What is 1/39 plus 5/13? (Answer: 16/39)

Exact Answer

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Problem: What is 1/39 plus 5/13?
Formula / Expression: 1/39 + 5/13
Final Answer: 16/39
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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 5/13 by 3 so both fractions share the common base 39.
Working: 1 × 1/39 × 1 = 1/39 and 5 × 3/13 × 3 = 15/39

Step 3: Add the Numerators
Now add the numerators (1 + 15 = 16) and keep the common denominator 39 unchanged.
Working: 1 + 15/39 = 16/39

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 16 and 39 is 1, confirming that 16/39 cannot be reduced further—it is already in its simplest irreducible form.
Working: 16/39

Step 5: Decimal & Percentage Representation
Dividing the numerator 16 by denominator 39 produces a repeating decimal (approximately 0.410256, or 41.0256%).
Working: 16 ÷ 39 = 0.410256 (41.0256%)

Key Values:
- Simplified Fraction: 16/39
- Mixed Number Form: 16/39
- Decimal Value: 0.410256
- Percentage: 41.0256%

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Solved with FractionsCalc:
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1/39 + 5/13 = 16/39

Simplified Fraction

16/39

Mixed Number

Proper (16/39)

Decimal Value

0.410256

Percentage

41.0256%

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Step-by-Step Solution: 1/39 + 5/13

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 5/13 by 3 so both fractions share the common base 39.

1 × 1/39 × 1 = 1/39 and 5 × 3/13 × 3 = 15/39

Step 3

Add the Numerators

Now add the numerators (1 + 15 = 16) and keep the common denominator 39 unchanged.

1 + 15/39 = 16/39

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 16 and 39 is 1, confirming that 16/39 cannot be reduced further—it is already in its simplest irreducible form.

16/39

Step 5

Decimal & Percentage Representation

Dividing the numerator 16 by denominator 39 produces a repeating decimal (approximately 0.410256, or 41.0256%).

16 ÷ 39 = 0.410256 (41.0256%)

Visual Representation

The diagram below illustrates 1/39 plus 5/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`16/39`
Mixed Number Form	`16/39`
Decimal Form	`0.410256`
Percentage	`41.0256%`

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Frequently Asked Questions

What is 1/39 plus 5/13 as a fraction?

1/39 + 5/13 in simplest fraction form is 16/39.

What is 1/39 plus 5/13 as a decimal?

1/39 + 5/13 converted to a decimal is 0.410256.

What is 1/39 plus 5/13 as a percentage?

1/39 + 5/13 expressed as a percentage is 41.0256%.

Does 1/39 plus 5/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.410256...) because the denominator contains prime factors other than 2 and 5.