BODMAS With Fractions: Examples and Solutions

📅 2025-09-05 ⏱ 6 min read

BODMAS applies to fractions the same way it applies to whole numbers. Solve brackets first, then orders, division, multiplication, addition, and subtraction. See 5 worked examples.

How BODMAS Works With Fractions

BODMAS (Brackets, Orders, Division, Multiplication, Addition, Subtraction) applies to fractions the same way it applies to whole numbers. Solve brackets first, then orders, then division and multiplication from left to right, then addition and subtraction from left to right. The fraction bar itself acts as a bracket — solve the numerator and denominator separately before dividing. You can also verify your fraction solutions step-by-step using our BODMAS calculator.

💡 Key Rule

A fraction bar acts as a bracket. The expression (8 + 4) ÷ 3 is the same as writing ^{8 + 4}⁄₃. Solve the numerator and denominator first, then divide.

5 BODMAS With Fractions Examples

Example 1: Addition and Fraction

Solve: ½ + ¼ × 2

Step 1 — Multiplication: ¼ × 2 = ¼ × 2/1 = 2/4 = ½

Step 2 — Addition: ½ + ½ = 1

½ + ¼ × 2 = 1

Example 2: Brackets With Fractions

Solve: (⅓ + ⅔) × 6

Step 1 — Brackets: ⅓ + ⅔ = 3/3 = 1

Step 2 — Multiplication: 1 × 6 = 6

(⅓ + ⅔) × 6 = 6

Example 3: Division of Fractions

Solve: ¾ ÷ ½ + 1

Step 1 — Division (flip and multiply): ¾ ÷ ½ = ¾ × 2/1 = 6/4 = 3/2

Step 2 — Addition: 3/2 + 1 = 3/2 + 2/2 = 5/2 = 2.5

¾ ÷ ½ + 1 = 5/2 (2.5)

Example 4: Mixed Operations With Fractions

Solve: 2 × ½ + 3 × ¼

Step 1 — First Multiplication: 2 × ½ = 1

Step 2 — Second Multiplication: 3 × ¼ = ¾

Step 3 — Addition: 1 + ¾ = 7/4 = 1.75

2 × ½ + 3 × ¼ = 7/4 (1.75)

Example 5: Fraction Bar as Bracket

Solve: (10 + 2) ÷ (4 − 1)

Step 1 — Numerator Bracket: (10 + 2) = 12

Step 2 — Denominator Bracket: (4 − 1) = 3

Step 3 — Division: 12 ÷ 3 = 4

(10 + 2) ÷ (4 − 1) = 4

3 Common Mistakes With Fractions in BODMAS

Forgetting the fraction bar acts as a bracket: Always solve the numerator and denominator separately before dividing.
Adding fractions before multiplying: BODMAS requires multiplication and division before addition and subtraction — this applies to fractions too.
Not finding a common denominator: Convert fractions to the same denominator before adding or subtracting.