Hi, this is Wyatt, and today we're going to be talking about how to evaluate algebraic expressions. This is usually taught in seventh-grade algebra, so let's get right to it!
Before we begin, remember the order of operations:
A common way to remember this is: Please Excuse My Dear Aunt Sally.
Evaluate: (2x)2 - 3 × 2 when x = 2.
Replace x with 2:
(2 × 2)2 - 3 × 2
Parentheses:
42 - 3 × 2
Exponents:
16 - 3 × 2
Multiplication:
16 - 6
Subtraction:
10
Answer: 10
Evaluate: (4xy2)/2 - 3/2 when x = 1 and y = 2.
(4 × 1 × 22)/2 - 3/2
Exponents:
(4 × 1 × 4)/2 - 3/2
Multiplication:
16/2 - 3/2
Subtraction:
(16 - 3)/2 = 13/2
Answer: 13/2
Evaluate: 4x-2 + yz when x = 1, y = 2, and z = 3.
Negative exponents mean:
x-2 = 1/x2
4/(12) + (2 × 3)
4/1 + 6
4 + 6 = 10
Answer: 10
Evaluate: y3/2/3 + (z/3)2 - 2/3
when y = 4 and z = 1.
First, evaluate:
43/2
A power of 3/2 means:
(√4)3
23 = 8
Rewrite the expression:
8/3 + 1/9 - 2/3
Convert to ninths:
24/9 + 1/9 - 6/9
25/9 - 6/9 = 19/9
As a mixed number:
2 1/9
Answer: 19/9 or 2 1/9
And that's how you evaluate algebraic expressions using substitution and PEMDAS. Thanks for watching, and bye for now!