CRCT Domain Review Algebra

Key Vocabulary Equivalent Equal to Evaluate To calculate the value of or substitute given values in for variables Simplify To make smaller Expressions= Combine Like Terms Fractions= Lowest Terms

Key Vocabulary Constant The value that does not change Coefficient The number attached to the variable Like Terms Terms that contain the same variable(s) raised to the same power(s) Substitution Putting in a value for a given variable

Write Expressions and Equations DO NOT have an equal sign and have various answers depending on the values given Equations DO have an EQUAL sign and one answer for the variable

Write Expressions and Equations Example: Expression Which expression represents the phrase below. 83 less than a number n 83 – n n – 83 83 ÷ n n ÷ 83

Write Expressions and Equations Example: Equation Lou had r rocks in his collection. He separated his rocks into 3 piles. He now has 12 rocks in each pile. Which equation represents this situation? r-3 = 12 r ÷ 3 = 12 r + 3 = 12 r x 3 = 12

Percent of a Number Change percent to a decimal and multiply by the number Or Use 𝑖𝑠 𝑜𝑓 = % 100 Commission- what is earned from the original Tax, tip, interest, mark-up- Add this amount to the original Original + tip = total due Discount, markdown, coupon, % off- Subtract this amount from the original Original – discount = sale price

Percent Change When an amount changes, it is sometimes helpful to find the “percent change”. This can be a “percent increase” if the amount went up, or a “percent decrease” if the amount went down. Both are calculated the same way: What is the percent change from 20 to 29?

Solving Equations Finding the value of a variable in an equation or solving a word problem. Solve using inverse operations. What is done on one side, must be done on the other.

Solving Equations Example: Justin is 10 years less than half his father’s age. If Justin is 12 years old, how old is his father? a) 22 b) 24 c) 32 d) 44

Solving Equations Example: Marissa bought 3 sweaters on sale for the same price. After using a coupon for $25, the total cost was $80. Write an algebraic equation AND solve to find the cost of each sweater.

Simplifying Expressions Combine Like Terms Use sign in FRONT of the number Clear parenthesis Cannot combine different variables or different powers EX. Simplify the following: 2x + 3y + 4x2 + 5y

Simplifying Expressions 3 + 5r – (2r – 5) 3r – 2 3r + 8 8r – 3 8r +3

Simplifying Expressions 8x + 4x + y + 3y 3(4x + y) 4(3x + y) 2(6x + y) 2(6x + 2y)

Translating Phrases (equations) Use the operational vocabulary to indicate what operation(s) will be required for the equation. Will have an equal sign Solve using inverse operations

Translating Phrases (equations) This season, the number of points Reggie scores was 36 less than 4 times the number Larry scored. Reggie scored 64 points this season. The equation below represents this situation. 4n – 36 = 64 What does n represent in the equation? the number of points Reggie scored the number of points Larry scored how many more points Reggie scored than Larry how many points Reggie and Larry scored in all

Inverse Operations Examples: 3g – 7 = 14 m/3 + 5 = 13 Do UnDo Addition Subtraction Multiplication Division Examples: 3g – 7 = 14 m/3 + 5 = 13