Evaluating Expressions: Step-by-Step Guide
Evaluating an expression means replacing each letter (variable) with a number you are given and then working out the answer. Use the order of operations (PEMDAS) to do the math in the right order.
Math Racer skill guide · Middle School · Grades 6-8
How to solve it, step by step
- Write down each variable and its value. List every letter in the expression and the number you are told to use for it.\[x = a,\; y = b,\; \dots\]
- Replace each variable using parentheses. Put each number in parentheses where its letter used to be. This helps you keep track of negative signs and exponents.\[f(x,y) \to f\bigl((a),(b)\bigr)\]
- Work it out using PEMDAS. Do the parentheses first, then exponents, then multiplication and division from left to right, then addition and subtraction from left to right.\[\text{P} \to \text{E} \to \text{MD} \to \text{AS}\]
- Write your answer and check it. State the final value. Check it by going through the steps again or doing it a different way.\[\text{value} = ?\]
Worked example
Evaluate 3x^2 - 2y + 5 when x = -2 and y = 4
Step 1: We are told x = -2 and y = 4.
Step 2: Replace the letters, using parentheses: 3(-2)^2 - 2(4) + 5.
Step 3: Exponents first: (-2)^2 = 4. Now we have 3(4) - 2(4) + 5.
Step 4: Multiply: 3 x 4 = 12 and 2 x 4 = 8. Now we have 12 - 8 + 5.
Step 5: Add and subtract from left to right: 12 - 8 = 4, then 4 + 5 = 9.
Check: Go through it again. 3(4) - 8 + 5 = 12 - 8 + 5 = 9. It matches.
Tips and common mistakes
- Always put the number in parentheses when you replace a letter, especially negative numbers. (-2)^2 = 4 but -2^2 = -4.
- Replace first, then work out the answer. Do not try to do both at once.
- When a number is written next to a letter, like 3x, it means multiply. If x = 4, then 3x = 3 x 4 = 12, not 34.
- If a letter shows up more than once, use the same number every time.
- Exponents come before multiplication. If x = 5, then 3x^2 = 3 x 25 = 75, not 15^2.
- If your answer seems strange, estimate it or try it again with easier numbers.