What is 2/6 plus 5/13? (Answer: 28/39)

Exact Answer

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Problem: What is 2/6 plus 5/13?
Formula / Expression: 2/6 + 5/13
Final Answer: 28/39
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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 5/13 by 6 so both fractions share the common base 78.
Working: 2 × 13/6 × 13 = 26/78 and 5 × 6/13 × 6 = 30/78

Step 3: Add the Numerators
Now add the numerators (26 + 30 = 56) and keep the common denominator 78 unchanged.
Working: 26 + 30/78 = 56/78

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 56 and 78, which is 2. Divide both the numerator and denominator by 2.
Working: 56 ÷ 2/78 ÷ 2 = 28/39

Step 5: Decimal & Percentage Representation
Dividing the numerator 28 by denominator 39 produces a repeating decimal (approximately 0.717949, or 71.7949%).
Working: 28 ÷ 39 = 0.717949 (71.7949%)

Key Values:
- Simplified Fraction: 28/39
- Mixed Number Form: 28/39
- Decimal Value: 0.717949
- Percentage: 71.7949%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-6-plus-5-13/
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2/6 + 5/13 = 28/39

Simplified Fraction

28/39

Mixed Number

Proper (28/39)

Decimal Value

0.717949

Percentage

71.7949%

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

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 5/13 by 6 so both fractions share the common base 78.

2 × 13/6 × 13 = 26/78 and 5 × 6/13 × 6 = 30/78

Step 3

Add the Numerators

Now add the numerators (26 + 30 = 56) and keep the common denominator 78 unchanged.

26 + 30/78 = 56/78

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 56 and 78, which is 2. Divide both the numerator and denominator by 2.

56 ÷ 2/78 ÷ 2 = 28/39

Step 5

Decimal & Percentage Representation

Dividing the numerator 28 by denominator 39 produces a repeating decimal (approximately 0.717949, or 71.7949%).

28 ÷ 39 = 0.717949 (71.7949%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`28/39`
Mixed Number Form	`28/39`
Decimal Form	`0.717949`
Percentage	`71.7949%`

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Frequently Asked Questions

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

2/6 + 5/13 in simplest fraction form is 28/39.

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

2/6 + 5/13 converted to a decimal is 0.717949.

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

2/6 + 5/13 expressed as a percentage is 71.7949%.

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

It results in a repeating decimal (approximately 0.717949...) because the denominator contains prime factors other than 2 and 5.