What is 3/13 plus 2/5? (Answer: 41/65)

Exact Answer

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Problem: What is 3/13 plus 2/5?
Formula / Expression: 3/13 + 2/5
Final Answer: 41/65
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 13 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 5 = 65.
Working: LCD(13, 5) = 65

Step 2: Convert to Equivalent Fractions with Common Denominator 65
Multiply the numerator and denominator of 3/13 by 5, and multiply the numerator and denominator of 2/5 by 13 so both fractions share the common base 65.
Working: 3 × 5/13 × 5 = 15/65 and 2 × 13/5 × 13 = 26/65

Step 3: Add the Numerators
Now add the numerators (15 + 26 = 41) and keep the common denominator 65 unchanged.
Working: 15 + 26/65 = 41/65

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 41 and 65 is 1, confirming that 41/65 cannot be reduced further—it is already in its simplest irreducible form.
Working: 41/65

Step 5: Decimal & Percentage Representation
Dividing the numerator 41 by denominator 65 produces a repeating decimal (approximately 0.630769, or 63.0769%).
Working: 41 ÷ 65 = 0.630769 (63.0769%)

Key Values:
- Simplified Fraction: 41/65
- Mixed Number Form: 41/65
- Decimal Value: 0.630769
- Percentage: 63.0769%

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3/13 + 2/5 = 41/65

Simplified Fraction

41/65

Mixed Number

Proper (41/65)

Decimal Value

0.630769

Percentage

63.0769%

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Step-by-Step Solution: 3/13 + 2/5

Step 1

Find the Least Common Denominator (LCD)

The denominators 13 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 5 = 65.

LCD(13, 5) = 65

Step 2

Convert to Equivalent Fractions with Common Denominator 65

Multiply the numerator and denominator of 3/13 by 5, and multiply the numerator and denominator of 2/5 by 13 so both fractions share the common base 65.

3 × 5/13 × 5 = 15/65 and 2 × 13/5 × 13 = 26/65

Step 3

Add the Numerators

Now add the numerators (15 + 26 = 41) and keep the common denominator 65 unchanged.

15 + 26/65 = 41/65

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 41 and 65 is 1, confirming that 41/65 cannot be reduced further—it is already in its simplest irreducible form.

41/65

Step 5

Decimal & Percentage Representation

Dividing the numerator 41 by denominator 65 produces a repeating decimal (approximately 0.630769, or 63.0769%).

41 ÷ 65 = 0.630769 (63.0769%)

Visual Representation

The diagram below illustrates 3/13 plus 2/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`41/65`
Mixed Number Form	`41/65`
Decimal Form	`0.630769`
Percentage	`63.0769%`

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Frequently Asked Questions

What is 3/13 plus 2/5 as a fraction?

3/13 + 2/5 in simplest fraction form is 41/65.

What is 3/13 plus 2/5 as a decimal?

3/13 + 2/5 converted to a decimal is 0.630769.

What is 3/13 plus 2/5 as a percentage?

3/13 + 2/5 expressed as a percentage is 63.0769%.

Does 3/13 plus 2/5 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.630769...) because the denominator contains prime factors other than 2 and 5.