Name Algebra I Block UNIT 2 STUDY GUIDE Ms. Metzger MATCHING. Match the correct vocabulary word with its definition 1. Whole Numbers 2. Integers A. A value for a variable that makes an equation true B. A fraction where the numerator and denominator are switched 3. Rational Numbers C. A math statement that includes numbers, symbols, and operators. It does NOT have an equal sign 4. Real Numbers D. Terms that have the same variable with the same exponents 5. Origin 6. Coordinate 7. Absolute value E. The number before a variable F. Whole numbers and their opposites G. An equation with multiple variables 8. Coefficient H. The value 0 on a number line or (0,0) on the coordinate plane. The location you start. 9. Like terms I. All numbers included in whole numbers, integers, rational numbers, and irrational numbers 10. Expression J. A point on a number line that corresponds to a value 11. Equation 12. Solution 13. Reciprocal K. The numbers 0, 1, 2, 3, 4 L. A math statement where two expressions are equal M. where a and b are integers and 14. Literal equation N. The distance between a number and zero (How far a number is from zero)
GRAPHING NUMBERS ON A NUMBER LINE Graph and label the real numbers on the number line below. (Remember to label your graph using the original numbers!) 1. ABSOLUTE VALUE Absolute value is the between a number and. Absolute value is always (positive/negative). Circle one. Evaluate the expression. 1. 2. 3. Ex: OPERATIONS WITH FRACTIONS Adding and subtracting fractions we need to have To find common denominators look for the
Multiplying fractions multiply together and multiply together Reduce your answer! You may cancel on the diagonal only when multiplying fractions! Dividing fractions we by the Reduce your answer!
PROPERTIES OF REAL NUMBERS Identify properties by comparing the left hand side of the equation to the right hand side. What changes? Order? commutative property Is your answer the same value you started with? Identity Property Grouping? associative property Is your answer the identity? Inverse Property Circle the correct choice. 1. The identity for addition is (zero/one). 2. The identity for multiplication is (zero/one). Go back to your notes or foldable and review the properties below: Associative Property of Addition Associative Property of Multiplication Commutative Property of Addition Commutative Property of Multiplication Additive identity Multiplicative Identity Additive Inverse Multiplicative Inverse Distributive Property Multiplicative Property of Zero Reflexive Symmetric Transitive Substitution
Identify the property in each of the following expressions. 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) COMBINING LIKE TERMS When combining like terms we the coefficients. Circle true or false for the statement below. When combining like terms, after we add or subtract the coefficients we leave the variable the same (True/False)
Simplify by combining like terms. 3x 2 4 6x 2 +2 7(2b+1) 2b -5n(4 + 8) + 5n 2 (3 + 5) 6(6k 3 +3) 5k 3 SOLVING EQUATIONS Our goal is to find a solution that makes our equation true. Inverse Operations are what we use to undo operations! The inverse operation of Multiplication is Subtraction is Addition is Division is No solution GUIDELINES TO SOLVING EQUATIONS Word bank Distributive property Positive Variable terms Least common denominator Inverse operations Like terms Infinite solutions
Fill in the blanks with the appropriate word from the word bank on the previous page. Simplify as much as possible first! - Use to undo parentheses - Combine on the same side when possible - Simplify signs - Get rid of fractions by multiplying by the or by multiplying by the reciprocal - Evaluate absolute value Isolate the variable - If you have on both sides, group them on one side. - Use to get the variable alone Always make sure your variable is - Undo negative signs my dividing each side by negative one. Remember- when do we have infinite solutions? No solution? Solve the equation. Show all work and check your answer. 1) 2) 3) 4)
5) 6) 7) 8) 9) 10) 11) 12) 13) 14) Solve for w. 15) Solve for x. 16)