Order of Operations with Fractions

Same BEDMAS rules — now the numbers can be fractions too.

▶ Practice this concept

🧱 See It

BEDMAS still decides the order — brackets, then multiply/divide, then add/subtract. The only new twist is that some of the numbers are fractions, so every add/subtract step also needs the common-denominator trick, and every multiply/divide step uses the straight-across and flip-and-multiply rules from the last two pages.

✏️ Draw It

Number the operations first, exactly like always — before converting or calculating anything:

1/2 ② + 1/4 ① × 2/3

Multiply happens first (①), then add (②) — the fractions don't change the order at all.

🔢 Write It

1/2 + 1/4 × 2/3

Step 1 — multiply first (straight across, then simplify):

1/4 × 2/3 = 2/12 = 1/6

Step 2 — now add (find a fresh common denominator for these two: LCM(2, 6) = 6):

1/2 + 1/6 = 3/6 + 1/6 = 4/6 = 2/3

Figure out the ORDER first (BEDMAS). Only worry about a common denominator when you actually reach an add or subtract step.

💡 Worked Examples

Example 1: 2/3 − 1/2 × 1/3

  1. Order: multiply first, then subtract.
  2. Multiply: 1/2 × 1/3 = 1/6
  3. Subtract (common denominator of 3 and 6 is 6, so 2/3 = 4/6): 4/6 − 1/6 = 3/6
  4. Simplify: GCF(3, 6) = 3, so 3/6 = 1/2
  5. Answer: 1/2

Example 2: (1/2 + 1/4) × 2

  1. Order: brackets first, then multiply.
  2. Brackets (common denominator 4, so 1/2 = 2/4): 2/4 + 1/4 = 3/4
  3. Multiply: 3/4 × 2 = 6/4
  4. Simplify: GCF(6, 4) = 2, so 6/4 = 3/2
  5. Answer: 3/2

🧠 Quick Reference

BEDMAS decides the order, exactly like always. Multiply/divide steps need no common denominator. Add/subtract steps need a common denominator, found fresh each time it's needed. Always simplify the final answer.
👪 For Parents & Tutors

BC Curriculum (Level 3 / Grade 8, Number & Operations): "Perform operations with fractions (addition, subtraction, multiplication, division, order of operations)." This page completes that content line.

Watch for: the instinct to hunt for ONE common denominator for the whole expression up front, before even knowing which operation happens first. That's backwards and creates unnecessary work. Insist on numbering the operations first (the pictorial technique on this page), and only worry about a common denominator at the specific step that actually needs one — it may be a different denominator each time.

Comes up again: this completes the fraction-operations sequence for this level, and resurfaces directly in Level 4 (Grade 9) rational number operations, where negatives join fractions in the same expressions.