𝑑 𝑛
𝑚÷𝑛