What is 2/13 plus 1/3? (Answer: 19/39)

Exact Answer

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Problem: What is 2/13 plus 1/3?
Formula / Expression: 2/13 + 1/3
Final Answer: 19/39
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 13 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 3 = 39.
Working: LCD(13, 3) = 39

Step 2: Convert to Equivalent Fractions with Common Denominator 39
Multiply the numerator and denominator of 2/13 by 3, and multiply the numerator and denominator of 1/3 by 13 so both fractions share the common base 39.
Working: 2 × 3/13 × 3 = 6/39 and 1 × 13/3 × 13 = 13/39

Step 3: Add the Numerators
Now add the numerators (6 + 13 = 19) and keep the common denominator 39 unchanged.
Working: 6 + 13/39 = 19/39

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 19 and 39 is 1, confirming that 19/39 cannot be reduced further—it is already in its simplest irreducible form.
Working: 19/39

Step 5: Decimal & Percentage Representation
Dividing the numerator 19 by denominator 39 produces a repeating decimal (approximately 0.487179, or 48.7179%).
Working: 19 ÷ 39 = 0.487179 (48.7179%)

Key Values:
- Simplified Fraction: 19/39
- Mixed Number Form: 19/39
- Decimal Value: 0.487179
- Percentage: 48.7179%

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Solved with FractionsCalc:
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2/13 + 1/3 = 19/39

Simplified Fraction

19/39

Mixed Number

Proper (19/39)

Decimal Value

0.487179

Percentage

48.7179%

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Step-by-Step Solution: 2/13 + 1/3

Step 1

Find the Least Common Denominator (LCD)

The denominators 13 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 3 = 39.

LCD(13, 3) = 39

Step 2

Convert to Equivalent Fractions with Common Denominator 39

Multiply the numerator and denominator of 2/13 by 3, and multiply the numerator and denominator of 1/3 by 13 so both fractions share the common base 39.

2 × 3/13 × 3 = 6/39 and 1 × 13/3 × 13 = 13/39

Step 3

Add the Numerators

Now add the numerators (6 + 13 = 19) and keep the common denominator 39 unchanged.

6 + 13/39 = 19/39

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 19 and 39 is 1, confirming that 19/39 cannot be reduced further—it is already in its simplest irreducible form.

19/39

Step 5

Decimal & Percentage Representation

Dividing the numerator 19 by denominator 39 produces a repeating decimal (approximately 0.487179, or 48.7179%).

19 ÷ 39 = 0.487179 (48.7179%)

Visual Representation

The diagram below illustrates 2/13 plus 1/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`19/39`
Mixed Number Form	`19/39`
Decimal Form	`0.487179`
Percentage	`48.7179%`

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Frequently Asked Questions

What is 2/13 plus 1/3 as a fraction?

2/13 + 1/3 in simplest fraction form is 19/39.

What is 2/13 plus 1/3 as a decimal?

2/13 + 1/3 converted to a decimal is 0.487179.

What is 2/13 plus 1/3 as a percentage?

2/13 + 1/3 expressed as a percentage is 48.7179%.

Does 2/13 plus 1/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.487179...) because the denominator contains prime factors other than 2 and 5.