Order of Operations (BEDMAS)

The rule: BEDMAS, top to bottom

BEDMAS is a word that helps you remember the order. (You may have seen PEMDAS instead, it is the exact same rule, just with "Parentheses" in place of "Brackets.") You work through the levels from the top down:

• B, Brackets first. Do anything inside ( ) before anything else.
• E, Exponents next. These are the small powers, like 3² meaning 3 × 3.
• D and M, Divide and Multiply, working left to right as they appear. Neither one outranks the other.
• A and S, Add and Subtract, also left to right. Again, they are equal partners.

Worked example #1: 6 + 4 × 3

Back to our opening puzzle. There are no brackets and no exponents, so we look for multiply or divide first.

• Multiply first: 4 × 3 = 12.
• Then add: 6 + 12 = 18.

  6 + 4 × 3
= 6 + 12      (do 4 × 3 first)
= 18

The most common mistake: left to right vs. the right order

The number one slip is doing everything straight across, left to right, as if the operations were all equal. They are not. Watch the same problem solved both ways:

  10 − 2 × 4
= 8 × 4    ✗
= 32

  10 − 2 × 4
= 10 − 8   ✓
= 2

Same numbers, very different answers (32 vs. 2). Whenever you see a mix of operations, pause and scan for brackets and exponents first, then multiply/divide, then add/subtract.

Worked example #2: 20 − (3 + 2)² ÷ 5

This one uses every level of BEDMAS, so it is a great full run-through. Take it one layer at a time.

• Brackets: 3 + 2 = 5.
• Exponent: 5² = 5 × 5 = 25.
• Divide: 25 ÷ 5 = 5.
• Subtract: 20 − 5 = 15.

  20 − (3 + 2)² ÷ 5
= 20 − 5²    ÷ 5    (brackets: 3 + 2 = 5)
= 20 − 25    ÷ 5    (exponent: 5² = 25)
= 20 − 5            (divide: 25 ÷ 5 = 5)
= 15               (subtract)

Worked example #3: −8 + 6 ÷ (−2) × 3

Now with negative numbers. The key here is that divide and multiply are a pair, so we go strictly left to right through them, do not save the multiply for last.

• Brackets: nothing to simplify inside (−2) is already a single number.
• Divide (leftmost): 6 ÷ (−2) = −3. A positive divided by a negative is negative.
• Multiply (next): −3 × 3 = −9.
• Add: −8 + (−9) = −17.

  −8 + 6 ÷ (−2) × 3
= −8 + (−3)   × 3    (divide first, left to right)
= −8 + (−9)          (then multiply)
= −17               (add)

Worked example #4: ½ + ¼ × 8

BEDMAS works exactly the same with fractions and decimals, the operations just sit inside fancier numbers. Multiply or divide still comes before add or subtract.

• Multiply first: ¼ × 8 = 8⁄4 = 2.
• Then add: ½ + 2 = 2½, which is 2.5 as a decimal.

  1/2 + 1/4 × 8
= 1/2 + 2        (do 1/4 × 8 = 2 first)
= 2 1/2  (= 2.5)

Tips that make BEDMAS feel easy

• Scan before you solve. Look at the whole expression first and find the brackets and exponents. Knock those out, then deal with multiply/divide, then add/subtract.
• Rewrite the whole line each step. Copy down the parts you have not touched yet, like in the examples above. It stops you from losing a number or a minus sign.
• Remember the pairs go left to right. "DM" and "AS" are not a ranking. When you see × and ÷ together (or + and − together), just read left to right.
• Treat a negative sign as part of its number. −9 travels as one value, so −8 + (−9) is just −17.

Your turn: practice problems

Work each one top-down with BEDMAS. Write out every step, then check yourself. No peeking until you have tried.

1. 12 − 2 × 5
2. (7 − 3)² + 6 ÷ 3
3. −5 + 18 ÷ (−3)
4. 2 + 0.5 × 6 − 1