What is 2/13 plus 4/5? (Answer: 62/65)

Exact Answer

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Problem: What is 2/13 plus 4/5?
Formula / Expression: 2/13 + 4/5
Final Answer: 62/65
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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 2/13 by 5, and multiply the numerator and denominator of 4/5 by 13 so both fractions share the common base 65.
Working: 2 × 5/13 × 5 = 10/65 and 4 × 13/5 × 13 = 52/65

Step 3: Add the Numerators
Now add the numerators (10 + 52 = 62) and keep the common denominator 65 unchanged.
Working: 10 + 52/65 = 62/65

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 62 and 65 is 1, confirming that 62/65 cannot be reduced further—it is already in its simplest irreducible form.
Working: 62/65

Step 5: Decimal & Percentage Representation
Dividing the numerator 62 by denominator 65 produces a repeating decimal (approximately 0.953846, or 95.3846%).
Working: 62 ÷ 65 = 0.953846 (95.3846%)

Key Values:
- Simplified Fraction: 62/65
- Mixed Number Form: 62/65
- Decimal Value: 0.953846
- Percentage: 95.3846%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-13-plus-4-5/
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2/13 + 4/5 = 62/65

Simplified Fraction

62/65

Mixed Number

Proper (62/65)

Decimal Value

0.953846

Percentage

95.3846%

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Step-by-Step Solution: 2/13 + 4/5

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 2/13 by 5, and multiply the numerator and denominator of 4/5 by 13 so both fractions share the common base 65.

2 × 5/13 × 5 = 10/65 and 4 × 13/5 × 13 = 52/65

Step 3

Add the Numerators

Now add the numerators (10 + 52 = 62) and keep the common denominator 65 unchanged.

10 + 52/65 = 62/65

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 62 and 65 is 1, confirming that 62/65 cannot be reduced further—it is already in its simplest irreducible form.

62/65

Step 5

Decimal & Percentage Representation

Dividing the numerator 62 by denominator 65 produces a repeating decimal (approximately 0.953846, or 95.3846%).

62 ÷ 65 = 0.953846 (95.3846%)

Visual Representation

The diagram below illustrates 2/13 plus 4/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`62/65`
Mixed Number Form	`62/65`
Decimal Form	`0.953846`
Percentage	`95.3846%`

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Frequently Asked Questions

What is 2/13 plus 4/5 as a fraction?

2/13 + 4/5 in simplest fraction form is 62/65.

What is 2/13 plus 4/5 as a decimal?

2/13 + 4/5 converted to a decimal is 0.953846.

What is 2/13 plus 4/5 as a percentage?

2/13 + 4/5 expressed as a percentage is 95.3846%.

Does 2/13 plus 4/5 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.953846...) because the denominator contains prime factors other than 2 and 5.