What is 2/13 plus 9/39? (Answer: 5/13)

Exact Answer

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Problem: What is 2/13 plus 9/39?
Formula / Expression: 2/13 + 9/39
Final Answer: 5/13
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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 9/39 by 1 so both fractions share the common base 39.
Working: 2 × 3/13 × 3 = 6/39 and 9 × 1/39 × 1 = 9/39

Step 3: Add the Numerators
Now add the numerators (6 + 9 = 15) and keep the common denominator 39 unchanged.
Working: 6 + 9/39 = 15/39

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 15 and 39, which is 3. Divide both the numerator and denominator by 3.
Working: 15 ÷ 3/39 ÷ 3 = 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-2-13-plus-9-39/
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2/13 + 9/39 = 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: 2/13 + 9/39

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 9/39 by 1 so both fractions share the common base 39.

2 × 3/13 × 3 = 6/39 and 9 × 1/39 × 1 = 9/39

Step 3

Add the Numerators

Now add the numerators (6 + 9 = 15) and keep the common denominator 39 unchanged.

6 + 9/39 = 15/39

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 15 and 39, which is 3. Divide both the numerator and denominator by 3.

15 ÷ 3/39 ÷ 3 = 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 2/13 plus 9/39 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 2/13 plus 9/39 as a fraction?

2/13 + 9/39 in simplest fraction form is 5/13.

What is 2/13 plus 9/39 as a decimal?

2/13 + 9/39 converted to a decimal is 0.384615.

What is 2/13 plus 9/39 as a percentage?

2/13 + 9/39 expressed as a percentage is 38.4615%.

Does 2/13 plus 9/39 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.