Lesson · M.1.2

Operations with rational numbers

The order of operations, applied by hand to integers, decimals, and fractions, so a multi-step calculation comes out the same way every time.

ObjectiveM.1.2Read2 minExam weightNumbers and Algebra ≈ 53% of Mathematics

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What you will be able to do

  • Apply PEMDAS correctly, including the left to right tiebreaker for multiplication or division and addition or subtraction.
  • Simplify expressions with fraction bars and mixed numbers before dividing.
  • Solve a multi-step expression by hand before entering it into the four-function calculator.

What the lesson concludes

  • Apply parentheses, then exponents and roots, then multiplication and division left to right, then addition and subtraction left to right.
  • Left to right means multiplication does not always beat division, and addition does not always beat subtraction. Whichever comes first in the expression goes first.
  • A fraction bar groups everything above and below it like a set of parentheses.
  • Convert mixed numbers to improper fractions before multiplying or dividing them.
  • The exam calculator will not sequence multi-step operations for you, so solve inside parentheses by hand first.