What is 1/12 plus 2/9? (Answer: 11/36)

Exact Answer

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Problem: What is 1/12 plus 2/9?
Formula / Expression: 1/12 + 2/9
Final Answer: 11/36
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 12 and 9 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 36 (which is smaller than their product 12 × 9 = 108, keeping the calculation simpler).
Working: LCD(12, 9) = 36

Step 2: Convert to Equivalent Fractions with Common Denominator 36
Multiply the numerator and denominator of 1/12 by 3, and multiply the numerator and denominator of 2/9 by 4 so both fractions share the common base 36.
Working: 1 × 3/12 × 3 = 3/36 and 2 × 4/9 × 4 = 8/36

Step 3: Add the Numerators
Now add the numerators (3 + 8 = 11) and keep the common denominator 36 unchanged.
Working: 3 + 8/36 = 11/36

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 11 and 36 is 1, confirming that 11/36 cannot be reduced further—it is already in its simplest irreducible form.
Working: 11/36

Step 5: Decimal & Percentage Representation
Dividing the numerator 11 by denominator 36 produces a repeating decimal (approximately 0.305556, or 30.5556%).
Working: 11 ÷ 36 = 0.305556 (30.5556%)

Key Values:
- Simplified Fraction: 11/36
- Mixed Number Form: 11/36
- Decimal Value: 0.305556
- Percentage: 30.5556%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-12-plus-2-9/
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1/12 + 2/9 = 11/36

Simplified Fraction

11/36

Mixed Number

Proper (11/36)

Decimal Value

0.305556

Percentage

30.5556%

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Step-by-Step Solution: 1/12 + 2/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 12 and 9 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 36 (which is smaller than their product 12 × 9 = 108, keeping the calculation simpler).

LCD(12, 9) = 36

Step 2

Convert to Equivalent Fractions with Common Denominator 36

Multiply the numerator and denominator of 1/12 by 3, and multiply the numerator and denominator of 2/9 by 4 so both fractions share the common base 36.

1 × 3/12 × 3 = 3/36 and 2 × 4/9 × 4 = 8/36

Step 3

Add the Numerators

Now add the numerators (3 + 8 = 11) and keep the common denominator 36 unchanged.

3 + 8/36 = 11/36

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 11 and 36 is 1, confirming that 11/36 cannot be reduced further—it is already in its simplest irreducible form.

11/36

Step 5

Decimal & Percentage Representation

Dividing the numerator 11 by denominator 36 produces a repeating decimal (approximately 0.305556, or 30.5556%).

11 ÷ 36 = 0.305556 (30.5556%)

Visual Representation

The diagram below illustrates 1/12 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`11/36`
Mixed Number Form	`11/36`
Decimal Form	`0.305556`
Percentage	`30.5556%`

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Frequently Asked Questions

What is 1/12 plus 2/9 as a fraction?

1/12 + 2/9 in simplest fraction form is 11/36.

What is 1/12 plus 2/9 as a decimal?

1/12 + 2/9 converted to a decimal is 0.305556.

What is 1/12 plus 2/9 as a percentage?

1/12 + 2/9 expressed as a percentage is 30.5556%.

Does 1/12 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.305556...) because the denominator contains prime factors other than 2 and 5.