Evaluated
Evaluate expressions by substituting given values for variables: replace each variable with its assigned value, apply order of operations carefully, and simplify to a numeric result.
Key Concepts
When you replace the variables in an expression with selected numbers and simplify using the order of operations, you have evaluated the expression.
Evaluate $a^2b b$ if $a = 3$ and $b = 5$. Solution: $( 3)^2( 5) ( 5) = (9)( 5) ( 5) = 45 + 5 = 40$. Evaluate $3ab + 2a^2$ if $a = 2$ and $b = 5$. Solution: $3( 2)(5) + 2( 2)^2 = 30 + 2(4) = 30 + 8 = 22$.
Think of it like a secret recipe! An expression is the recipe with mystery ingredients 'x' and 'y'. To 'evaluate' it, you swap those ingredients with actual numbers and follow the order of operations to see what delicious numerical result you cook up. It’s all about finding that one final value hiding in the math.
Common Questions
What does it mean to evaluate an expression?
Evaluating an expression means substituting specific numeric values for each variable and then simplifying the result using order of operations. The output is a single number that represents the expression's value at those particular variable values.
What is the correct order of operations when evaluating?
Follow PEMDAS: Parentheses first, then Exponents, then Multiplication and Division left to right, then Addition and Subtraction left to right. Skipping steps or changing order leads to incorrect results. Write out each step to avoid order-of-operations errors.
How do negative substituted values affect the evaluation?
When substituting a negative value, always enclose it in parentheses before raising to a power or multiplying. For f(x)=x^2 with x=-3: write (-3)^2=9, not -3^2=-9. Failing to parenthesize negatives is one of the most common evaluation errors in Grade 10 algebra.