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

Exact Answer

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Problem: What is 2/39 plus 2/6?
Formula / Expression: 2/39 + 2/6
Final Answer: 5/13
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 39 and 6 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 78 (which is smaller than their product 39 × 6 = 234, keeping the calculation simpler).
Working: LCD(39, 6) = 78

Step 2: Convert to Equivalent Fractions with Common Denominator 78
Multiply the numerator and denominator of 2/39 by 2, and multiply the numerator and denominator of 2/6 by 13 so both fractions share the common base 78.
Working: 2 × 2/39 × 2 = 4/78 and 2 × 13/6 × 13 = 26/78

Step 3: Add the Numerators
Now add the numerators (4 + 26 = 30) and keep the common denominator 78 unchanged.
Working: 4 + 26/78 = 30/78

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 30 and 78, which is 6. Divide both the numerator and denominator by 6.
Working: 30 ÷ 6/78 ÷ 6 = 5/13

Step 5: Decimal & Percentage Representation
Dividing the numerator 5 by denominator 13 produces a repeating decimal (approximately 0.384615, or 38.4615%).
Working: 5 ÷ 13 = 0.384615 (38.4615%)

Key Values:
- Simplified Fraction: 5/13
- Mixed Number Form: 5/13
- Decimal Value: 0.384615
- Percentage: 38.4615%

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

Simplified Fraction

5/13

Mixed Number

Proper (5/13)

Decimal Value

0.384615

Percentage

38.4615%

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Step-by-Step Solution: 2/39 + 2/6

Step 1

Find the Least Common Denominator (LCD)

The denominators 39 and 6 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 78 (which is smaller than their product 39 × 6 = 234, keeping the calculation simpler).

LCD(39, 6) = 78

Step 2

Convert to Equivalent Fractions with Common Denominator 78

Multiply the numerator and denominator of 2/39 by 2, and multiply the numerator and denominator of 2/6 by 13 so both fractions share the common base 78.

2 × 2/39 × 2 = 4/78 and 2 × 13/6 × 13 = 26/78

Step 3

Add the Numerators

Now add the numerators (4 + 26 = 30) and keep the common denominator 78 unchanged.

4 + 26/78 = 30/78

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 30 and 78, which is 6. Divide both the numerator and denominator by 6.

30 ÷ 6/78 ÷ 6 = 5/13

Step 5

Decimal & Percentage Representation

Dividing the numerator 5 by denominator 13 produces a repeating decimal (approximately 0.384615, or 38.4615%).

5 ÷ 13 = 0.384615 (38.4615%)

Visual Representation

The diagram below illustrates 2/39 plus 2/6 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`5/13`
Mixed Number Form	`5/13`
Decimal Form	`0.384615`
Percentage	`38.4615%`

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Frequently Asked Questions

What is 2/39 plus 2/6 as a fraction?

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

What is 2/39 plus 2/6 as a decimal?

2/39 + 2/6 converted to a decimal is 0.384615.

What is 2/39 plus 2/6 as a percentage?

2/39 + 2/6 expressed as a percentage is 38.4615%.

Does 2/39 plus 2/6 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.384615...) because the denominator contains prime factors other than 2 and 5.