Lesson 1.1 - Using Variables

1.1 Using Variables : 

1.1 Using Variables

Vocabulary : 

Vocabulary A variable represents a number that can have many values. Variables represent numbers that can vary Generally, letters are used as variables An algebraic expression is a phrase that can include numbers, variables and operation symbols. n – 7 x2 + 8 An equation is a math sentence that uses an equal sign. y ? 5 = 20 An open sentence is an equation that contains one or more variables. k + m = 14

Operation Terms : 

Operation Terms Sum: Addition, + More than, plus Difference: Subtraction, – Less than, less, minus Product: Multiplication, ? times Quotient: Division, ? , ? Divided by

1. Writing Algebraic Expressions : 

1. Writing Algebraic Expressions the sum of n and 8 the sum of n and 8 n + 8 Because addition is commutative, order doesn’t matter six less than b six less than b 6 – b b – 6 Because subtraction is not commutative, order does matter c) the product of 7 and n the product of 7 and n 7 ? n 7n Because multiplication is commutative, order doesn’t matter. d) the quotient of n and 8 the quotient of n and 8 n ? 8 Because division is not commutative, order does matter.

2. Define a Variable & Write an Algebraic Expression : 

2. Define a Variable & Write an Algebraic Expression ten more than twice a number ten more than twice a number Let n = a number 10 + 2n three times a number minus six three times a number minus six Let b = a number 3 ? b – 6 3b – 6 c) four less than a number divided by eight four less than a number divided by eight Let y = a number 4 – y ? 8 d) the product of one half a number and twelve the product of one half a number and twelve Let a = a number ½ a ?12 12 ? ½ a 6a (remember, with multiplication, order doesn’t matter)

3. Write an Equation : 

3. Write an Equation a) The total income from selling tickets to a school play for $5 each. RELATE: total income is 5 times the # of tickets sold What does ‘is’ mean in mathematical terms? DEFINE: Let t = total income Let s = # of tickets sold EQUATION: t = 5 ? s t = 5s

3. Write an Equation : 

3. Write an Equation b) the perimeter of a regular hexagon is 6 times the length of one side RELATE: the perimeter is 6 times the length of one side DEFINE: Let p = perimeter Let s = length of one side EQUATION: p = 6 ? s p = 6s

4. Write an Equation : 

4. Write an Equation RELATE: How are the numbers in each pair related to one another? the # of miles traveled is 20 times the # of gallons used the # of miles traveled is 20 times the # of gallons used How else could we say these two sets are related to each other? DEFINE: Let m = the # of miles traveled Let g = the # of gallons used EQUATION: m = 20g