What is 1/39 plus 3/13? (Answer: 10/39)

Exact Answer

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Problem: What is 1/39 plus 3/13?
Formula / Expression: 1/39 + 3/13
Final Answer: 10/39
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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 3/13 by 3 so both fractions share the common base 39.
Working: 1 × 1/39 × 1 = 1/39 and 3 × 3/13 × 3 = 9/39

Step 3: Add the Numerators
Now add the numerators (1 + 9 = 10) and keep the common denominator 39 unchanged.
Working: 1 + 9/39 = 10/39

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 10 and 39 is 1, confirming that 10/39 cannot be reduced further—it is already in its simplest irreducible form.
Working: 10/39

Step 5: Decimal & Percentage Representation
Dividing the numerator 10 by denominator 39 produces a repeating decimal (approximately 0.25641, or 25.641%).
Working: 10 ÷ 39 = 0.25641 (25.641%)

Key Values:
- Simplified Fraction: 10/39
- Mixed Number Form: 10/39
- Decimal Value: 0.25641
- Percentage: 25.641%

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Solved with FractionsCalc:
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1/39 + 3/13 = 10/39

Simplified Fraction

10/39

Mixed Number

Proper (10/39)

Decimal Value

0.25641

Percentage

25.641%

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Step-by-Step Solution: 1/39 + 3/13

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

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

Step 3

Add the Numerators

Now add the numerators (1 + 9 = 10) and keep the common denominator 39 unchanged.

1 + 9/39 = 10/39

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 10 and 39 is 1, confirming that 10/39 cannot be reduced further—it is already in its simplest irreducible form.

10/39

Step 5

Decimal & Percentage Representation

Dividing the numerator 10 by denominator 39 produces a repeating decimal (approximately 0.25641, or 25.641%).

10 ÷ 39 = 0.25641 (25.641%)

Visual Representation

The diagram below illustrates 1/39 plus 3/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`10/39`
Mixed Number Form	`10/39`
Decimal Form	`0.25641`
Percentage	`25.641%`

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Frequently Asked Questions

What is 1/39 plus 3/13 as a fraction?

1/39 + 3/13 in simplest fraction form is 10/39.

What is 1/39 plus 3/13 as a decimal?

1/39 + 3/13 converted to a decimal is 0.25641.

What is 1/39 plus 3/13 as a percentage?

1/39 + 3/13 expressed as a percentage is 25.641%.

Does 1/39 plus 3/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.25641...) because the denominator contains prime factors other than 2 and 5.