Order of Operations with Variables

Pre-Algebra · Axiom Academy

LESSON Order of Operations with Variables PEMDAS doesn't change when letters appear — substitute the values, then work inside-out in the same fixed order. The order of operations tells us which calculation to do first when we evaluate an expression. Whether the expression holds numbers or variables, the rule never changes — it just fixes the order so everyone reaches the same answer. 2. Variables Follow the Same Rules When an expression contains variables like x , y , or a , we still obey PEMDAS. The letters are just placeholders for numbers, so the order of attack is set even before we know their values. Same expression, no values yet — but the order is already fixed Even without knowing x and y , we can name the order we will follow: To evaluate an expression with variables, replace each letter with its given value and then follow PEMDAS to simplify, innermost piece first. Evaluate 3x^2 + 2y when x = 4 and y = 5 4. Watch Out for Negative Numbers When you substitute a negative number, you must wrap it in parentheses. Skipping them is the single most common way to lose a sign and wreck the answer. Evaluate x^2 - 3y when x = -2 and y = -4 Read as . The lost parentheses flipped x^2 from 4 to -4 . Exponents: (-2)^2 = 4 . Multiply: 3(-4) = -12 . Subtract: 4 - (-12) = 4 + 12 = 16 . Now put every rule together on an expression that has parentheses, an exponent, and negative values — the full PEMDAS run, inside-out. Evaluate 2(x - 3)^2 + 4y when x = -1 and y = -2

This is the written version of the interactive lesson above. See the full Pre-Algebra course.