What is 2/65 plus 3/13? (Answer: 17/65)

Exact Answer

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Problem: What is 2/65 plus 3/13?
Formula / Expression: 2/65 + 3/13
Final Answer: 17/65
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 65 is an exact multiple of 13 (13 × 5 = 65). The Least Common Denominator (LCD) is simply 65, meaning we only need to scale one fraction.
Working: LCD(65, 13) = 65

Step 2: Convert to Equivalent Fractions with Common Denominator 65
Multiply the numerator and denominator of 2/65 by 1, and multiply the numerator and denominator of 3/13 by 5 so both fractions share the common base 65.
Working: 2 × 1/65 × 1 = 2/65 and 3 × 5/13 × 5 = 15/65

Step 3: Add the Numerators
Now add the numerators (2 + 15 = 17) and keep the common denominator 65 unchanged.
Working: 2 + 15/65 = 17/65

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 17 and 65 is 1, confirming that 17/65 cannot be reduced further—it is already in its simplest irreducible form.
Working: 17/65

Step 5: Decimal & Percentage Representation
Dividing the numerator 17 by denominator 65 produces a repeating decimal (approximately 0.261538, or 26.1538%).
Working: 17 ÷ 65 = 0.261538 (26.1538%)

Key Values:
- Simplified Fraction: 17/65
- Mixed Number Form: 17/65
- Decimal Value: 0.261538
- Percentage: 26.1538%

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Solved with FractionsCalc:
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2/65 + 3/13 = 17/65

Simplified Fraction

17/65

Mixed Number

Proper (17/65)

Decimal Value

0.261538

Percentage

26.1538%

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Step-by-Step Solution: 2/65 + 3/13

Step 1

Find the Least Common Denominator (LCD)

Notice that 65 is an exact multiple of 13 (13 × 5 = 65). The Least Common Denominator (LCD) is simply 65, meaning we only need to scale one fraction.

LCD(65, 13) = 65

Step 2

Convert to Equivalent Fractions with Common Denominator 65

Multiply the numerator and denominator of 2/65 by 1, and multiply the numerator and denominator of 3/13 by 5 so both fractions share the common base 65.

2 × 1/65 × 1 = 2/65 and 3 × 5/13 × 5 = 15/65

Step 3

Add the Numerators

Now add the numerators (2 + 15 = 17) and keep the common denominator 65 unchanged.

2 + 15/65 = 17/65

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 17 and 65 is 1, confirming that 17/65 cannot be reduced further—it is already in its simplest irreducible form.

17/65

Step 5

Decimal & Percentage Representation

Dividing the numerator 17 by denominator 65 produces a repeating decimal (approximately 0.261538, or 26.1538%).

17 ÷ 65 = 0.261538 (26.1538%)

Visual Representation

The diagram below illustrates 2/65 plus 3/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`17/65`
Mixed Number Form	`17/65`
Decimal Form	`0.261538`
Percentage	`26.1538%`

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Frequently Asked Questions

What is 2/65 plus 3/13 as a fraction?

2/65 + 3/13 in simplest fraction form is 17/65.

What is 2/65 plus 3/13 as a decimal?

2/65 + 3/13 converted to a decimal is 0.261538.

What is 2/65 plus 3/13 as a percentage?

2/65 + 3/13 expressed as a percentage is 26.1538%.

Does 2/65 plus 3/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.261538...) because the denominator contains prime factors other than 2 and 5.