Evaluate variable expressions involving rational numbers

Learning Objectives Substitute rational numbers (fractions, decimals, integers) for variables in algebraic expressions. Correctly apply the order of operations (PEMDAS/BEDMAS) to simplify expressions with rational numbers. Accurately perform addition, subtraction, multiplication, and division with positive and negative rational numbers within an expression. Evaluate polynomial expressions (up to degree 2) for given rational values. Manage negative signs and fractional coefficients correctly during substitution and simplification. Convert between fractions and decimals strategically to simplify the evaluation process. Ever tried to split a restaurant bill where some people had discounts and others added a custom tip? 🧾 You're already evaluating expressions with rational...

TermDefinitionExample Variable ExpressionA mathematical phrase that contains a combination of variables, numbers, and at least one operation. It does not have an equals sign.5x - 3/4y 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, terminating decimals, and repeating decimals.-7, 2/5, 0.65, -4.333... EvaluateTo find the single numerical value of an expression after substituting given numbers for all variables.To evaluate 2a + 1 for a = 3.5, you calculate 2(3.5) + 1 = 7 + 1 = 8. SubstitutionThe action of replacing a variable in an expression with its assigned numerical value. It's best practice to use parentheses during substitution.In the expression 10 - 4k, substituting k = -1/2 looks like this:...

The Substitution Principle If a = b, then a can be replaced by b in any mathematical expression. This is the core idea of evaluation. To avoid sign errors, always enclose the value you are substituting in parentheses, especially if it's negative or a fraction. For example, to evaluate x² for x = -5, write it as (-5)². Order of Operations (PEMDAS) 1. P: Parentheses/Brackets 2. E: Exponents 3. MD: Multiplication and Division (from left to right) 4. AS: Addition and Subtraction (from left to right) This strict hierarchy must be followed after substitution to simplify the expression correctly. The fraction bar also acts as a grouping symbol, meaning you must simplify the entire numerator and the entire denominator before dividing. Rules for Operations with Rational Numb...