Math Resources Hub

Order of Operations

Geometry formulas stack operations together — 12bh\tfrac{1}{2}bh, s2s^2, a2+b2a^2 + b^2. Plug numbers in and you get a multi-step expression, and there's exactly one correct value — but only if you evaluate it in the agreed order. This card makes that order automatic so your formula work is never off by a hidden mis-step.

Skill

Order of Operations

  1. What & why

    Read 4+3×54 + 3 \times 5 left to right and you'd get 3535. Multiply first and you get 1919. Both can't be right — so mathematicians agreed on a fixed order, and it isn't arbitrary: multiplication is repeated addition, so it "binds tighter" than the addition around it.

    The order is PEMDAS:

    • Parentheses
    • Exponents
    • Multiplication and Division — together, left to right
    • Addition and Subtraction — together, left to right

    The pairs matter: M and D are the same rank (do them in the order they appear), and so are A and S. They are not four separate steps but two ranked tiers riding on grouping and powers.

  2. Watch how it works

    Multiplication before addition. In 4+3×54 + 3 \times 5, the 3×53 \times 5 happens first:

    4+3×5=4+15=194 + 3 \times 5 = 4 + 15 = 19

    Parentheses override that. Wrap the addition and it goes first — same numbers, different answer:

    (4+3)×5=7×5=35(4 + 3) \times 5 = 7 \times 5 = 35

    Exponents come before multiply/add. In 2+322 + 3^2, square first:

    2+32=2+9=112 + 3^2 = 2 + 9 = 11

    Work one operation at a time and rewrite the whole expression after each step — that habit is what keeps long ones from going sideways.

  3. Reason through one together

    Here's the trap: an operation that comes later in reading order can still have to go first. Picture the steps before you choose.

    Make a prediction: Evaluate 20 − 12 ÷ 4.

  4. Practice until it’s automatic

    Fresh problems, one at a time. Build a streak — the goal is getting them right without stopping to think.

    Streak0/ 5Accuracy0%(0/0)

    6 × 9 + 11 = ?

  5. Prove it

    Harder, applied problems at the level you’ll meet on the Regents. Get them all right to earn this skill.

    Question 1 of 8

    Evaluate 4 + 3 × 5.

For teachers

Standard, common misconceptions, and suggested use will live here.