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

Exact Answer

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Problem: What is 1/39 plus 2/13?
Formula / Expression: 1/39 + 2/13
Final Answer: 7/39
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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 1/39 by 1, and multiply the numerator and denominator of 2/13 by 3 so both fractions share the common base 39.
Working: 1 × 1/39 × 1 = 1/39 and 2 × 3/13 × 3 = 6/39

Step 3: Add the Numerators
Now add the numerators (1 + 6 = 7) and keep the common denominator 39 unchanged.
Working: 1 + 6/39 = 7/39

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 7 and 39 is 1, confirming that 7/39 cannot be reduced further—it is already in its simplest irreducible form.
Working: 7/39

Step 5: Decimal & Percentage Representation
Dividing the numerator 7 by denominator 39 produces a repeating decimal (approximately 0.179487, or 17.9487%).
Working: 7 ÷ 39 = 0.179487 (17.9487%)

Key Values:
- Simplified Fraction: 7/39
- Mixed Number Form: 7/39
- Decimal Value: 0.179487
- Percentage: 17.9487%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-39-plus-2-13/
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1/39 + 2/13 = 7/39

Simplified Fraction

7/39

Mixed Number

Proper (7/39)

Decimal Value

0.179487

Percentage

17.9487%

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Step-by-Step Solution: 1/39 + 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 1/39 by 1, and multiply the numerator and denominator of 2/13 by 3 so both fractions share the common base 39.

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

Step 3

Add the Numerators

Now add the numerators (1 + 6 = 7) and keep the common denominator 39 unchanged.

1 + 6/39 = 7/39

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 7 and 39 is 1, confirming that 7/39 cannot be reduced further—it is already in its simplest irreducible form.

7/39

Step 5

Decimal & Percentage Representation

Dividing the numerator 7 by denominator 39 produces a repeating decimal (approximately 0.179487, or 17.9487%).

7 ÷ 39 = 0.179487 (17.9487%)

Visual Representation

The diagram below illustrates 1/39 plus 2/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`7/39`
Mixed Number Form	`7/39`
Decimal Form	`0.179487`
Percentage	`17.9487%`

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Frequently Asked Questions

What is 1/39 plus 2/13 as a fraction?

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

What is 1/39 plus 2/13 as a decimal?

1/39 + 2/13 converted to a decimal is 0.179487.

What is 1/39 plus 2/13 as a percentage?

1/39 + 2/13 expressed as a percentage is 17.9487%.

Does 1/39 plus 2/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.179487...) because the denominator contains prime factors other than 2 and 5.