Introduction to Equations

Expression vs. Equation Round 1 Equation is derived from the word equate, which means one thing is the same as another thing. Which symbol would you associate with equate? An = sign! In Math, an equation always has an = sign. Notice the word equation has part of the word equal. So when you see equation, you know you must have an equal sign.

= = Equation Examples Notice they all have an = sign. = =

Expression vs. Equation Round 2 Expression is derived from the word express, which means high speed or quick. An expression does not have an = sign. Notice the word expression has the word express. This is a reminder we want to write the expression as quickly as possible, which means no =.

Expression Examples Notice no = sign.

Expression vs. Equation Round 3 What is the relationship between an equation and an expression? Such as 3x - 5 = 8 and 23a + 5b Notice each side of the equation is actually an expression. An equation is made from 2 equal expressions.

How to build an equation... Start with 2 expressions Put one expression on the left side of the = And the other on the right side Now we have an equation.

Identify as an Equation or Expression 3x + 2y = 5 Equation -3ab Expression 987 = x ⅔p - ¾q = r V = lwh 987,456.23 ⁵⁄₈ − ⁴⁄₇x

An equation is like a balance. The 2 side are always equal.

Write an equation to represent ... Each piece of candy costs $.55. The price of p pieces of candy is $4.40. What are we equating? The total cost to the cost of the p pieces. The amount charged for the candy is found by multiplying the cost by how many bought. Write the equation 4.40 = .55p

Write an equation to represent ... James made a withdrawal of d dollars from his checking account. His old balance was $980.23, and his new balance is $526.87. What does withdrawal mean? Withdrawal indicates something being taken away. What are we equating? Old balance minus withdrawal = New balance 980.23 − d = 526.87

Mya organized a pancake breakfast to raise money to donate to the Habitat for Humanity. She spent $35.23 on supplies and plans to charge $4.25 for each breakfast. If P is the profit and n is number of breakfast’s sold, what is the equation Mya can use to determine her profit based on the number of breakfasts sold? What is being equated? The profit to the amount spent on supplies and amount charged. How do you show spent mathematically? Spent indicates subtraction. Write the equation P = 4.25n − 35.23

You try... Aiden’s parent’s deposited $1250 into a savings account for him when he was born and contributed $325 each year, y. Write the equation that represents the total amount, T. What is being equated? The amounts put into the account and the total amount. What operation does deposited and contributed indicate? Addition Write the equation T = 1250 + 325y

You try... Tyler receives $15 a week for school lunch, and the cafeteria charges $2.35 for a lunch.  If Tyler purchases a lunch daily, write an equation to determine the amount of money left, A, after d days. What are we equating? Amount left = money received minus amount spent on lunch A = 15 − 2.35d

Key Points to Remember An equation has an = sign, an expression does not. When writing equations, determine what 2 things are being equated. Look for key words to determine the operation to use.