What is 2/6 plus 7/13? (Answer: 34/39)

Exact Answer

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Problem: What is 2/6 plus 7/13?
Formula / Expression: 2/6 + 7/13
Final Answer: 34/39
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 78
Multiply the numerator and denominator of 2/6 by 13, and multiply the numerator and denominator of 7/13 by 6 so both fractions share the common base 78.
Working: 2 × 13/6 × 13 = 26/78 and 7 × 6/13 × 6 = 42/78

Step 3: Add the Numerators
Now add the numerators (26 + 42 = 68) and keep the common denominator 78 unchanged.
Working: 26 + 42/78 = 68/78

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 68 and 78, which is 2. Divide both the numerator and denominator by 2.
Working: 68 ÷ 2/78 ÷ 2 = 34/39

Step 5: Decimal & Percentage Representation
Dividing the numerator 34 by denominator 39 produces a repeating decimal (approximately 0.871795, or 87.1795%).
Working: 34 ÷ 39 = 0.871795 (87.1795%)

Key Values:
- Simplified Fraction: 34/39
- Mixed Number Form: 34/39
- Decimal Value: 0.871795
- Percentage: 87.1795%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-6-plus-7-13/
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2/6 + 7/13 = 34/39

Simplified Fraction

34/39

Mixed Number

Proper (34/39)

Decimal Value

0.871795

Percentage

87.1795%

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

Step 1

Find the Least Common Denominator (LCD)

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

LCD(6, 13) = 78

Step 2

Convert to Equivalent Fractions with Common Denominator 78

Multiply the numerator and denominator of 2/6 by 13, and multiply the numerator and denominator of 7/13 by 6 so both fractions share the common base 78.

2 × 13/6 × 13 = 26/78 and 7 × 6/13 × 6 = 42/78

Step 3

Add the Numerators

Now add the numerators (26 + 42 = 68) and keep the common denominator 78 unchanged.

26 + 42/78 = 68/78

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 68 and 78, which is 2. Divide both the numerator and denominator by 2.

68 ÷ 2/78 ÷ 2 = 34/39

Step 5

Decimal & Percentage Representation

Dividing the numerator 34 by denominator 39 produces a repeating decimal (approximately 0.871795, or 87.1795%).

34 ÷ 39 = 0.871795 (87.1795%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`34/39`
Mixed Number Form	`34/39`
Decimal Form	`0.871795`
Percentage	`87.1795%`

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Frequently Asked Questions

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

2/6 + 7/13 in simplest fraction form is 34/39.

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

2/6 + 7/13 converted to a decimal is 0.871795.

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

2/6 + 7/13 expressed as a percentage is 87.1795%.

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

It results in a repeating decimal (approximately 0.871795...) because the denominator contains prime factors other than 2 and 5.