Translating Verbal Phrases: Algebraic Expressions

1. Algebra 1 Ch 1.5 Translating Verbal Phrases

2. Objective • Students will translate verbal phrases into algebraic expressions

3. Introduction • The ability to translate verbal phrases has real-life application… • Suppose you wanted to throw a party and you only have $250 to work with…you contact several catering companies and they give you prices ranging from $7.50 to $10.00 per person…you also have to buy decorations with the $250.00 • In real life you will need to be able to calculate the total cost to know that you have enough money to pay for the party…Which will tell you how many friends you can invite… • In this instance you can create an algebraic expression to know the number of friends you can invite and to make sure that you stay within your budget.

4. Translating Verbal Phrases • The key to translating verbal phrases it to know what the English words mean mathematically… • It’s expected that you know the words that mean add, subtract, multiply and divide • Let’s do a quick review to refresh your memory…

5. Words that mean Add or Subtract AdditionSubtraction Plus Minus Increased by Less Subtract Sum In all Less than More than Decreased by Total Difference

6. Words that mean Multiply or Divide MultiplyDivide Divided Times Rate Multiplied Product Quotient Each An, in, or per Of Ratio Factors Separate

7. Translating Verbal Phrases • The starting point to translate verbal phrases is to identify the variable first… • Most often you will know what the variable is by the phrase “a number”… • One more thing that you need to know…the Commutative Property applies to addition and multiplication…generally, the property states “it doesn’t matter which order you add or multiply…you will get the same results” • However, when subtracting or dividing it DOES matter which order you place the numbers….

8. Example # 1 Five yearsolder thanher brother 1.First identify the variable…in this case the variable is her brother’s age…lets call that a 2. The term “older than” means to add 3. Five years means the number 5 So the above expression can be written as: 5 +a

9. Comments • It is very difficult to teach this concept to students as each student reads and has a different understanding… • However, the key to converting expressions and equations to algebraic terms is identifying the variable first… • Finally…there is no getting around it…to master this concept…you must practice it…you will definitely see this on my tests, county semester tests, and FCAT

10. Strategies • Some strategies that you can use when working with this concept are: • Read the expression or sentence more than once… • Use colored markers, pencils or highlighters to identify each term • Underline, circle, or box each of the terms as you identify them • Lets look at some more examples….

11. Example # 2 Six dollars an hour times the number of hours • Hour is the variable …let’s call it h • Times means to multiply • Six dollars means the number 6 The algebraic expression is: 6∙h This can also be written as 6h

12. Example # 3 Three more thanthe quantityfive times a number • 5 times a number is the variable …let’s call it 5n • More than means to add • Three means the number 3 The algebraic expression is: 5n + 3

13. Example # 4 Two less than the sum of 6 and a number m • A number m is the variable • The sum of 6 and m means to add • Two less than means to subtract 2 • In this instance you have to add before you subtract…so the sum of 6 and m would go in parenthesis The algebraic expression is: (6 +m) – 2

14. Example # 5 A number xdecreased by the sum of 10 and the square of a number y • A number x is the variable • Decreased means to subtract • The sum means to add • In this instance you have to add the sum of 10 and the square of a number y. Since you have to perform this function first before you subtract …10 and the square of y would go in parenthesis The algebraic expression is: x– ( 10 + y2)

15. Verbal Sentences • You can also translate verbal sentences into equations and inequalities • The word “is” and “total” mean equal • The words for inequalities are as follows: Less than < Less than or equal to ≤ Greater than > Greater than or equal to ≥

16. Example # 6 Nine less than the product of ten and a number d iseleven • The variable is 10 and a number d, which is written as 10d • Nine less means to subtract 9 • “is” means equal • The total is 11 The algebraic expression is: 10d – 9=11

17. Comments • On the next couple of slides are some practice problems…The answers are on the last slide… • Do the practice and then check your answers…If you do not get the same answer you must question what you did…go back and problem solve to find the error… • If you cannot find the error bring your work to me and I will help…

18. Your Turn • Translate the verbal phrase into an algebraic expression. Use x for the variable in your expression • Nine more than an number • Three more than ½ a number • The quotient of a number and two tenths • The difference of ten and a number • Five squared minus a number

19. Your Turn • Write each sentence as an algebraic equation or inequality • Nine is greater than three times a number • Twenty-five is the quotient of a number y and 3.5 • Three times the quantity two less than a number x is ten • The quotient of thirty-five and a number t is less than or equal to seven • A number q is equal to or greater than one hundred

20. 9 + x or x + 9 ½x + 3 or 3 + ½x x  2/10 10 – x 52 – x 9 > 3x 25 = y/3.5 3(2 – x) = 10 35/t ≤ 7 q ≥ 100 Your Turn Solutions