Verbal Phrases Involving Addition The algebraic expression a + b can be used to represent several different verbal phrases. a plus b the sum of a and b a added to b a is increased by b b is added to a b more than a The word exceeds means “is more than”. So, the number that exceeds 5 by 2 can be written as “ 2 more than 5” or 5 + 2.
Verbal Phrases Involving Subtraction The algebraic expression a - b can be used to represent several different verbal phrases. a minus b b subtracted from a a decreased by b b less than a a diminished by b a reduced by b the difference between a and b
Verbal Phrases Involving Multiplication The algebraic expressions a X b, a. b, (a)(b), and ab can be used to represent several different verbal phrases. a times b the product of a and b The preferred form to indicate multiplication in algebra is ab. The multiplication symbol X is avoided in algebra because it can be confused with the variable x. b multiplied by a In algebraic expressions, parenthesis may be used but are not needed.
Verbal Phrases Involving Division The algebraic expressions and can be used to represent several different verbal phrases. a divided by b and the quotient of a and b means one-forth of a as well as a divided by 4. The product of x and y, decreased by 2. The product of x and y decreased by 2. Commas are very important in some verbal phrases. .
Translating Words to Algebra 3 more than a number 5 less than a number decreased by 7 the product of 6 and a number twice a number decreased by 4 25, diminished by 4 times a number the sum of a number and 2, divided by 9
More Translating Words to Algebra Translate the following phrases into an algebraic expression. A distance that is 20 meters shorter than x meters. A bill for n baseball caps, each costing d dollars. A weight that is 40 pounds heavier than p pounds. An amount of money that is twice d dollars.
Word Problem Brianna paid 17 dollars for batteries and film for her camera. If the batteries cost x dollars, express the cost of the film in terms of x. batteries + film = 17 dollars - batteries film = (17 – x) dollars That was easy
Word Problems from page 93 Represent the number of pounds of grapes you can buy with d dollars if each pound costs b dollars. The number of kilometers traveled by a bus is represented by x. If a train traveled 200 kilometers farther than the bus, represent the number of kilometers traveled by the train. The cost of a mountain bike is 5 times the cost of a skateboard. If the skateboard costs x dollars, represent the cost of the mountain bike. After 12 centimeters had been cut from a piece of lumber, c centimeters were left. Represent the length of the original piece of lumber.
Factors of a Term If a term contains 2 or more numbers or variables, then each number, each variable, and each product of numbers and variables is called a factor of the term, or a factor of the product. Factors of 3 xy 1, 3, x, y, 3 x, 3 y, xy, 3 xy The coefficient of a term is the number in front of the variable. Factors and Coefficients of Terms Factors Coefficient 1, 7, a, b, 7 a, 7 b, ab, 7 ab 7 7 ab bd 1, b, d, bd 1
Bases, Exponents, and Powers The exponent is the number of times the base is used as a factor. Coefficient Base Exponent
Evaluating Algebraic Expressions To evaluate an algebraic expression, replace the variables with the given values, and then follow the proper order of operations. Don’t forget about my dear Aunt Sally. Evaluate when Rewrite the expression with empty parenthesis where the variables are Replace the variables with the given values Follow the proper order of operations
More Evaluating Algebraic Expressions Evaluate when
Using a Calculator to Evaluate Algebraic Expressions Evaluate The given values can be stored in the calculator. when Press (-) 4 STO [ ALPHA A ENTER 10 STO [ ALPHA N ENTER 3 STO [ ALPHA D ENTER 2 A/5+(N-1)D Evaluate when ENTER 10 STO [ ALPHA A ENTER (-) 6 STO [ ALPHA N ENTER (-) 5 STO [ ALPHA D ENTER 2 A/5+(N-1)D ENTER
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