Seven is less than 11. Four more than seventeen. Four is not equal to three.

Transcription

1 Prealgebra.1: Translations, Simplifying and Evaluating Expressions Words such as,, and indicate addition. Words such as,, and indicate subtraction. Translate each of the following into mathematical symbols. The sum of 4 and 11 Fifteen subtracted from 0 Words such as and indicate multiplication. Words such as and indicate division. The product of 5 and a number The quotient of a number and another number Translate the following into algebraic expressions. Five times a number plus 4 The difference between three times a number and twenty-two Translate the word statements into symbols. Seven is less than 11. Four more than seventeen Four is not equal to three.

2 Prealgebra.1, page Thirteen is greater than or equal to twelve. Twelve is less than or equal to thirteen. Fifteen is greater than five. Six is less than twelve. Translate the following into symbols. Fourteen decreased by three equals eleven. Two times five increased by seven equals seventeen. Six divided by two equals three. The product of seven and three is greater than twenty. A is a symbol used to represent an unknown number. It is denoted by a letter such as x, y, or p. Note: In subtraction it is important to carefully to determine which number is being and which is the number. Often the number mentioned first is placed and vice versa. Translate the following into symbols. The sum of a number and 11 3 subtracted from a number The product of 11 and a number

3 Prealgebra.1, page 3 The quotient of a number and four The quotient of 4 and a number Five times a number plus 4 The difference between twice a number and 7 Identify whether each of the following is an equation or an expression. 4x 5y An is a statement that expresses equality between two. The symbol must be present. 4x 5y 0 7x 9x 1 3x y x y Translate the following into mathematical symbols and identify each result as an expression or an equation. Seventeen times a number decreased by five Seventeen times a number decreased by five equals two. Expression: 3x 4x 5 Terms Coefficients: The expression 3x 4x 5 is an in. It has three Variable parts:

4 :,, and. Prealgebra.1, page 4 Identify the numerical coefficient and the variable part of the following terms: Term Numerical Coefficient Variable Part 3 x 3x y Terms which differ only in their and have identical are called terms. From the following list of terms, identify the group of like terms. 3 x, 5 xyz, 4 x, 9, 6 x, 1 xyz, 15, x Terms which are not terms are called terms. are combined by finding the sum of the and attaching it to the common. terms cannot be. Simplify the expressions by combining like terms. 4x + 7x -7p + 5p 18t 1t y + 10y 30y Write the following products without grouping symbols using the distributive property. To simplify algebraic expressions: 1. Use the property to multiply any expression that involve a factor times a grouping of terms.. like terms. (x + y) = 3x ( + y) = -(x + 3y) = -4x(3x 7y + 4) =

5 Prealgebra.1, page 5 Simplify the following expressions. 3(x + 4) (x 5) + 1 b(a + ) a( b) + (a + b 1) When multiplying b a it is customary to write the product as ab. To evaluate an algebraic expression: 1. Substitute the for the variable using.. Simplify the result using. Evaluate 4x 3y + 1 for x = 5 and y =. 4x 3y + 1 = Evaluate the expressions. x + 5, for x = -. -4x + 5x 3, for x = -3 x 3-5x + 7x 36 for x = 3 6y 4 5y 3 + 3y + 1 for y = - Prealgebra.1, Page 6

6 To find an average: 1... the sum by the of numbers in the group. Find the average of the group of numbers. 87 and 115 7, 35, 48, 5, and , 4089 and 513 Find the average of 567, 917, 855, and 345 using a calculator. Calculator entry: Weekly earnings, in dollars, of 10 employees of a software company are: $,780; $,030; $3,300; $850; $,540; $1,760; $1,360; $,100; $1,580; $1,800. What is the average earnings of the workers? At the beginning of a 14-day trip, the odometer on a car read 10,78 miles. It read 13,638 miles at the end of the trip. What was the average number of miles traveled each day?