1. WRITING AND EVALUATING ALGEBRAIC EXPRESSIONS Algebra Review Unit

2. A LGEBRA MAGIC 1. Think of a number – shh! Don’t tell me! 2. Double it in your head. 3. Add 6. 4. Divide by 2. 5. Subtract the original number from your new number – shh! Let me guess the number you ended up with…..

3. D ID YOU GET … 3 I bet you’re wondering how I knew that! Let’s use some algebra to find out!

4. L ET ’ S TRANSLATE OUR WORDS INTO ALGEBRA 1. Think of a number. 2. Double it in your head. 3. Add 6. 4. Divide by 2. 5. Subtract the original number from your new number. Let’s call our number n n + n = 2n 2n + 6 2n + 6 simplifies to: n + 3 2 n + 3 – n simplifies to: 3 WORDSALGEBRA

5. L ET ’ S REVIEW SOME IMPORTANT VOCABULARY WORDS A variable is a symbol that represents one or more numbers. Examples of variables are: n number of students t time in minutes x may represent any number for any reason A term is a number, variable or the product of a number and variable(s). Examples of terms are: 3xz 2ab5y 3

6. A coefficient is the numeric factor of your term. An algebraic expression is a mathematical phrase with at least one variable. Examples of algebraic expressions are: 3m4t + 12 2x - 3n + 8 TERMCOEFFICIENT 3x3 2ab2 5y 3 5 z1

7. ALGEBRAIC EXPRESSIONS CAN REPRESENT WORD PHRASES WORD PHRASEALGEBRAIC EXPRESSION a temperature of t degrees increased by 5 degrees t + 5 five cats fewer than c cats c - 5 the product of 5 and n tickets 5n a dinner bill of d dollars divided among five friends d5d5

8. K EY WORDS AND PHRASES USED TO DESCRIBE MATHEMATICAL OPERATIONS OPERATIONKEY WORDS OR PHRASES Additionsum more than increased by total added to Subtractiondifference less than fewer than decreased by OPERATIONKEY WORDS OR PHRASES Multiplicationproduct times multiplied by per each Divisionquotient of divided by

9. W RITE AN ALGEBRAIC EXPRESSION FOR EACH WORD PHRASE swimming m meters per minute for 3 minutes 12 heartbeats more than x heartbeats a price p decreased by 16 the quotient of q and 6 3m3m x + 12 p - 16 q 6

10. The cost of a package of markers is d dollars. Write an algebraic expression for the total cost in dollars of 7 packages of markers. WORDS: NUMBER OF PACKAGES TIMES COST PER PACKAGE Let d = cost per package An algebraic expression for the total cost in dollars is 7d

11. Nine students will purchase b books each. Write an algebraic expression for the total number of books the students will buy. WORDS: NUMBER OF STUDENTS TIMES # OF BOOKS PURCHASED EACH Let b = # of books purchased each An algebraic expression for the total number of books is 9b

12. What is the cost of one pen if a package of 12 pens costs d dollars? WORDS: COST PER PACKAGE DIVIDED BY # OF PENS IN PACKAGE Let d = cost per package An algebraic expression for the total cost in dollars is d 12

13. WE CAN ALSO WRITE WORD PHRASES FROM ALGEBRAIC EXPRESSIONS Write three different word phrases for x + 2 a number plus 2 a number increased by 2 two more than a number Write three different word phrases for c - 50 a number minus 50 a number decreased by 50 50 less than a number

14. STEPS FOR EVALUATING ALGEBRAIC EXPRESSIONS 1. Replace the variables with the values that have been given. 2. Follow the rules for the order of operations. Example: Evaluate 50 – 3 x when x = 7 a. write the expression 50 – 3 x b. replace the variable with its given value 50 – 3(7) c. multiply 50 – 21 d. subtract 29

15. E VALUATE THESE ALGEBRAIC EXPRESSIONS 8 x + 2 let x = 3 9 n let n = 4 6 10 ab – 15 let a = 2 let b = 5 8(3) + 2 24 + 2 26 9(4) 6 36 = 6 6 10(2)(5) – 15 20(5) – 15 100 – 15 85