Math 8 Chapter 2-- Expressions
2.1 Properties of Addition
Example Term
3 & -3
Name _______________________________
Definition
Additive inverse - two numbers that add up to zero
(2+3) 4=2+(3 4)
Associative property of addition – grouping can change
-10 + -10 = -20
Closure property of addition – if you add integers, the
answer will be an integer
Commutative property of addition – order can change
2+3=3+2
2=2
Equivalent – have the same value
Identity element of addition - zero
2+0=2
Identity property of addition – you can add zero – same value
-3 + 3 = 0
Inverse property of addition – adding a number and its
opposite equals zero
opposite – same distance from zero, other side of 0
1. To use properties of addition to simplify expressions – (mental math)
3 + (-7 + y) = (3 + -7) + y [associative property – y – 4]
Math 8 Chapter 2-- Expressions
Name _______________________________
2.2 Properties of Multiplication
Example Term
Definition
2 ·(3·4) =(2·3)·4
Associative property of multiplication – grouping can
change
-12 ·-12 = 144
Closure property of multiplication – if you multiply integers,
the answer will be an integer
6 ·2=2·6
Commutative property of multiplication – you can change
the order
Identity element of multiplication – 1
6 ·1 = 6
Identity property of multiplication – multiply by 1, equals
starting number
0 ·12 = 0
Zero property of multiplication – multiply by zero equals
zero
1. To use the properties of multiplication to simplify expressions –
(mental math)
6 · 6 · 12 · 12 · 0 = 0 [forget the math; times 0 will be 0]
Rearrange order, remove parenthesis, etc. to make “easy” math.
Math 8 Chapter 2-- Expressions
Name _______________________________
2.3 Distributive Property
Example Term
Definition
2(3 + 4) = 6 + 8 Distributive property – multiply outside by both
insides is the same as PEDMAS
1. To use the distributive property to write and simplify expressions –
Multiply the outside by both insides, add (or subtract) last
6(2 + 5) = (6 · 2) + (6 · 5)
a(b + c) = ab + ac
useful in mental math:
8 · 31 = 8(30 + 1) = (8 · 30) + (8 · 1)
works for subtraction, too
4 · 28 = 4(30 – 2) = (4 · 30) – (4 · 2)
Math 8 Chapter 2-- Expressions
Name _______________________________
2.4 Evaluating Expressions
Example Term
Definition
6z - 12
Algebraic expression – a mathematical expression using
operations, numbers and variables (letters)
3+5·3
Numerical expression – a mathematical expressing using
operations and numbers (no letters)
1. To find evaluate an algebraic expression given the value of the variable
Put given number in for letter, solve using PEDMAS rules
6a; if a = 3 [smooshed means multiply]
6 · 3 = 18
3b – 4 =; if b = 5
3·5–4
15 – 4 = 11
4 + 3c – 2c; if c = 2 [same letter, use same number]
4+3·2–2·2
4+6–4
10 – 4
6
Math 8 Chapter 2-- Expressions
Name _______________________________
2.5 Simplifying Expressions
Example Term
Definition
6
Constant – a fixed number (no letters smooshed)
4a & 6a
Like terms – terms that contain an identical variable (or
variables,) including identical exponents
3b
Numerical coefficient – the constant factor of a term
6ab
Term – a constant, a variable, or a combination
(smooshed)
1. To tell the difference between terms, coefficients, and constants –
Constant – plain number (counted as a term)
Coefficient – smooshed to the front of a letter or group of smooshed
letters
Term – the set of smooshed numbers and/or letters
3a + 2 – 6ab2
3 terms in this expression
Math 8 Chapter 2-- Expressions
Name _______________________________
2.6 Translating Word Phrases
Addition
subtraction
Multiplication
added to
*subtracted from
multiplied by
+sum
+difference
+product
increased by
decreased by
times
*more than
*less than
twice (x2)
plus
minus
doubled (x2)
+ definition includes “answer to”
*Switch the order
Division
divided by
+quotient
ratio of
halved (÷2)
1. To translate word phrases into numerical or algebraic expressions –
Remember special “grammar” rules
Always use lower case letters for variables
a+b
Always smoosh to show multiplication if possible
6a, not 6 · a
When smooshing numbers and letters, put number first
not a6
Show division with fraction form (first on TOP)
instead of 10÷2
If more than one operation, words like “sum” and “difference”
probably mean you need to use parenthesis
6 times the sum of 3 and 4 [answer to add]
6(3+4)
For complicated ones, look for the “of” and “and” pair. The
operation sign goes where the “and” is. (Whatever is between them
goes before it.)
The difference of a number and 12 increased by 7
n – 12 + 7
Math 8 Chapter 2-- Expressions
Name _______________________________
2.7 Estimating
Example
Term
Definition
234 + 362
Front-end estimation – strategy used when numbers
200 + 300 = 50
have same number of digits, uses only the front
34 + 62 ≈ 100
place , then “adjusts” by combining the next place
≈ 600
value into convenient “chunks.”
1. To round a number to an indicated place value –
1) find the place,
2) use the neighbor after it to decide “stay” or “rise.”
3) Copy the front, zero the back.
6,139 to the nearest hundred
13 is closer to 10 (stay)
6,100
copy the 6 in front, put zero after 10
2. To estimate a sum or a difference by rounding to the highest place value.
61,239 + 49, 789
round to the front
60,000 + 50,000 ≈110,000 add (or subtract)
3. To estimate a product or a quotient using rounding.
Multiply – round to the front & multiply
456 · 358
500 · 400 ≈ 2,000
Divide – round the 2nd number to front, round the 1st to multiple
6,203 ÷ 89
6,300 ÷ 90
[ 9 · 7 = 63 ]
≈ 70
4. To estimate a sum or difference using front-end estimation
34,578 – 11,845 [round to the front]
30,000 – 10,000 ≈ 20,000 [4,000 – 1,000 = 3,000]
20,000 + 3,000 ≈23,00