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MATH 7 everything notes
Decimals
Add zeros to the end
of a # as necessary
Mental
Math
10% = .10 = .1
1% = .01
to mult by 10% move decimal left once
to mult by 1% move decimal left twice
Ex. 12% of 30 10% = 3 so 1% = .3 so 2% = .6 so
12% = 10% + 2% = 3 + .6 = 3.6
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MATH 7 everything notes
ROUNDING
If 5 or more round before up 1
Ex. Round 1.596 to the hundredths place
Underline the 9 in the hundredths place
Look at the right spot, 6, so round 9 up
to 10 or the 59 up to 60
Answer: 1.60 (0 needs to be in
hundredths spot)
COMBINING INTEGERS
SIGNS
ANSWER
Same
Add and Keep
the Sign
Subtract and take
the Sign of the
Bigger Absolute
Value
Different
Adding and Subtracting Integers
Positive  right or + for a chip
Negative  left or – for a chip
!!!!!Change subtraction to adding the
opposite!!!!!
3 – 7 = 3 + -7
Ask Yourself “Are there more negative or more
positives?” “How many more?”
Chip example: - 5 – (-14) or - 5 + 14
Negative = Remove
For real life word
problems
Say 5 negatives and 14 positives, how many
more positives? 9 positives so +9 (there are 5
zero pairs that cross off)
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MATH 7 everything notes
FRACTIONS
MIXED TO IMPROPER:
Mult then add, keep denom, recopy any neg signs
ADDING (or subtracting) FRACTIONS:
Must have common denominator, find LCD
Multiply by Special One
MULTIPLYING OR
DIVIDING INTEGERS
Factors:
if there is one neg it’s neg
Ex.
+
=
LCD:
SIGNS
ANSWER
Same
Positive
Different
Negative
i
Multipling Fractions:
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1. Change to improper, write down + or - sign for answer
2. Numerator times numerator, denom times denom
3.
Reduceblock[4].htm
during problem, numerator ÷ denominator
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Dividing Fractions:
1. Change to improper, write down + or
– sign for answer
2. STAY, CHANGE to mult, FLIP
(2nd fraction (reciprocal))
3. Mult across, reduce up and down
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0
MATH 7 everything notes
0
00
Comparing and Ordering #’s
Must have like units, all fractions
with common denominator, get
decimals by doing division, add
zeros so everything has same # of
digits
Example: Conversions
fraction, decimal , %
2 ½ = 2.5 = 250%
Frac decimal
just divide
Decimalfrac
Say it using correct place
value, then reduce
Constant of Proportionality = k
or
y = kx
graph of a line through origin (0,0)
K
Something is proportional if you divide and get the same # every time
Example to right: (0,0) (1,9) (2,18) y/x = 9/1 = 18/2 so k = 9
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MATH 7 everything notes
Ratio and Proportion
Q: Find the number of feet in 96 inches
Cross multiply
Simplify
divide
Make sure to LABEL & match up units.
Write conversions as a ratio.
Cross multiply.
Divide by coefficient.
Sometimes you may have to do more than one proportion to
finish a problem. ie. seconds in a year….
SCALE FACTOR # you multiply by
Percent Proportion
Find it by doing new ÷ old
Markup, % increases, Tax, Tip - % added on
Markdown, % decreases, Discount - % taken off
Example: Find the % increase if I used to
weigh 110 and now I weigh 135.
% / 100 = amount increase / original total
What is your total after taxes (8%) on a $20 Bill?
% after tax / 100 = amount after tax / original $
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MATH 7 everything notes
SIMPLIFYING EXPRESSIONS
Change subtraction to adding the opposite
Distribution
Keep signs in mind when you distribute, copy the other stuff down
Organize like terms
Use the # line or chips if necessary
3x
When you have more than one, do
whichever comes 1st
If there are two multiplications than left first
If division is before multiplication do
division 1st
A or S whichever comes 1st
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MATH 7 everything notes
Exponent Rules
8th
Writing Equations of Lines:
Given 2 points is the hardest one.
You could also be given the slope and y
intercept already.
You could be given 1 point and the slope, so
you solve for b.
Y = -3.5x + 17.5
You can also graph what you are given and
write equation from looking at the slope (rise
over run) and the y intercept
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MATH 7 everything notes
8th
DEFINITION OF A FUNCTION:
Every x has only one y
X (input) Y(output)
VERTICAL LINE TEST: If you draw
vertical lines over your graph or plotted
points and it only touches goes through 1
point it passes. This graph is a function 
Not a function.
One element of the domain
Matches with more than one element
of the range.
FROM A TABLE OR LIST:
FUNCTION: (0,1) (1,1) (2,1)
no repeated x’s
NOT A FUNCTION: (1,-3), (2,4) , (1,5)
has repeated x’s
Take your information and
change it to a mapping
diagram, a list of points or a
graph as you wish
Solving Equations
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MATH 7 everything notes
5(x+3) – 2x = 11 – x
5x + 15 – 2x = 11 – x
3x + 15 = 11 – x
+1x
+x
4x + 15 = 11
- 15 - 15
4x
=-4
4
4
x
= -1
1. ( ) Distribute
2. Same Side Combining
(try keeping x positive)
3. Opposite Sides Opposite
4. Get rid of + or 5. Get rid of Mult or Divide
6. Check
Rewrite, Substitute, Verify w/ Pemdas
**A check is a good way to do a multiple choice question.**
< less than
≤ less than or = to, cannot
exceed, at most, maximum
> greater than, more than
≥ greater than or = to,
at least, minimum
** REMEMBER – Write the x on the left BEFORE you graph.
FLIP INEQ. when you Mult. or Divide by a NEGATIVE!!
INEQUALITIES
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MATH 7 everything notes
GCF – finding the greatest common factor which will divide
into all terms evenly, reverse distributive property
Factor Trees help. Factor 18x – 21y
Both trees have one 3, so gcf = 3 answer: 3(6x-7y)
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DISTRIBUTING
Example: 18x2 + 24 x = 6x(3x + 4)
FACTORING
More
Advanced 
2
GCF is 4xy
4xy( 9x + 4)= 36x2y + 16xy
PROBABILITY & STATISTICS
TREE DIAGRAMS: BRANCH OUT
FOR EACH NEW CATEGORY OR TRIAL
P(E) = Prob of an Event
Toss a
coin 3
times
52 cards, JQK face
13 in each suit,
Heart & Diamonds Red, Spades & Clubs Black
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MATH 7 everything notes
Counting Principle and Permutations: Make lines for number of categories and
put in the # of choices.
Permutations: How many ways can
Horses come in 1st, 2nd and 3rd
in a race of 8 horses
8 7 6
1st 2nd 3rd
Counting Principle: How many 5 digit
combinations can you make, repeats allowed
10
1st
10 10 10 10
2nd 3rd 4th 5th
Read carefully!
Read Carefully!
Repeats oror
Not
Repeats
Not
etc.
…
ex. P(Red Card and flip Head) =
STATISTICS
e
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MATH 7 everything notes
BOX PLOT: Put numbers in order, cut them half, cut each half in half, plot on # line
List:
15 16 17 18 | 20 21 21 21 | 22 23 24 25 | 25 29 29 29
min
Q1
med
Q3
max
distance around
Space inside
Remember:
Cherry
is Delicious
Apple ’s aRe 2
Area and Perimeter
Review
Base and height always make
right angles
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MATH 7 everything notes
Triangles
Triangle Inequality
5 + 3 > 7 yes so makes triangle
Short side + short side > long side
8th grade
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MATH 7 everything notes
Angle Info!
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MATH 7 everything notes
MATH 7 everything notes
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Volume of a Prism
A prism is a polyhedron with two parallel, congruent faces called bases that are polygons.
STEP 1: Name the shape
STEP 2: COPY FORMULA ONTO PAPER
STEP 3: Recognize the b and h
STEP 4: Substitution
Volume units are in units cubed (in3 , ft3 , cm3 , m3 , et cetera). STEP 5: Evaluate (use calculator)
The volume V of a prism is the (AREA OF BASE) B times the height h .
OR
Volume Pyramid = (Area of Base Shape x Height) / 3

V =(A x H ) / 3
Area of Triangle Base = .5 b h = .5(8)(14)= 56
V = (56 x 17) / 3 = 317.
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MATH 7 everything notes
Transformations