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1-1 Variables and Expressions You would be wise to listen carefully and take notes! Copy material that is highlighted the same color as the above title.

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Presentation on theme: "1-1 Variables and Expressions You would be wise to listen carefully and take notes! Copy material that is highlighted the same color as the above title."— Presentation transcript:

1 1-1 Variables and Expressions You would be wise to listen carefully and take notes! Copy material that is highlighted the same color as the above title. In this section we are going to learn about mathematical expressions and how to “translate” verbal expressions into mathematical expressions. Algebra 1A by Gregory Hauca Glencoe adapted from presentations by Linda Stamper

2 Pre Quiz 1) increase 2) decrease 3) more than 4) less than 5) product 7) difference 8) quotient 9) sum 6) plus+ − + − x + − ÷ + 10) times x Write and translate each word into an operation symbol. Write and answer the following problems. 1) 2) 3) 4) 5) 7) 8) 9) 6) 10)

3 In Algebra, an expression is a mathematical phrase that contains operations, numbers, and/or variables.. An expression that represents a particular number is called a numerical expression. A variable expression consists of numbers, variables and operations. numbers- ex. 2,-3, π variables – letters ex. a,x,y operations - addition, subtraction, multiplication and division +, -,, ÷ Ex ÷ 3 Ex. 3x 2 + 2x - 1 You can use letters to represent one or more numbers. When a letter is used to represent a value that can change or vary, it is called a variable.

4 In variable expressions, a raised dot or parentheses are often used to indicate multiplication as the symbol x can be easily mistaken for the variable x. Here are some ways to represent the product of x and y. In general, good algebraic form is the xy version! In each expression, the quantities being multiplied are called factors, and the result is called the product. Multiplication Symbols Examples. 2y, 3xy Example. the product of x and y

5 Powers base exponent word description: four to the third power or four cubed factored form: evaluated form: 64 Powers consist of a base and an exponent A power is a short way of writing a repeating multiplication. Example:

6 1. Write problem Write word description. or seven squared 3. Write factored form. 7 Ex.1 Express the power 7 2 in words. Then write the factored form and evaluate it. seven to the second power Ex.1 4. Evaluate. 49

7 Writing expressions in exponential or power form. y4y4 y y Ex.2Ex (3x) 4 3x 3x Ex.4 Must have parentheses! Evaluating expressions Ex.5Ex Ex.7 Remember! An exponent applies only to what is directly in front of it. (-3) 2 9 -(3 3)-3

8 In English there is a difference between a phrase and a sentence. Sentences have verbs and phrases do not. In this section we are only going to translate phrases into expressions. Phrases Phrases are translated into expressions. Sentences Sentences are translated into equations and inequalities. Remember! A numeric expression is made up of numbers and operations (ex. 5 – 3). A variable expression is made up of variables, numbers and operations. (ex x).

9 Words representing operations. add plus sum increased by total more than added to subtract minus difference decreased by diminished by less than subtracted from less multiply times product of twice divide quotient

10 Translating phrases into variable expressions greater than a number n The sum of a number and 30 n A number decreased by 75 n – 75 Note that translation of this phrase “switches” the order of what is read. The expression 11 + n would NOT be correct. 4. a number subtracted from – n The translation of this phrase also “switches” the order of what is read. 5. The product of 5 and a number 5n Not 5·n or 5(n) or (5)(n) 6. The product of a number and 4 4n In products of numbers and variables the number is always placed first. Do not write “ n4 ”. 7. The quotient of a number and 6 n 6 Use a fraction bar in algebra to designate division! Not a ÷ symbol. The first number is always the numerator (on top) n ÷ 6

11 1. Twice a number plus 7 2n The difference of 8 and three times a number more than the product of a number and 4 4n + 5 Multiple Operation Phrases Some phrases require more than one operation or variable when translating them. In some you will need grouping symbols to show the correct order of operations. 2 n n+ 5 3 n 8 – 3n 4. A number cubed divided by 2 2

12 Class Practice Translate: n - 12 six times a number 6n a number divided by 8 a number minus 12 the sum of 15 and a number 15 + n the difference of a number and 6.7 n – 6.7 the quotient of 17 and a number

13 Translate: n + 15 the product of a number and 6 6n 5.2 less than a number not n6 15 more than a number the product of 6 and a number, subtract 10 6n - 10 the quotient of a number and 10, plus twice the sum of a number and 15 2 (n + 15) not 2n + 15 the difference of a number and 6, divided by 4

14 HW1–A2 Pages 8-9 #13-22,26,28,30-33,46.

15 Teacher Contact Information: I can be reached at school by phone at x1602 or by at Chapter assignment guides showing homework assignments and powerpoint lessons can be downloaded from my website at: Powerpoints Password - student Student individual test/class grades can also be accessed at my website. Click on Student Grades Find class Enter login name – student’s last name Enter password – student’s school ID number

16 Whiteboard Practice Translate: A number minus 12 n - 12 Translate: six times a number 6n Translate: a number divided by 8

17 Translate: the sum of 15 and a number 15 + n Translate: the difference of a number and 6.7 n – 6.7 Translate: The quotient of 17 and a number

18 Translate: 15 more than a number n + 15 Translate: the product of a number and 6 6n Translate: 5.2 less than a number not n6

19 The product of 6 and a number, subtract 10 6n - 10 The quotient of a number and 10, plus 2 + 2

20 Twice the sum of a number and 15 2 (n + 15) The difference of a number and 6, divided by 4 not 2n + 15

21 Did you use a fraction bar to designate division? a. 11 greater than a number n + 11 b. a number subtracted from – n c. The sum of a number and 30 n + 30 Ex.1. d. Maria’s age minus 27 a – 27 e. The quotient of 18 and a number 18 n f. The sum of a number and ten, divided by two.

22 a. The difference of a number and 7 n – 7 b. 32 increased by a number32 + n c. 25 less than a number – Writing word phrases as algebraic expressions. d. The quotient of a number and six. n 6 Use a fraction bar to designate division! 25n e. The product of a number and five5n The number always comes before the variable? f. 10 less the product of 5 and a number cubed 10 – 5n 3

23 Remember! Use a fraction bar to designate division? a. 11 greater than a number n + 11 b. a number subtracted from – n c. The sum of a number and 30 n + 30 Ex.1 d. Maria’s age minus 27 a – 27 e. The quotient of 18 and a number 18 n f. The sum of a number and ten, divided by two.

24 a. eight more than a number n + 8 b. seven less the product of 4 and a number x 7 – 4x c. n cubed divided by 2 Ex.2 d. 9 more than the quotient of b and 5 e. one third the original area of a f. thirteen less than a number n - 13

25 c. 32 increased by a number32 + x Translating phrases into variable expressions. d. 11 greater than a numberp + 11 a. The sum of a number and 30n + 30 Addition phrases : e. 7 more than a numbery + 7 b. 12 plus a number12 + a Note that translation of this phrase “switches” the order of what is read. The expression 11 + p would NOT be correct. The translation of this phrase also “switches” the order of what is read. The word “than” often indicates you may need to switch.

26 a. The difference between a number and 7 n – 7 d. 25 less than a numbery – 25 c. A number decreased by 75a – 75 e. a number subtracted from 1515 – p b. A number minus 27x – 27 Subtraction phrases : Note that translation of this phrase “switches” the order of what is read. The expression 25 - y would NOT be correct. The translation of this phrase also “switches” the order of what is read.

27 Multiplication phrases : c. Twice a number2p a. The product of 5 and a number5n b. The product of a number and 55n In products of numbers and variables the number is always placed first. Do not write “ n5 ”. d. 300 times a number300x e. A number times 77a Twice means 2 times. Remember in products the number always comes before the variable. Not 5·n or 5(n) or (5)(n)

28 a. The quotient of a number and 6 n 6 Use a fraction bar in algebra to designate division! Not a ÷ symbol. The first number is always the numerator (on top) Division phrases: b. The quotient of 18 and a number18 x c. A number divided by 12 a 12 n ÷ 6


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