What is 3/38 plus 5/13? (Answer: 229/494)

Exact Answer

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Problem: What is 3/38 plus 5/13?
Formula / Expression: 3/38 + 5/13
Final Answer: 229/494
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 38 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 38 × 13 = 494.
Working: LCD(38, 13) = 494

Step 2: Convert to Equivalent Fractions with Common Denominator 494
Multiply the numerator and denominator of 3/38 by 13, and multiply the numerator and denominator of 5/13 by 38 so both fractions share the common base 494.
Working: 3 × 13/38 × 13 = 39/494 and 5 × 38/13 × 38 = 190/494

Step 3: Add the Numerators
Now add the numerators (39 + 190 = 229) and keep the common denominator 494 unchanged.
Working: 39 + 190/494 = 229/494

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 229 and 494 is 1, confirming that 229/494 cannot be reduced further—it is already in its simplest irreducible form.
Working: 229/494

Step 5: Decimal & Percentage Representation
Dividing the numerator 229 by denominator 494 produces a repeating decimal (approximately 0.463563, or 46.3563%).
Working: 229 ÷ 494 = 0.463563 (46.3563%)

Key Values:
- Simplified Fraction: 229/494
- Mixed Number Form: 229/494
- Decimal Value: 0.463563
- Percentage: 46.3563%

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Solved with FractionsCalc:
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3/38 + 5/13 = 229/494

Simplified Fraction

229/494

Mixed Number

Proper (229/494)

Decimal Value

0.463563

Percentage

46.3563%

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Step-by-Step Solution: 3/38 + 5/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 38 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 38 × 13 = 494.

LCD(38, 13) = 494

Step 2

Convert to Equivalent Fractions with Common Denominator 494

Multiply the numerator and denominator of 3/38 by 13, and multiply the numerator and denominator of 5/13 by 38 so both fractions share the common base 494.

3 × 13/38 × 13 = 39/494 and 5 × 38/13 × 38 = 190/494

Step 3

Add the Numerators

Now add the numerators (39 + 190 = 229) and keep the common denominator 494 unchanged.

39 + 190/494 = 229/494

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 229 and 494 is 1, confirming that 229/494 cannot be reduced further—it is already in its simplest irreducible form.

229/494

Step 5

Decimal & Percentage Representation

Dividing the numerator 229 by denominator 494 produces a repeating decimal (approximately 0.463563, or 46.3563%).

229 ÷ 494 = 0.463563 (46.3563%)

Visual Representation

The diagram below illustrates 3/38 plus 5/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`229/494`
Mixed Number Form	`229/494`
Decimal Form	`0.463563`
Percentage	`46.3563%`

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Frequently Asked Questions

What is 3/38 plus 5/13 as a fraction?

3/38 + 5/13 in simplest fraction form is 229/494.

What is 3/38 plus 5/13 as a decimal?

3/38 + 5/13 converted to a decimal is 0.463563.

What is 3/38 plus 5/13 as a percentage?

3/38 + 5/13 expressed as a percentage is 46.3563%.

Does 3/38 plus 5/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.463563...) because the denominator contains prime factors other than 2 and 5.