How to Add, Subtract, Multiply & Divide Fractions (With Examples)

The Quick Rules

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Adding Fractions Step by Step

Same Denominator (Easy Case)

When denominators match, just add the numerators:

3/8 + 2/8 = 5/8

That's it. The denominator stays the same.

Different Denominators

This is where most people get stuck. You need a common denominator first.

Example: 1/3 + 1/4

Step 1: Find the Least Common Denominator (LCD)

• Multiples of 3: 3, 6, 9, 12, 15...
• Multiples of 4: 4, 8, 12, 16...
• LCD = 12

Step 2: Convert each fraction

• 1/3 = 4/12 (multiply top and bottom by 4)
• 1/4 = 3/12 (multiply top and bottom by 3)

Step 3: Add the numerators

• 4/12 + 3/12 = 7/12

Step 4: Simplify if possible

• 7/12 is already simplified (GCD of 7 and 12 is 1)

Shortcut: The Cross-Multiply Method

For adding two fractions a/b + c/d, use this formula:

(a × d + b × c) / (b × d)

Example: 2/5 + 3/7

• Numerator: (2 × 7) + (5 × 3) = 14 + 15 = 29
• Denominator: 5 × 7 = 35
• Result: 29/35

This always works, though the result may need simplifying.

Subtracting Fractions

Same process as addition, but subtract instead:

Example: 5/6 − 1/4

1. LCD of 6 and 4 = 12
2. 5/6 = 10/12, and 1/4 = 3/12
3. 10/12 − 3/12 = 7/12

Multiplying Fractions

Multiplication is the easiest fraction operation — no common denominator needed.

Just multiply straight across:

• Numerator × Numerator
• Denominator × Denominator

Example: 2/3 × 4/5

• 2 × 4 = 8
• 3 × 5 = 15
• Result: 8/15

Pro tip: Cross-cancel before multiplying to keep numbers small.

Example: 3/8 × 4/9

• Cancel 3 and 9 (divide both by 3): 1/8 × 4/3
• Cancel 8 and 4 (divide both by 4): 1/2 × 1/3
• Result: 1/6

Dividing Fractions

Keep, Change, Flip (KCF):

1. Keep the first fraction
2. Change ÷ to ×
3. Flip the second fraction (reciprocal)

Example: 3/4 ÷ 2/5

1. Keep: 3/4
2. Change: ×
3. Flip 2/5 → 5/2
4. Multiply: 3/4 × 5/2 = 15/8 = 1 7/8

Mixed Numbers

A mixed number combines a whole number and a fraction, like 2 3/4.

Converting Mixed Numbers to Improper Fractions

Formula: (whole × denominator + numerator) / denominator

Example: 2 3/4

• (2 × 4 + 3) / 4 = 11/4

Adding Mixed Numbers

Example: 1 1/3 + 2 1/4

1. Convert: 1 1/3 = 4/3, and 2 1/4 = 9/4
2. Find LCD: 12
3. Convert: 16/12 + 27/12 = 43/12
4. Convert back: 43 ÷ 12 = 3 remainder 7 → 3 7/12

How to Simplify Fractions

Find the Greatest Common Divisor (GCD) of the numerator and denominator, then divide both by it.

Example: 24/36

• Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
• Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
• GCD = 12
• 24/36 = (24 ÷ 12) / (36 ÷ 12) = 2/3

Converting Fractions

Fraction to Decimal

Divide the numerator by the denominator:

• 3/4 = 3 ÷ 4 = 0.75
• 1/3 = 1 ÷ 3 = 0.333...

Fraction to Percentage

Divide, then multiply by 100:

• 3/4 = 0.75 × 100 = 75%
• 2/5 = 0.4 × 100 = 40%

Common Fraction-Decimal-Percent Equivalents

Key Takeaways

• Addition/subtraction require a common denominator; multiplication/division do not
• For multiplication, multiply straight across and simplify
• For division, flip the second fraction and multiply
• Always simplify your answer by finding the GCD
• Convert mixed numbers to improper fractions before calculating