What is 4/13 plus 2/3? (Answer: 38/39)

Exact Answer

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Problem: What is 4/13 plus 2/3?
Formula / Expression: 4/13 + 2/3
Final Answer: 38/39
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 13 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 3 = 39.
Working: LCD(13, 3) = 39

Step 2: Convert to Equivalent Fractions with Common Denominator 39
Multiply the numerator and denominator of 4/13 by 3, and multiply the numerator and denominator of 2/3 by 13 so both fractions share the common base 39.
Working: 4 × 3/13 × 3 = 12/39 and 2 × 13/3 × 13 = 26/39

Step 3: Add the Numerators
Now add the numerators (12 + 26 = 38) and keep the common denominator 39 unchanged.
Working: 12 + 26/39 = 38/39

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 38 and 39 is 1, confirming that 38/39 cannot be reduced further—it is already in its simplest irreducible form.
Working: 38/39

Step 5: Decimal & Percentage Representation
Dividing the numerator 38 by denominator 39 produces a repeating decimal (approximately 0.974359, or 97.4359%).
Working: 38 ÷ 39 = 0.974359 (97.4359%)

Key Values:
- Simplified Fraction: 38/39
- Mixed Number Form: 38/39
- Decimal Value: 0.974359
- Percentage: 97.4359%

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Solved with FractionsCalc:
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4/13 + 2/3 = 38/39

Simplified Fraction

38/39

Mixed Number

Proper (38/39)

Decimal Value

0.974359

Percentage

97.4359%

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Step-by-Step Solution: 4/13 + 2/3

Step 1

Find the Least Common Denominator (LCD)

The denominators 13 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 3 = 39.

LCD(13, 3) = 39

Step 2

Convert to Equivalent Fractions with Common Denominator 39

Multiply the numerator and denominator of 4/13 by 3, and multiply the numerator and denominator of 2/3 by 13 so both fractions share the common base 39.

4 × 3/13 × 3 = 12/39 and 2 × 13/3 × 13 = 26/39

Step 3

Add the Numerators

Now add the numerators (12 + 26 = 38) and keep the common denominator 39 unchanged.

12 + 26/39 = 38/39

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 38 and 39 is 1, confirming that 38/39 cannot be reduced further—it is already in its simplest irreducible form.

38/39

Step 5

Decimal & Percentage Representation

Dividing the numerator 38 by denominator 39 produces a repeating decimal (approximately 0.974359, or 97.4359%).

38 ÷ 39 = 0.974359 (97.4359%)

Visual Representation

The diagram below illustrates 4/13 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`38/39`
Mixed Number Form	`38/39`
Decimal Form	`0.974359`
Percentage	`97.4359%`

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Frequently Asked Questions

What is 4/13 plus 2/3 as a fraction?

4/13 + 2/3 in simplest fraction form is 38/39.

What is 4/13 plus 2/3 as a decimal?

4/13 + 2/3 converted to a decimal is 0.974359.

What is 4/13 plus 2/3 as a percentage?

4/13 + 2/3 expressed as a percentage is 97.4359%.

Does 4/13 plus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.974359...) because the denominator contains prime factors other than 2 and 5.