```7th Grade SCReady Study Guide
Operations with Integers:
❖ Multiplying and Dividing integers –
o Same signs when multiplying or dividing always equal a positive.
Neg and Neg = Pos
or
Pos and Pos = Pos
o Different signs when multiplying or dividing always equal a negative
Pos and Neg = Neg
or
Neg and Pos = Neg
▪ Ex
-5 + -3 = -8
or 5 + 3 = 8
o Different signs: subtract and answer keeps the sign of the number with the
largest absolute value.
▪ Ex -5 + 6 = 1
or -15 + 8 = -7
❖ Subtracting Integers –
o Keep first number, change subtraction to addition, and then change the
2nd number to the opposite sign.
▪ Ex. -12 - 8
Ex. 15 - (-8)
Ex. -5 – (-8)
-12 + (-8)
- 20
15 + 8
23
-5 + 8
3
❖
Operations with Fractions
❖ Must have like denominator; add or subtract numerator
Multiplying fractions:
❖ Multiply numerators and multiply denominators.
Dividing fractions:
❖ Invert last fraction, then multiply the fractions.
1
2
1
2
1
2
2
3
3
6
− =
2
1&times;2
3
2&times;3
&times; =
2
1
3
2
&divide; =
4
−1
6
6
− =
2
1
6
3
= =
3
3
2
4
&times; =
FDP - Fraction Decimal Percent
❖ Convert Fractions to Decimals – Divide numerator by denominator.
❖ Convert Decimals to Fractions – Look at the last digit of your decimal number and
determine its place value. This place value number is the denominator of the
fraction, then rewrite the number without a decimal as the numerator. Make sure
Ex: 0. 35 =
35
=
7
EX. 2.5 = 2
5
= 2
1
10
2
100
20
DP (Doctor Pepper)
❖ Convert decimals to percent: move decimal two places to right
Example: 0.56 = 56% or 6 = 600%
❖ Convert percent to decimals: move decimals two places to the left.
Example: 84% = 0.84 or 135% = 1.35
❖ Convert percent to fraction - convert to decimal and then follow directions for
converting decimals to fractions.
❖ Convert fractions to percent – divide numerator by denominator (convert fraction to
decimal) then follow directions for converting decimals to percent.
Order of operations: PEMDAS
1) Grouping symbols – includes parentheses and brackets, absolute value, fraction bar, and
square roots
2) Exponents
3) Multiplication or Division LEFT TO RIGHT – whichever comes first is the operation you do
first.
4) Addition or Subtraction LEFT TO RIGHT - – whichever comes first is the operation you do
first.
Solving Equations:
1)
2)
3)
4)
Distribute if necessary
Combine any like terms if necessary
Add or subtract like terms off each side using inverse operations.
Multiply or Divide to isolate variables using inverse operations.
5x + 4 = 34
-4
-4
5x = 30
/5
/5
x = 6
Solving Inequalities
❖ Follow steps for solving equations.
❖ JUST REMEMBER WHEN YOU MULTIPLY OR DIVIDE BOTH SIDES BY A NEGATIVE NUMBER
THE INEQUALITY SIGN FIIPS!
❖ You can flip an inequality if you change the sign. 7 &gt; x is the same as x &lt; 7
❖ when graphing, &lt; and &gt; is a closed circle, &lt; and &gt; is open circle.
❖ x &gt; 4 - open circle at 4 and arrow to the right
Proportions
❖ Unit Rates, Constant of Proportionality
Unit rate is rate per one. If I can fill 20 jars in 4 hours, unit rate is 5 jars per 1
hour. Constant of Proportionality is same as Unit Rate.
❖ To solve a proportion, set up 2 ratios, cross multiply, set up as an equation and solve.
𝑥
28
=
5.6x = 1.4(28)
1.4
5.6
Your Turn: 5 is to 8 as 15 is to w.
Sales tax, discount, tip, part of whole
❖ Always put your percent over 100 and part over whole, then solve
14 is 25% of what number?
25
Set up as:100 =
14
𝑥
25x = 1400
𝑃𝑎𝑟𝑡
𝑤ℎ𝑜𝑙𝑒
%
= 100
x = 56
Finding missing lengths with scale factors
Ex: Wyheim is building a model airplane that is 1/80 the size of the real airplane. If the
real one has a wingspan of 120 feet, what will be the wingspan of the model?
𝑚𝑜𝑑𝑒𝑙
1
𝑥
MAKE YOURSELF A KEY!!! 𝑟𝑒𝑎𝑙 𝑡ℎ𝑒𝑛 𝑠𝑒𝑡 𝑢𝑝 ∶ 80 = 120
Fundamental counting principle: (FCP)
❖ Multiply the number of choices together in each category to find the total possible
arrangements. This is better and quicker at finding just the TOTAL number of
possibilities than tree diagrams.
Example 1: Tom is going to subway to buy lunch. If he chooses one item from each
category, how many lunch combinations are possible if he can choose from 12 different
sandwiches, 6 different types of chips, 4 types of cookies, and 9 different types of drinks?
Example 2: James bought a new lock that allows him to create his own 4 digit code. If he can
chose any number from 0 thru 9 and numbers can repeat, how many different possible
codes can be created?
Probability:
𝒏𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒘𝒂𝒚 𝒆𝒗𝒆𝒏𝒕 𝑨 𝒐𝒄𝒄𝒖𝒓𝒔
P(A) =
𝒐𝒗𝒆𝒓 𝒕𝒐𝒕𝒂𝒍 𝒑𝒐𝒔𝒔𝒊𝒃𝒍𝒆 𝒆𝒗𝒆𝒏𝒕𝒔
❖ Theoretical probability: Probability that is based on what SHOULD happen!
❖ Experimental probability: Probability that is based on what DID happen…not what
should!
Compound Probability (2 probabilities multiplied together)
❖ Independent Probability: (one event can NOT effect following events)
P(A and B) = P(A) ● P(B)
❖ Dependent Probability: The event of one even CAN effect the following events.
P(A and B) = P(A) ● P(B after A)
Laws of Exponents
▪
Product Rule – add exponents (must have same base)
34 ∙ 37 =
▪
Quotient Rule – subtract exponents ( must have same base)
49
▪
45
=
44
Power to a Power Rule – multiply exponents
(83 )4
▪
311
= 812
Product to a Power Rule – distribute exponent
(8 ∙ 17)4 = 84 ∙ 174
▪
Quotient to a Power Rule – distribute exponent to numerator and denominator
4 3
43
(11)
▪
=
113
Zero Power Property – always equals 1
210 = 1
Properties
❖ Commutative – terms change order
❖ Associative – always stays same order, but parentheses move
❖ Identity
o Adding 0 or multiplying by 1
❖ Inverse
o Adding or multiplying the opposite
2 3
o Ex: 4 + -4 = 0 and 3 &deg; 2 = 1
❖ Distributive 5 (x + 4) = 5x + 20
❖ Substitution: If x = 3, then x – 2 is 3 – 2
❖ Zero Product Property or Multiplicative Property of Zero
o Anything times 0 is 0
Verbal Translations
❖ Remember order switchers are “more than”, “less than”, “subtracted from”,
❖ Ex: six less than x is nineteen x – 6 = 19
Geometric Constructions
❖ Any two sides of a triangle will always add up to be greater than the third side.
o 2”, 7.5” and 5” cannot make a triangle because 2 + 5 is less than 7.5
o Can 8, 5 and 2.5 be the sides of a triangle?
o Strategies: Draw pictures to help understand the questions.
o What quadrilateral has all congruent sides and no right angles?
o What quadrilateral has right angles and opposite sides parallel ?
Statistics
❖
❖
❖
❖
Mean is average (add all numbers and divide by how many there are)
Median is the middle number when arranged least to greatest
Mode is number appearing most often
o Subtract each number from the mean
o Take absolute value of each (make positive)
o Find the average of those numbers
Circles
Radius is from center to edge.
Diameter is across the circle.
Circumference is around the circle.
r = &frac12;d
d = 2r
C = πd or C = 2πr
Area = πr2
Volume and Surface Area
V = lwh
SA = 2lw + 2lh + 2wh
Volume is how much it holds.
Surface area is found by adding together the areas of all the
sides.
V = &frac12; blh
SA = bl + ah + ch + bh
Volume is how much it holds.
Surface area is found by adding together the areas of all the
sides.
Cross Sections
❖ A cross section is created when a figure is sliced.
❖ What 2D shapes are created by slicing the 3D figure?
Angles
❖
❖
❖
❖
❖
Supplementary angles add up to 180&deg;
Complementary angles add up to 90&deg;
Vertical angles are across from each other
Adjacent angles are beside each other
A linear pair is two angles that are supplementary and adjacent
Your Turn: Find each missing angle!
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