Download Sem. 1 Practice Notes

7th Grade 1st Semester Benchmark Review Notes
Commutative, Associative, Identity, and Distributive Properties
Commutative – Same answer no matter what order of the numbers
Addition:
Multiplication:
6+2=2+6
3٠5=5٠3
The order does not matter
Associative – The location of the parentheses does not change the answer
Addition:
Multiplication:
6 + (3 + 4) = (6 + 3) + 4
2 ٠ (4 ٠ 8) = (2 ٠ 4) ٠ 8
Parentheses move
Numbers do not change order though
Identity – Start and end with same number
Addition (Add zero):
Multiplication (Multiply by 1)
Distributive – Distribute to all, then add or subtract
3(4+7)
6+0=6
3(4) + 3(7)
12 + 21
4٠1=4
33
Write algebraic expressions
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Decide if order matters
Addition and subtraction in same order unless a flip phrase
Multiplication – number first, then variable
Division – fraction format only
Flip Phrases for Addition and Subtraction
Less than – 6 less than d
or d – 6
More than – 3 more than f
or f + 3
Greater than – a greater than 4 or 4 + a
Fewer than – b fewer than 8
or 8 – b
Absolute Value
 The absolute value of a number is the distance from zero on a number line.
The answer is never negative.
 Write the absolute value of the number.
 Then follow order of operations.
 Absolute value symbols are grouping symbols.
|𝟏𝟎| − |−𝟓|
𝟏𝟎 − 𝟓
𝟓
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|𝟖| + (−𝟏𝟐)
𝟖 + (−𝟏𝟐)
(−𝟒)
Order of operations
*** Use Ice Cream Math ***
Please Excuse My Dear Aunt Sally
1) P = Parenthesis (or other grouping symbols)
32 + (4 x 5) ÷ 2
32 + 20 ÷ 2
2) E = Exponents
3) M or D = Multiplication or Division (in order left to right) 9 + 20 ÷ 2
4) A or S = Addition or Subtraction (in order left to right)
9 + 10
19
Add, subtract, multiply and divide integers
*** Use the songs ***
Subtracting Integers
Adding Integers
Leave, change, opposite
Then follow the rules for addition
If the signs are the same,
add and keep the sign
+6 + (+6) = +12
-6 + (-6) = -12
-12 - (-8) = X
-12 + (+8) = X
-4 = X
Multiplying and dividing integers
If the signs are different, subtract and
keep sign of the higher number.
-6 + (+7) = 1
If the signs are the same… the answer is POSITIVE
6 x 6 = 36
-6 x (-6) = +36
If the signs are different… the answer is NEGATIVE
-6 x 6 = (-36)
Multiply and divide fractions/mixed numbers
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Denominators do NOT need to be the same
Work horizontally (across)
Change mixed numbers and whole numbers to improper fractions
Cross-reduce before multiplying if you want to
Remember with division, you need to leave, change, flip (LCF)
L C F
3• 1
1 9
=
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3¹ • 1 = 1
1
9³
3
5÷ 2
8 1
=
5 • 1
8 2
=
5
8
Function Tables:
Complete the following function table. Use the values given for x in the
equation to determine the value of y.
5x – 3 = y
4x + 7 = y
x
1
2
3
4
Function Rule:
4x + 7
4(1) + 7 = 11
4(2) + 7 = 15
4(3) + 7 = 19
4(4) + 7 = 23
y
(x,y)
x
11
15
19
23
(1, 11)
(2, 15)
(3, 19)
(4, 23)
1
2
3
4
Function Rule:
5x – 3
5(1) – 3
5(2) – 3
5(3) – 3
5(4) – 3
y
(x,y)
2
7
12
17
(1,2)
(2,7)
(3,12)
(4,17)
Solve 1-step equations
*** Use your recipes ***
Examples:
a + 3 = 12
+-3 +- 3
a=9
g – 6 = 12
g + –6 = 12
+6 +6
g = 18
Solving 2 – Step Equations
3p + 5 = 17
1. Solve addition or subtraction part
a. LCO (only if it is subtraction)
b. Adding the opposite on both sides
c. Cancel
2. Solve multiplication or division part
a. Make both fractions
b. Use ( ) to show multiplication
c. Multiply by the reciprocal on both sides
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1 (3m) = (21) 1
3 1
1 3
m=7
3p + 5 = 17
1
3
+(–5)
+(–5)
3p
12
( ) =( )
1
1
p = 4
1
3
5y – 4 = – 14
5y + (–4) = – 14
+4
+4
1 5y
−10
1
( ) =(
)
5 1
1
5
y = (– 2 )