What is 2/13 plus 7/39? (Answer: 1/3)

Exact Answer

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Problem: What is 2/13 plus 7/39?
Formula / Expression: 2/13 + 7/39
Final Answer: 1/3
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 39 is an exact multiple of 13 (13 × 3 = 39). The Least Common Denominator (LCD) is simply 39, meaning we only need to scale one fraction.
Working: LCD(13, 39) = 39

Step 2: Convert to Equivalent Fractions with Common Denominator 39
Multiply the numerator and denominator of 2/13 by 3, and multiply the numerator and denominator of 7/39 by 1 so both fractions share the common base 39.
Working: 2 × 3/13 × 3 = 6/39 and 7 × 1/39 × 1 = 7/39

Step 3: Add the Numerators
Now add the numerators (6 + 7 = 13) and keep the common denominator 39 unchanged.
Working: 6 + 7/39 = 13/39

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 13 and 39, which is 13. Divide both the numerator and denominator by 13.
Working: 13 ÷ 13/39 ÷ 13 = 1/3

Step 5: Decimal & Percentage Representation
Dividing the numerator 1 by denominator 3 produces a repeating decimal (approximately 0.333333, or 33.3333%).
Working: 1 ÷ 3 = 0.333333 (33.3333%)

Key Values:
- Simplified Fraction: 1/3
- Mixed Number Form: 1/3
- Decimal Value: 0.333333
- Percentage: 33.3333%

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Solved with FractionsCalc:
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2/13 + 7/39 = 1/3

Simplified Fraction

1/3

Mixed Number

Proper (1/3)

Decimal Value

0.333333

Percentage

33.3333%

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Step-by-Step Solution: 2/13 + 7/39

Step 1

Find the Least Common Denominator (LCD)

Notice that 39 is an exact multiple of 13 (13 × 3 = 39). The Least Common Denominator (LCD) is simply 39, meaning we only need to scale one fraction.

LCD(13, 39) = 39

Step 2

Convert to Equivalent Fractions with Common Denominator 39

Multiply the numerator and denominator of 2/13 by 3, and multiply the numerator and denominator of 7/39 by 1 so both fractions share the common base 39.

2 × 3/13 × 3 = 6/39 and 7 × 1/39 × 1 = 7/39

Step 3

Add the Numerators

Now add the numerators (6 + 7 = 13) and keep the common denominator 39 unchanged.

6 + 7/39 = 13/39

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 13 and 39, which is 13. Divide both the numerator and denominator by 13.

13 ÷ 13/39 ÷ 13 = 1/3

Step 5

Decimal & Percentage Representation

Dividing the numerator 1 by denominator 3 produces a repeating decimal (approximately 0.333333, or 33.3333%).

1 ÷ 3 = 0.333333 (33.3333%)

Visual Representation

The diagram below illustrates 2/13 plus 7/39 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`1/3`
Mixed Number Form	`1/3`
Decimal Form	`0.333333`
Percentage	`33.3333%`

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Frequently Asked Questions

What is 2/13 plus 7/39 as a fraction?

2/13 + 7/39 in simplest fraction form is 1/3.

What is 2/13 plus 7/39 as a decimal?

2/13 + 7/39 converted to a decimal is 0.333333.

What is 2/13 plus 7/39 as a percentage?

2/13 + 7/39 expressed as a percentage is 33.3333%.

Does 2/13 plus 7/39 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.333333...) because the denominator contains prime factors other than 2 and 5.