Evaluating Algebraic Expressions

Evaluating Algebraic Expressions

Replacing Variables with Number Values

Evaluating algebraic expressions means replacing

the variables with real numbers and performing the arithmetic operations in the expression. Although this sounds easy enough, it is critical

that you remember to follow the correct order of operations according to

PEMDAS. This is an important skill because many real-life situations are

modeled using algebraic expressions.

Multiple Choice

What is evaluating algebraic expressions?

• replacing

  the variables with real numbers and performing the arithmetic operations in the expression.

• redoing the terms in an expression and replacing them with a variable(s)

• Use PEMDAS and divide every term,then multiply 2.

Evaluating Single Variable Expressions

The most basic algebraic expressions contain only one variable and are

called single-variable expressions. Since one example is the

expression that represents the perimeter of a square. The perimeter of a

polygon is the distance around it and the formula for the perimeter of a

square is perimeter = 4s, where s represents the length of one of its four congruent sides. If we want to find the perimeter of a square piece of property

that has a side length of 62 feet, we replace the s in the expression 4s with

the value of 62:

Here’s a common type of problem

for evaluating expressions:

• What is the value of the expression 3(4x + 50) when x = –10?

• Replace the x with –10 and follow the appropriate order

  of operations mapped out in PEMDAS:

• 3(4(–10) + 50); do the multiplication inside the parentheses

  first

• 3(–40 + 50); next do the addition inside the parentheses

• 3(10); multiply

• 30 is your final answer

Subbing Negative Values in for Variables

Did you notice that when you substituted the –5 in for x 2 , the negative sign canceled out when (–5) 2 was performed? When substituting a negative value in for a variable, use parentheses

and include the negative sign in the operation instructed by the exponent.Therefore, even exponents will always cancel out the negative sign of a negative base since every product of two negative factors is positive. All odd exponents will preserve the negative sign of a negative base since

after all the multiplication, there will be one negative factor left over.

Even exponents will cancel out the sign of a negative base: (–3) 2 = (–3)(–3) = 9

Odd exponents will preserve the sign of a negative base: (–2) 3 = (–2)(–2)(–2) = –8

ERROR ALERT

A common mistake students make is using a negative

coefficient to cancel out a negative base before acting upon the exponent.

This is an especially easy mistake to make when the coefficient is –1! For example, when evaluating –x 2 for x = –4, it is required that you do negative four squared first, before multiplying it by the –1 coefficient:

Example: Evaluate –x 2 for x = –4

Solution: The coefficient here is –1 and that will get multiplied by x 2

after the exponent is done: –1(–4) 2 = –1(16) = –16. Notice that even

though the exponent is even, the answer is negative since the coefficient is negative. Watch out for this common mistake!

Multiple Choice

What is the value of 40 ÷ p × 2 when p = 10?

• 20

• 56

• 92

• 8

Poll

Let w represent any real number other than zero. Will the value of the

expression –w² sometimes, always, or never be negative?

• sometimes

• always

• never

Evaluating Multivariable Expressions

Although the formulas for area, surface area, and volume of cubes have just

one variable for side length, many algebraic expressions contain multiple

variables. These types of expressions are called multivariable expressions. If

you’ve ever calculated the perimeter of a rectangle using the formula perimeter = 2l + 2w, then you already have some experience with multivariable

expressions. To evaluate a multivariable expression, replace each variable

in the expression with the given value for that variable. As you did with

single variable expressions, remember to be careful as you work through

the order of operations.

Example: Evaluate the expression –3m – 10n for m = –5 and n = –2

• Solution: Replace m with –5 and n with –2 and let PEMDAS be your guide as you work through your operations:

• –3(–5) – 10(–2); do the multiplication first

• 15 – (–20); subtracting a negative is the same as adding a positive

• 15 + 20; add to get 35 as your final answer

Multiple Choice

Write an expression to model w is tripled and reduced by 10. Evaluate it

for w = 9

• 3w - 10 at w=9 will equal 21

• 3w - 10 at w=9 will equal 17

• 3w - 10 at w=9 will equal 19

• 3w - 10 at w=9 will equal 45

Poll

Did you enjoy this lesson?

• Yes, I learned a lot!

• Yes, but I didn't learn anything

• No, it was horrible!

• No, but I learned something

Open Ended

That's it! Tomorrow our lesson will be about: Writing Equivalent Expressions, until then see ya!😉 -ZZBZZ