LEMMA

Foundations

Order of operations

ALEKS · foundation repairTEAS math

Work from the inside out, and read a fraction bar as invisible parentheses.

What this covers

()→exponents→×÷→+−
  • Clear grouping symbols starting from the innermost pair.
  • Apply exponents before any multiplication.
  • Multiply and divide left to right — neither outranks the other.
  • Add and subtract left to right, last.

Worked example

Worked example

Evaluate 12 - 2(5 - 3)^2 ÷ 4.

  1. 12−2(2)2÷4Innermost parentheses first: 5 - 3 = 2.
  2. 12−2⋅4÷4Exponent before multiplying: 2^2 = 4.
  3. 12−8÷4Multiplication is further left than the division.
  4. 12−2=10Divide, then subtract.
Another worked example

Evaluate 24 ÷ 6 × 2 + 1.

  1. 24÷6×2+1=4×2+1Division and multiplication have equal priority; the leftmost is division.
  2. 4×2+1=8+1=9Finish multiplication before addition.

A common mistake

A mistake Lemma catches

From 24÷6×2+1

24÷12+14×2+1

“Multiplication does not outrank division: they share one rank and go left to right. 24 ÷ 6 comes first: 24 ÷ 6 = 4, then 4 × 2 = 8. Doing 6 × 2 = 12 first gives 24 ÷ 12 = 2 instead.”

Try one

Sample problem

Evaluate using the order of operations.

4+2⋅3

Practice order of ops free

No account, no email. Every line you type is checked by the same computer algebra system as the worked example above.

Where this fits

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