What is 1/12 plus 3/13? (Answer: 49/156)

Exact Answer

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Problem: What is 1/12 plus 3/13?
Formula / Expression: 1/12 + 3/13
Final Answer: 49/156
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 12 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 12 × 13 = 156.
Working: LCD(12, 13) = 156

Step 2: Convert to Equivalent Fractions with Common Denominator 156
Multiply the numerator and denominator of 1/12 by 13, and multiply the numerator and denominator of 3/13 by 12 so both fractions share the common base 156.
Working: 1 × 13/12 × 13 = 13/156 and 3 × 12/13 × 12 = 36/156

Step 3: Add the Numerators
Now add the numerators (13 + 36 = 49) and keep the common denominator 156 unchanged.
Working: 13 + 36/156 = 49/156

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 49 and 156 is 1, confirming that 49/156 cannot be reduced further—it is already in its simplest irreducible form.
Working: 49/156

Step 5: Decimal & Percentage Representation
Dividing the numerator 49 by denominator 156 produces a repeating decimal (approximately 0.314103, or 31.4103%).
Working: 49 ÷ 156 = 0.314103 (31.4103%)

Key Values:
- Simplified Fraction: 49/156
- Mixed Number Form: 49/156
- Decimal Value: 0.314103
- Percentage: 31.4103%

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Solved with FractionsCalc:
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1/12 + 3/13 = 49/156

Simplified Fraction

49/156

Mixed Number

Proper (49/156)

Decimal Value

0.314103

Percentage

31.4103%

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Step-by-Step Solution: 1/12 + 3/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 12 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 12 × 13 = 156.

LCD(12, 13) = 156

Step 2

Convert to Equivalent Fractions with Common Denominator 156

Multiply the numerator and denominator of 1/12 by 13, and multiply the numerator and denominator of 3/13 by 12 so both fractions share the common base 156.

1 × 13/12 × 13 = 13/156 and 3 × 12/13 × 12 = 36/156

Step 3

Add the Numerators

Now add the numerators (13 + 36 = 49) and keep the common denominator 156 unchanged.

13 + 36/156 = 49/156

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 49 and 156 is 1, confirming that 49/156 cannot be reduced further—it is already in its simplest irreducible form.

49/156

Step 5

Decimal & Percentage Representation

Dividing the numerator 49 by denominator 156 produces a repeating decimal (approximately 0.314103, or 31.4103%).

49 ÷ 156 = 0.314103 (31.4103%)

Visual Representation

The diagram below illustrates 1/12 plus 3/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`49/156`
Mixed Number Form	`49/156`
Decimal Form	`0.314103`
Percentage	`31.4103%`

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Frequently Asked Questions

What is 1/12 plus 3/13 as a fraction?

1/12 + 3/13 in simplest fraction form is 49/156.

What is 1/12 plus 3/13 as a decimal?

1/12 + 3/13 converted to a decimal is 0.314103.

What is 1/12 plus 3/13 as a percentage?

1/12 + 3/13 expressed as a percentage is 31.4103%.

Does 1/12 plus 3/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.314103...) because the denominator contains prime factors other than 2 and 5.