What is 2/13 plus 5/8? (Answer: 81/104)

Exact Answer

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Problem: What is 2/13 plus 5/8?
Formula / Expression: 2/13 + 5/8
Final Answer: 81/104
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 13 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 8 = 104.
Working: LCD(13, 8) = 104

Step 2: Convert to Equivalent Fractions with Common Denominator 104
Multiply the numerator and denominator of 2/13 by 8, and multiply the numerator and denominator of 5/8 by 13 so both fractions share the common base 104.
Working: 2 × 8/13 × 8 = 16/104 and 5 × 13/8 × 13 = 65/104

Step 3: Add the Numerators
Now add the numerators (16 + 65 = 81) and keep the common denominator 104 unchanged.
Working: 16 + 65/104 = 81/104

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 81 and 104 is 1, confirming that 81/104 cannot be reduced further—it is already in its simplest irreducible form.
Working: 81/104

Step 5: Decimal & Percentage Representation
Dividing the numerator 81 by denominator 104 produces a repeating decimal (approximately 0.778846, or 77.8846%).
Working: 81 ÷ 104 = 0.778846 (77.8846%)

Key Values:
- Simplified Fraction: 81/104
- Mixed Number Form: 81/104
- Decimal Value: 0.778846
- Percentage: 77.8846%

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Solved with FractionsCalc:
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2/13 + 5/8 = 81/104

Simplified Fraction

81/104

Mixed Number

Proper (81/104)

Decimal Value

0.778846

Percentage

77.8846%

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Step-by-Step Solution: 2/13 + 5/8

Step 1

Find the Least Common Denominator (LCD)

The denominators 13 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 8 = 104.

LCD(13, 8) = 104

Step 2

Convert to Equivalent Fractions with Common Denominator 104

Multiply the numerator and denominator of 2/13 by 8, and multiply the numerator and denominator of 5/8 by 13 so both fractions share the common base 104.

2 × 8/13 × 8 = 16/104 and 5 × 13/8 × 13 = 65/104

Step 3

Add the Numerators

Now add the numerators (16 + 65 = 81) and keep the common denominator 104 unchanged.

16 + 65/104 = 81/104

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 81 and 104 is 1, confirming that 81/104 cannot be reduced further—it is already in its simplest irreducible form.

81/104

Step 5

Decimal & Percentage Representation

Dividing the numerator 81 by denominator 104 produces a repeating decimal (approximately 0.778846, or 77.8846%).

81 ÷ 104 = 0.778846 (77.8846%)

Visual Representation

The diagram below illustrates 2/13 plus 5/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`81/104`
Mixed Number Form	`81/104`
Decimal Form	`0.778846`
Percentage	`77.8846%`

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Frequently Asked Questions

What is 2/13 plus 5/8 as a fraction?

2/13 + 5/8 in simplest fraction form is 81/104.

What is 2/13 plus 5/8 as a decimal?

2/13 + 5/8 converted to a decimal is 0.778846.

What is 2/13 plus 5/8 as a percentage?

2/13 + 5/8 expressed as a percentage is 77.8846%.

Does 2/13 plus 5/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.778846...) because the denominator contains prime factors other than 2 and 5.