What is 5/13 plus 2/3? (Answer: 41/39)

Exact Answer

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Problem: What is 5/13 plus 2/3?
Formula / Expression: 5/13 + 2/3
Final Answer: 1 2/39 (41/39)
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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 5/13 by 3, and multiply the numerator and denominator of 2/3 by 13 so both fractions share the common base 39.
Working: 5 × 3/13 × 3 = 15/39 and 2 × 13/3 × 13 = 26/39

Step 3: Add the Numerators
Now add the numerators (15 + 26 = 41) and keep the common denominator 39 unchanged.
Working: 15 + 26/39 = 41/39

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 41 and 39 is 1, confirming that 41/39 cannot be reduced further—it is already in its simplest irreducible form.
Working: 41/39

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (41) is greater than the denominator (39), divide 41 by 39: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/39.
Working: 41/39 = 1 2/39

Step 6: Decimal & Percentage Representation
Dividing the numerator 41 by denominator 39 produces a repeating decimal (approximately 1.051282, or 105.1282%).
Working: 41 ÷ 39 = 1.051282 (105.1282%)

Key Values:
- Simplified Fraction: 41/39
- Mixed Number Form: 1 2/39
- Decimal Value: 1.051282
- Percentage: 105.1282%

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Solved with FractionsCalc:
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5/13 + 2/3 = 41/39

Simplified Fraction

41/39

Mixed Number

1 2/39

Decimal Value

1.051282

Percentage

105.1282%

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Step-by-Step Solution: 5/13 + 2/3

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 5/13 by 3, and multiply the numerator and denominator of 2/3 by 13 so both fractions share the common base 39.

5 × 3/13 × 3 = 15/39 and 2 × 13/3 × 13 = 26/39

Step 3

Add the Numerators

Now add the numerators (15 + 26 = 41) and keep the common denominator 39 unchanged.

15 + 26/39 = 41/39

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 41 and 39 is 1, confirming that 41/39 cannot be reduced further—it is already in its simplest irreducible form.

41/39

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (41) is greater than the denominator (39), divide 41 by 39: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/39.

41/39 = 12/39

Step 6

Decimal & Percentage Representation

Dividing the numerator 41 by denominator 39 produces a repeating decimal (approximately 1.051282, or 105.1282%).

41 ÷ 39 = 1.051282 (105.1282%)

Visual Representation

The diagram below illustrates 5/13 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`41/39`
Mixed Number Form	`1 2/39`
Decimal Form	`1.051282`
Percentage	`105.1282%`

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Frequently Asked Questions

What is 5/13 plus 2/3 as a fraction?

5/13 + 2/3 in simplest fraction form is 41/39 (or 1 2/39 as a mixed number).

What is 5/13 plus 2/3 as a decimal?

5/13 + 2/3 converted to a decimal is 1.051282.

What is 5/13 plus 2/3 as a percentage?

5/13 + 2/3 expressed as a percentage is 105.1282%.

How do you write 5/13 plus 2/3 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 41/39 can be written as the mixed number 1 2/39.

Does 5/13 plus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.051282...) because the denominator contains prime factors other than 2 and 5.