What is 2/13 plus 6/7? (Answer: 92/91)

Exact Answer

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Problem: What is 2/13 plus 6/7?
Formula / Expression: 2/13 + 6/7
Final Answer: 1 1/91 (92/91)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 13 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 7 = 91.
Working: LCD(13, 7) = 91

Step 2: Convert to Equivalent Fractions with Common Denominator 91
Multiply the numerator and denominator of 2/13 by 7, and multiply the numerator and denominator of 6/7 by 13 so both fractions share the common base 91.
Working: 2 × 7/13 × 7 = 14/91 and 6 × 13/7 × 13 = 78/91

Step 3: Add the Numerators
Now add the numerators (14 + 78 = 92) and keep the common denominator 91 unchanged.
Working: 14 + 78/91 = 92/91

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 92 and 91 is 1, confirming that 92/91 cannot be reduced further—it is already in its simplest irreducible form.
Working: 92/91

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (92) is greater than the denominator (91), divide 92 by 91: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/91.
Working: 92/91 = 1 1/91

Step 6: Decimal & Percentage Representation
Dividing the numerator 92 by denominator 91 produces a repeating decimal (approximately 1.010989, or 101.0989%).
Working: 92 ÷ 91 = 1.010989 (101.0989%)

Key Values:
- Simplified Fraction: 92/91
- Mixed Number Form: 1 1/91
- Decimal Value: 1.010989
- Percentage: 101.0989%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-13-plus-6-7/
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2/13 + 6/7 = 92/91

Simplified Fraction

92/91

Mixed Number

1 1/91

Decimal Value

1.010989

Percentage

101.0989%

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Step-by-Step Solution: 2/13 + 6/7

Step 1

Find the Least Common Denominator (LCD)

The denominators 13 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 7 = 91.

LCD(13, 7) = 91

Step 2

Convert to Equivalent Fractions with Common Denominator 91

Multiply the numerator and denominator of 2/13 by 7, and multiply the numerator and denominator of 6/7 by 13 so both fractions share the common base 91.

2 × 7/13 × 7 = 14/91 and 6 × 13/7 × 13 = 78/91

Step 3

Add the Numerators

Now add the numerators (14 + 78 = 92) and keep the common denominator 91 unchanged.

14 + 78/91 = 92/91

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 92 and 91 is 1, confirming that 92/91 cannot be reduced further—it is already in its simplest irreducible form.

92/91

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (92) is greater than the denominator (91), divide 92 by 91: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/91.

92/91 = 11/91

Step 6

Decimal & Percentage Representation

Dividing the numerator 92 by denominator 91 produces a repeating decimal (approximately 1.010989, or 101.0989%).

92 ÷ 91 = 1.010989 (101.0989%)

Visual Representation

The diagram below illustrates 2/13 plus 6/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`92/91`
Mixed Number Form	`1 1/91`
Decimal Form	`1.010989`
Percentage	`101.0989%`

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Frequently Asked Questions

What is 2/13 plus 6/7 as a fraction?

2/13 + 6/7 in simplest fraction form is 92/91 (or 1 1/91 as a mixed number).

What is 2/13 plus 6/7 as a decimal?

2/13 + 6/7 converted to a decimal is 1.010989.

What is 2/13 plus 6/7 as a percentage?

2/13 + 6/7 expressed as a percentage is 101.0989%.

How do you write 2/13 plus 6/7 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 92/91 can be written as the mixed number 1 1/91.

Does 2/13 plus 6/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.010989...) because the denominator contains prime factors other than 2 and 5.