Evaluate variable expressions involving rational numbers

Learning Objectives Define key terms such as variable, expression, and rational number. Correctly substitute given rational number values for variables in an expression. Apply the order of operations to simplify expressions after substitution. Accurately perform arithmetic operations with fractions and decimals within expressions. Evaluate variable expressions containing one or more variables and rational numbers. Identify and correct common errors made when evaluating expressions with rational numbers. Ever wonder how mathematicians solve puzzles with missing numbers? 🕵️‍♀️ Imagine you have a secret code where letters stand for numbers! In this lesson, you'll learn how to find the exact value of mathematical expressions when you know what the 'mystery letters&#03...

TermDefinitionExample VariableA letter or symbol that represents an unknown or changing numerical value in a mathematical expression.In the expression 'x + 5', 'x' is the variable. ExpressionA mathematical phrase that can contain numbers, variables, and operation symbols (like +, -, ×, ÷) but does not have an equals sign.Examples include '2y - 7', 'a + b', or '3/4 × z'. Rational NumberAny number that can be written as a fraction $\frac{a}{b}$, where 'a' and 'b' are integers and 'b' is not zero. This includes whole numbers, integers, fractions, and terminating or repeating decimals.Examples include $\frac{1}{2}$, $0.75$, $-3$, and $5$ (which can be written as $\frac{5}{1}$). EvaluateTo find the numerical value...

Substitution Principle If a variable, such as $x$, is given a specific value, say $a$, then you must replace every instance of $x$ in the expression with $a$. This is the first step in evaluating any variable expression. Always replace the letters with their given numbers carefully. Order of Operations (PEMDAS) Perform operations in the following order: 1. **P**arentheses (or other grouping symbols) 2. **E**xponents (powers and roots) 3. **M**ultiplication and **D**ivision (from left to right) 4. **A**ddition and **S**ubtraction (from left to right) After substituting, follow this order strictly to ensure you get the correct final answer. Multiplication and division have equal priority, as do addition and subtraction; always work from left to right for these pairs. I...