Evaluate variable expressions with decimals, fractions, and mixed numbers

Learning Objectives Identify variables, constants, and terms within an algebraic expression. Substitute given rational number values (decimals, fractions, mixed numbers) for variables in an expression. Apply the order of operations (PEMDAS/BODMAS) correctly when evaluating expressions. Perform arithmetic operations (addition, subtraction, multiplication, division) with decimals accurately. Perform arithmetic operations with fractions and mixed numbers accurately, including converting mixed numbers to improper fractions. Simplify expressions involving various rational number forms to a single numerical value. Recognize and avoid common errors when evaluating expressions with rational numbers. Ever wonder how engineers calculate the exact amount of material needed for a brid...

TermDefinitionExample VariableA letter or symbol that represents an unknown numerical value that can change.In the expression `3x + 5`, 'x' is the variable. Algebraic ExpressionA mathematical phrase that contains numbers, variables, and at least one operation symbol, but no equals sign.`2.5y - 1/2` EvaluateTo find the numerical value of an expression by substituting given values for the variables and performing the operations according to the order of operations.To evaluate `x + 3` when `x = 4` means `4 + 3 = 7`. Rational NumberAny number that can be expressed as a fraction `p/q` where `p` and `q` are integers and `q` is not zero. This includes integers, fractions, terminating decimals, and repeating decimals.`0.75` (which is `3/4`), `-2` (which is `-2/1`), `1/3`, `2 1/2`. Decim...

Order of Operations (PEMDAS/BODMAS) `P`arentheses (or `B`rackets), `E`xponents (or `O`rders), `M`ultiplication and `D`ivision (from left to right), `A`ddition and `S`ubtraction (from left to right). This rule dictates the precise sequence in which operations must be performed to correctly evaluate any mathematical expression, ensuring a single correct answer. Converting Mixed Numbers to Improper Fractions `a \frac{b}{c} = \frac{(a \times c) + b}{c}` Before performing multiplication or division with mixed numbers, and often for addition/subtraction, it is generally easiest and most accurate to convert them into improper fractions. Substituting Values Replace each variable in the expression with its given numerical value. Use parentheses around substituted values, especi...