What is 2/5 plus 6/13? (Answer: 56/65)

Exact Answer

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Problem: What is 2/5 plus 6/13?
Formula / Expression: 2/5 + 6/13
Final Answer: 56/65
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 5 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 13 = 65.
Working: LCD(5, 13) = 65

Step 2: Convert to Equivalent Fractions with Common Denominator 65
Multiply the numerator and denominator of 2/5 by 13, and multiply the numerator and denominator of 6/13 by 5 so both fractions share the common base 65.
Working: 2 × 13/5 × 13 = 26/65 and 6 × 5/13 × 5 = 30/65

Step 3: Add the Numerators
Now add the numerators (26 + 30 = 56) and keep the common denominator 65 unchanged.
Working: 26 + 30/65 = 56/65

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 56 and 65 is 1, confirming that 56/65 cannot be reduced further—it is already in its simplest irreducible form.
Working: 56/65

Step 5: Decimal & Percentage Representation
Dividing the numerator 56 by denominator 65 produces a repeating decimal (approximately 0.861538, or 86.1538%).
Working: 56 ÷ 65 = 0.861538 (86.1538%)

Key Values:
- Simplified Fraction: 56/65
- Mixed Number Form: 56/65
- Decimal Value: 0.861538
- Percentage: 86.1538%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-5-plus-6-13/
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2/5 + 6/13 = 56/65

Simplified Fraction

56/65

Mixed Number

Proper (56/65)

Decimal Value

0.861538

Percentage

86.1538%

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Step-by-Step Solution: 2/5 + 6/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 5 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 13 = 65.

LCD(5, 13) = 65

Step 2

Convert to Equivalent Fractions with Common Denominator 65

Multiply the numerator and denominator of 2/5 by 13, and multiply the numerator and denominator of 6/13 by 5 so both fractions share the common base 65.

2 × 13/5 × 13 = 26/65 and 6 × 5/13 × 5 = 30/65

Step 3

Add the Numerators

Now add the numerators (26 + 30 = 56) and keep the common denominator 65 unchanged.

26 + 30/65 = 56/65

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 56 and 65 is 1, confirming that 56/65 cannot be reduced further—it is already in its simplest irreducible form.

56/65

Step 5

Decimal & Percentage Representation

Dividing the numerator 56 by denominator 65 produces a repeating decimal (approximately 0.861538, or 86.1538%).

56 ÷ 65 = 0.861538 (86.1538%)

Visual Representation

The diagram below illustrates 2/5 plus 6/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`56/65`
Mixed Number Form	`56/65`
Decimal Form	`0.861538`
Percentage	`86.1538%`

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Frequently Asked Questions

What is 2/5 plus 6/13 as a fraction?

2/5 + 6/13 in simplest fraction form is 56/65.

What is 2/5 plus 6/13 as a decimal?

2/5 + 6/13 converted to a decimal is 0.861538.

What is 2/5 plus 6/13 as a percentage?

2/5 + 6/13 expressed as a percentage is 86.1538%.

Does 2/5 plus 6/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.861538...) because the denominator contains prime factors other than 2 and 5.