What is 2/13 plus 5/6? (Answer: 77/78)

Exact Answer

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Problem: What is 2/13 plus 5/6?
Formula / Expression: 2/13 + 5/6
Final Answer: 77/78
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 13 and 6 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 6 = 78.
Working: LCD(13, 6) = 78

Step 2: Convert to Equivalent Fractions with Common Denominator 78
Multiply the numerator and denominator of 2/13 by 6, and multiply the numerator and denominator of 5/6 by 13 so both fractions share the common base 78.
Working: 2 × 6/13 × 6 = 12/78 and 5 × 13/6 × 13 = 65/78

Step 3: Add the Numerators
Now add the numerators (12 + 65 = 77) and keep the common denominator 78 unchanged.
Working: 12 + 65/78 = 77/78

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 77 and 78 is 1, confirming that 77/78 cannot be reduced further—it is already in its simplest irreducible form.
Working: 77/78

Step 5: Decimal & Percentage Representation
Dividing the numerator 77 by denominator 78 produces a repeating decimal (approximately 0.987179, or 98.7179%).
Working: 77 ÷ 78 = 0.987179 (98.7179%)

Key Values:
- Simplified Fraction: 77/78
- Mixed Number Form: 77/78
- Decimal Value: 0.987179
- Percentage: 98.7179%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-13-plus-5-6/
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2/13 + 5/6 = 77/78

Simplified Fraction

77/78

Mixed Number

Proper (77/78)

Decimal Value

0.987179

Percentage

98.7179%

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

Step 1

Find the Least Common Denominator (LCD)

The denominators 13 and 6 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 6 = 78.

LCD(13, 6) = 78

Step 2

Convert to Equivalent Fractions with Common Denominator 78

Multiply the numerator and denominator of 2/13 by 6, and multiply the numerator and denominator of 5/6 by 13 so both fractions share the common base 78.

2 × 6/13 × 6 = 12/78 and 5 × 13/6 × 13 = 65/78

Step 3

Add the Numerators

Now add the numerators (12 + 65 = 77) and keep the common denominator 78 unchanged.

12 + 65/78 = 77/78

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 77 and 78 is 1, confirming that 77/78 cannot be reduced further—it is already in its simplest irreducible form.

77/78

Step 5

Decimal & Percentage Representation

Dividing the numerator 77 by denominator 78 produces a repeating decimal (approximately 0.987179, or 98.7179%).

77 ÷ 78 = 0.987179 (98.7179%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`77/78`
Mixed Number Form	`77/78`
Decimal Form	`0.987179`
Percentage	`98.7179%`

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Frequently Asked Questions

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

2/13 + 5/6 in simplest fraction form is 77/78.

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

2/13 + 5/6 converted to a decimal is 0.987179.

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

2/13 + 5/6 expressed as a percentage is 98.7179%.

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

It results in a repeating decimal (approximately 0.987179...) because the denominator contains prime factors other than 2 and 5.