ALGEBRA 1 Lesson 1-1 Warm-Up Are the following answers reasonable? Use estimation to determine why or why not

ALGEBRA 1 “Using Variables” (1-1) What is a “variable”? What is an “algebraic expression”? How do you translate a phrase into an algebraic expression? variable: a symbol, usually a letter, that stands for a number algebraic expression: a number sentence (includes numbers and operation symbols) that includes at least one variable “is” means “=“ “a number” means a variable, like “x” “+” words = plus, more than, sum, increased by “-” words = minus, less than, difference, decreased by “x” words = of, times, product (We show multiplication by placing the factor right next to the variable. Example: 19k means “the product of k and 19”) “  ” words = divide, quotient Tip: Write the numbers of most phrases in the order of the words, except “more than” and “less than”. Example: “7 decreased by 3” is translated as “7 – 3” Example: “the quotient of 21 and 3” is translated as “21 ÷ 3” Example: “three times a number minus 6 ” is translated as “3n - 6”

ALGEBRA 1 “Using Variables” (1-1) – Cont. How do write an algebraic expression for a word problem? When you see the phrases “more than” and “less than”, start with the second number. Example: “14 less than 17” means subtract 14 from 17, so it is translated as “17 – 14” Example: “23 less than m” means subtract 23 from m, so it is translated as “m – 23” Example: “32 less than 5 times c” means subtract 32 from 5 times c, so start with 5 times c, which is translated into 5c and subtract it from 32 = “5c - 32” Example: Jerry is 4 years younger than his brother Steve. Write an algebraic expression to describe Jerry’s age. First, we have to know how old Steve is. We do not have an age for Steve, so we will use a variable: Let S = Steve’s age. Now that we have determined Steve’s age as S, we can use it to determine Jerry’s age. Jerry, J, is 4 years younger than Steve, so: J = S - 4 Example: If Steve is 22 years old, how old is Jerry? Since we know S = 22, we can substitute (replace) s for 22 in J = S – 4: J = 22 – 4 = 18 So, Jerry is 18 years old.

ALGEBRA 1 “Using Variables” (1-1) – Cont. How do write an algebraic expression for a table? Example: Write an equation to show the total income from selling tickets to a school play for $5 each. = = Equation: 5 x Answer: I = 5t Example: Write an equation for the data in the table. Define: = Answer: m = 20g Words:The total income is 5 times the number of tickets sold. i Define: the number of tickets sold t the total income t i = Gallons Used Miles Traveled Words: Miles traveled 20 times the number of gallons. m miles traveled g Number of gallons Equations: m 20 x g. equals =

ALGEBRA 1 Write an algebraic expression for each phrase less than 9 2. the product of 8 and p 3. 4 more than twice c Define variables and write an equation to model each situation. 4. The total cost is the number of sandwiches times $ The perimeter of a regular hexagon is 6 times the length of one side. 9 – 7 8p8p 2c + 4 Let c = the total cost and s = the number of sandwiches; c = 3.5s Let p = the perimeter and s = the length of a side; p = 6s Using Variables LESSON 1-1 Lesson Quiz