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

Exact Answer

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Problem: What is 3/39 plus 2/13?
Formula / Expression: 3/39 + 2/13
Final Answer: 3/13
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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(39, 13) = 39

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

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

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

Step 5: Decimal & Percentage Representation
Dividing the numerator 3 by denominator 13 produces a repeating decimal (approximately 0.230769, or 23.0769%).
Working: 3 ÷ 13 = 0.230769 (23.0769%)

Key Values:
- Simplified Fraction: 3/13
- Mixed Number Form: 3/13
- Decimal Value: 0.230769
- Percentage: 23.0769%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-39-plus-2-13/
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3/39 + 2/13 = 3/13

Simplified Fraction

3/13

Mixed Number

Proper (3/13)

Decimal Value

0.230769

Percentage

23.0769%

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Step-by-Step Solution: 3/39 + 2/13

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(39, 13) = 39

Step 2

Convert to Equivalent Fractions with Common Denominator 39

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

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

Step 3

Add the Numerators

Now add the numerators (3 + 6 = 9) and keep the common denominator 39 unchanged.

3 + 6/39 = 9/39

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 9 and 39, which is 3. Divide both the numerator and denominator by 3.

9 ÷ 3/39 ÷ 3 = 3/13

Step 5

Decimal & Percentage Representation

Dividing the numerator 3 by denominator 13 produces a repeating decimal (approximately 0.230769, or 23.0769%).

3 ÷ 13 = 0.230769 (23.0769%)

Visual Representation

The diagram below illustrates 3/39 plus 2/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`3/13`
Mixed Number Form	`3/13`
Decimal Form	`0.230769`
Percentage	`23.0769%`

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Frequently Asked Questions

What is 3/39 plus 2/13 as a fraction?

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

What is 3/39 plus 2/13 as a decimal?

3/39 + 2/13 converted to a decimal is 0.230769.

What is 3/39 plus 2/13 as a percentage?

3/39 + 2/13 expressed as a percentage is 23.0769%.

Does 3/39 plus 2/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.230769...) because the denominator contains prime factors other than 2 and 5.