Math Common Core Standards + Glencoe Course 2 Volume 2
(Chapter 2: Percents) Percent Equation
% * X = Y (Convert percent to decimal then multiply)
(Chapter 1: Ratios and Proportional Relationships) How would you solve this proportional percent problem? If you cannot solve it, practice. Jasmine buys the magic carpet on sale for $374. Jasmine saved $66 off the regular price. What percent was the price of the magic carpet discounted?
17.65%. Formula to find x is what percent of Y = P% * X. P% = Y/X ( / = divide)
(Chapter 4: Rational Numbers) Add and subtract like and unlike fractions
Add Like fractions: Just add normally Add Unlike fractions: Butterfly Method Subtract like fractions: Just subtract normally Subtract unlike fractions: Butterfly Method
(Chapter 4: Rational Numbers) Add and subtract mixed numbers
Add unlike denominators: Find least common multiple, change denominator, add normally Add like denominators: Add normally Subtract like denominators: Subtract normally Subtract unlike denominators: Find a least common multiple, change denominator, subtract normally WHATEVER YOU DO TO DENOMINATOR DO TO NUMERATOR
(Chapter 3: Integers): How to add & subtract integers
Add: (positive + positive = positive) (negative + negative = negative) (more positive + negative = positive) (more negative + positive = negative) Subtract: ( positive - positive) - (negative) ( positive - negative ) - (positive) (Negative - positive) - (negative) (negative - negative) - (positive)
(Chapter 5: Expressions) Add & Subtract linear expressions
Combine like terms
(Chapter 6: Equations and Inequalities) Solve equations with rational coefficients
Combine like terms and solve
(Chapter 5: Expressions) Properties of operations
Commutative: When you can change the order of numbers in an equation without changing the answer, you are using the commutative property (+ x) Associative: When you can list a group of numbers in any order and combine them however you wish without changing the answer, you are using the associative property. (+ x) Distributive: Equations with parentheses use the distributive property. When you distribute, you take a number and do the same operation to all the numbers inside the parentheses. Identity: An identity refers to numbers that don't change when combined with another number. There are two identities:
(Chapter 2: Percents) Sales tax, tips, markup, discount
Convert percent to decimal, divide decimal from total before addition, then take or add that number from total before addition to find your final answer.
(Chapter 1: Ratios and Proportional Relationships) What is, and how do you find, a disproportional relationship?
Disproportional relationships are relationships between two variables where their ratios aren't equivalent. To find a disproportional relationship, you have to try and find a pattern between two variables. If you can't, then you have a disproportional relationship. For example X=2 Y=5, X=3 Y=7. You can see there isn't a pattern.
(Chapter 6: Equations and Inequalities) Solve two step equations addition and subtraction
Do opposite then finish equation normally (show work)
(Chapter 6: Equations and Inequalities) One step addition & subtraction
Do the opposite of what it says: Ex: m-6=-3 (Add 6 to negative 3)
(Chapter 5: Expressions) Distributive property
Equations with parentheses use the distributive property. When you distribute, you take a number and do the same operation to all the numbers inside the parentheses. The distributive property of math is usually referred to as the distributive property of one operation - most often multiplication - over another operation - generally addition or subtraction. The rule for distribution of multiplication over addition is that you multiply a number by each of the numbers added together in a set of parentheses. Example: 5(n + 3) = (5 x n) + (5 x 3) or 5n + 15 The distributive property of multiplication over subtraction works the same way. The only difference is you are subtracting instead of adding. Example: 5(n - 3) = (5 x n) - (5 x 3) or 5n - 15
(Chapter 4: Rational Numbers) Compare and Order rational numbers
Find a common denominator (multiply denominators and numerators) than compare using = < >
(Chapter 1: Ratios and Proportional Relationships) Word Problem Example: If Susan makes 8 cakes in 2 hours. How many cakes can she make in 5 hours?
How to solve: First, you would make two fractions, 8/2 X/5. Then, you would want to find the unit rate for 8/2, so you would divide it in two since the line between the numerator & denominator is basically a division sign. Thus, you would be left with 4/1 (4 cakes in 1 hour). Next, you want to find how many cakes Susan can make in 5 hours, so multiply the unit rate by 5. This (4x5) leaves you with an answer of 20.
(Chapter 1: Ratios and Proportional Relationships) How do you solve complex fractions?
If it's two fractions on top of each other, split them and "divide" them. (Keep Change Flip)
(Chapter 1: Ratios and Proportional Relationships) How can you immediately tell a proportional relationship or not by using a graph?
In proportional relationships, when X equals 0, Y will always equal 0.
(Chapter 2: Percents) Percent of change
Increase: change divided by original x 100% (Stays the same) Decrease: Take percent leftover, convert to decimal, and multiply by total (100%) .8 (80%) x 60 = 48
(Chapter 1: Ratios and Proportional Relationships) How do you convert unit rates?
It's unlikely this will be on the test since who would remember the conversion factor. But if it is, you solve it this way. You first write the number your converting, for example, 1oz. to the right of it you put your conversion factor in parenthesis. 10LBS (2.2lb = 1kg) Then divide the two similar measurements by each other, and that with the new measurement label is your answer. (10 divided by 2.2 = 4.55.
(Chapter 4: Rational Numbers) Multiply and divide fractions
Multiply normally or butterfly method with different denominators. To divide fractions KCF (Keep, change, flip)
(Chapter 3: Integers): How to multiply and divide integers
Multiply: (- x -) = (+) (+ x +) = (+) (+ x -) = (-) (- x +) = (-) Divide: Same formula
(Chapter 5: Expressions) Algebraic Expressions
PEMDAS
(Chapter 5: Expressions) Sequences
Patterns "Each term is obtains by doing X"
(Chapter 2: Percents) Percent of a number
Percent * X = Y (Convert percent to a decimal and times by whole to get answer)
(Chapter 1: Ratios and Proportional Relationships) What is, and how do you find a proportional relationship?
Proportional relationships are relationships between two variables where their ratios are equivalent. To find a proportional relationship, you have to try and find a pattern between two variables. For example, X=1 Y=3, X=2 Y=6. You can see a pattern in that whenever X goes up 1, Y goes up 3.
(Chapter 2: Percents) Percent proportion
Questions like X is P% of Y. What is P% of Y (Y=P*X) What percent of x is y (P*X=Y) X + P% is What? (P% = Y/X) (P%*X=Y) X - (X × P%) = YX(1 - P%) = Y
(Chapter 5: Expressions) Simplify algebraic expressions
Remove any grouping symbol such as brackets and parentheses by multiplying factors. Use the exponent rule to remove grouping if the terms are containing exponents. Combine the like terms by addition or subtraction Combine the constants
(Chapter 2: Percents) Simple & compound interest
Simple: Compound:
(Chapter 4: Rational Numbers) Terminating and repeating decimals
Terminating: Like .25 doesn't repeat (Just ends) Repeating: Goes on forever, usually rounds up at third decimal has a cap, or you put an (X) next to it
(Chapter 1: Ratios and Proportional Relationships) Are you able to tell what points (x, y) means on a number graph in terms of situation? (Like if a point is the unit rate, or a variable, etc.
This probably will not be important on the test, but it is good to look over just in case.
(Chapter 1: Ratios and Proportional Relationships) If you had to solve a proportional equation such as 8/36 = 10/n, how would you do it?
To solve, you had divided 36 by 8 to find the unit rate. The unit rate for this problem would be 4.5, so you would multiply 10 by the unit rate to get your answer. (10 x 4.5 = 45)
(Chapter 1: Ratios and Proportional Relationships) How do you determine a proportional relationship in a coordinate plane?
When X increases or decreases on the coordinate plane, Y will always increase or decrease by the same rate.
(Chapter 2: Percents) Percent and estimation
When given a percent like 79% round to the nearest ten. This will make it easier on you, and give you an estimate. (Saves you time)
(Chapter 1: Ratios and Proportional Relationships) What is, and how do you find a unit rate?
When you divide something by its parts, a unit rate is a singular part. For example, $200 in 5 hours as a unit rate is $40 in 1 hour.
(Chapter 1: Ratios and Proportional Relationships) How would you write a rate as a ratio?
When you see a rate written as a ratio, you will see it written in 3 primary ways. So, for example, if you had a rate of $30 per hour, you would see it written in one of these ways, 30 miles / 1 hour, 30/1, 30:1.
(Chapter 1: Ratios and Proportional Relationships) How do you represent proportional relationships by equations? (Direct Variation)
You use the formula y=kx. The K in the formula represents the constant of proportionality. So, for example, the ratio 32:1 's constant proportionality would be 32 because that is what 1 is multiplied by.
(Chapter 1: Ratios and Proportional Relationships) What is a complex fraction?
a fraction with a fraction or mixed number in the numerator or denominator or both
Chapter 1: Ratios and Proportional Relationships) Rate of change
change y / change x (For example) +1/+5
(Chapter 1: Ratios and Proportional Relationships) Video/Website links.
https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-ratios-prop-topic/cc-6th-rates/v/introduction-to-rates and https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-ratio-proportion/cc-7th-write-and-solve-proportions/a/multi-step-ratio-and-proportion-problems
Chapter 1: Ratios and Proportional Relationships) How to find slope
y2-y1/x2-x1. Your first number will always be x and the second will be y in each pair.
