Let me tell you a story about evaluating expressions…
Once upon a time
"Once upon a time, there lived a girl in a tower
She was there every day, hour after hour."
"Her name was Rap-Punzel,
a mischievious damsel, whose hair was a handful"
"The love of her life, Prince MC,
was in love with Rap-Punzel... as in love as can be.
They waited for the day and waited for the time
when the prince could scale the tower with a short little climb."
"But he's tired of waiting, what a waste of days.
He should evaluate expressions but he doesn't know the way"
Let's help MC Prince. At the start of this tale, Rap-Punzel’s hair is 50 inches long. Each month, it grows 5 inches." Let’s write this as an expression… 50 is the constant number in this expression, meaning it does not change. We said before that her hair grows at a rate of 5 inches per month. The number of months is the unknown quantity, which we will call x. We can also use any other variable.
Expression for the length of Rap-Punzel's hair
The number five is the coefficient of the variable. So… the expression to describe the length of Rap-Punzel's hair after a variable number of months is 5x + 50. Ok, let's use our expression to evaluate the length of Rap-Punzel's glorious hair over a period of a few months. Let’s set up a function table… When evaluating expressions, always remember to use the correct order of operations.
Calculation of further growth
After 1 month, the length of her hair is equal to 5(1) + 50, for a total length of 55 inches. After 2 months, the length is 2(5) + 50, which equals 60. Let’s fill in the table... OMG, after 6 months, Rap-Punzel’s hair is a staggering 80 inches long! But, disaster struck and Rap-Punzel discovered that her glorious hair was not so glorious after all ... - it was full of split ends. (Pause). Impulsively, ....
... she cut her hair. Now it's just 10 inches long. To keep her hair healthy, Rap-Punzel must trim her hair two inches every month. Despondent, MC Prince wondered, how much longer must he wait to be with his beloved? Let's modify our expression. 5x for the growth per month minus 2x for the trimming per month plus ten for the starting length.
Insert the right numbers
Now, simplify the expression. 3x + 10. MC Prince wondered, '...after six more months, how long will her hair be?...' Evaluate the expression, this time, letting x equal six… use the correct order of operations, 3(6) = 18; plus ten it is equal to twenty-eight. Her hair will only be twenty-eight inches long!
"Still waiting outside, MC Prince began to doubt
without Rapunzel in his life, he's like a plant in a drought
he had an idea, on which he was keen"
what's this? OH NO...he bought magic beans...
Before evaluating expressions or solving equations, your goal is to always simplify as much as possible. To do this, you should follow some simple steps, especially where variables are concerned. You should know how to use the Distributive Property as well as the rules for combining variables.
If you have complex expressions or equations, you first look for addition or subtraction inside the parentheses. Then, you can simply follow the rest of the order of operations (PEMDAS, BEDMAS, BODMAS, BIDMAS). Afterwards, you group like terms before combining like terms.
In case you were wondering what like terms and unlike terms are and how to group and combine like and unlike terms when variables are involved, this video will enlighten you. If you had problems with what to combine, always keep in mind, that different variables should be treated like different species in real life. That being said, you will master simplifying variable expressions in no time, promised.
Don't try to sneak past this topic in maths if you have difficulties; simplifying variable expressions is one of the most important issues for all your future math topics and in our video it will be explained step by step to you. Relax, lean back, watch and learn.
Use properties of operations to generate equivalent expressions.