7 Th Grade Pre Algebra Study Guide
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1
27
th
Grade Pre-Algebra Study Guide
Number Sense
1) When (+) or (-) integers keep the sign the same
15) To convert a decimal to a percent, move the
if all the integers have the same sign.
decimal two places to the right.
2) When (+) or (-) integers with different signs,
16) To convert a percent to a decimal, move the
find the difference of the two integers and keep
decimal two places to the left.
the sign of the integer with the larger |absolute
value|.
17) Order of Operations: follow P, E, M/D, A/S
3) When subtracting integers, change to addition
18) Rules for exponents:
and follow the rules above.
* When multiplying numbers with the same
base, add the exponents.
4) When (x) or ( ÷ ) integers follow these rules:
* When dividing numbers with the same
base, subtract the exponents.
*(x) or (÷) two negatives equals a positive
* When raising a number to a power
*(x) or (÷) two positives equals a positive
4
4
16
multiply the exponents (3
)
= 3
.
*(x) or (÷) different signs equals a negative
19) When writing numbers in Scientific Notation,
move the decimal behind the first non zero digit
5) |Absolute value| means the distance a number is
-5
(0.0000768 = 7.68 x 10
or 6,534,000 = 6.534 x
from 0 on a number line & the answer is always
6
10
).
expressed as a positive. The only exception is if
there is a (-) symbol outside the symbols -|4| = -
20) When calculating the percent of increase or
4.
st
nd
decrease 1
find the difference, 2
divide the
rd
difference by the original amount, & 3
change
6) Associative Property of (+) or (x)
the final answer to a percent.
* 2 + (5 + 8) = (2 + 5) + 8
21) When calculating a markup or discount multiply
7) Commutative Property of (+) or (x)
the beginning amount by the correct decimal
* 2 x 5 x 8 = 5 x 2 x 8
equivalent to the percent then add that amount to
the
original
amount
(%
markup
or
8) Distributive Property of (x)
tax/tip/commission added) or subtract that
* 6(n + 4) = 6n + 24
amount from the original amount (% decrease)
9) Identity Property of (+)
22) To convert a decimal to a percent, move the
* 2 + 0 = 2; 56 + 0 = 56
decimal to the right two places.
10) Identity Property of (x)
23) Rational number:
* 2 x 1 = 2; 56 x 1 = 56
Fractions/Decimals: 2/5, 5/8, 0.3, 0.666….
Integer:
11) Zero Property of (x)
Whole Number: 0, 4, 167, 1,023,000
* 2 x 0 = 0; 56 x 0 = 0
Negative Integer: -6, -23, -409
Irrational Number:
12) To convert a fraction to a decimal, divide the
Non-perfect squares, decimals
numerator by the denominator.
24) Most word “percent” problems can be solved
13) To convert a decimal to a fraction, write the
with a proportion or an equation. The words
number above the appropriate denominator (ie.
rate, per, and unit means that one of the ratios in
10ths, 100ths, 1000ths, etc.).
the proportion has the number 1 as a divisor.
14) To convert a fraction to a percent, change it to a
Algebra & Functions
decimal then move the decimal two places to the
To solve an equation always use the inverse
right or find a common denominator that is
operation to isolate the variable:
equal to 10ths or 100ths.
x + 4
x – 7
2x
x/3
- 4
+ 7
2
• 3
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