What is 13/38 plus 9/13? (Answer: 511/494)

Exact Answer

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Problem: What is 13/38 plus 9/13?
Formula / Expression: 13/38 + 9/13
Final Answer: 1 17/494 (511/494)
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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 13/38 by 13, and multiply the numerator and denominator of 9/13 by 38 so both fractions share the common base 494.
Working: 13 × 13/38 × 13 = 169/494 and 9 × 38/13 × 38 = 342/494

Step 3: Add the Numerators
Now add the numerators (169 + 342 = 511) and keep the common denominator 494 unchanged.
Working: 169 + 342/494 = 511/494

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 511 and 494 is 1, confirming that 511/494 cannot be reduced further—it is already in its simplest irreducible form.
Working: 511/494

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (511) is greater than the denominator (494), divide 511 by 494: it goes in 1 whole time(s) with a remainder of 17, giving the mixed number 1 17/494.
Working: 511/494 = 1 17/494

Step 6: Decimal & Percentage Representation
Dividing the numerator 511 by denominator 494 produces a repeating decimal (approximately 1.034413, or 103.4413%).
Working: 511 ÷ 494 = 1.034413 (103.4413%)

Key Values:
- Simplified Fraction: 511/494
- Mixed Number Form: 1 17/494
- Decimal Value: 1.034413
- Percentage: 103.4413%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-13-38-plus-9-13/
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13/38 + 9/13 = 511/494

Simplified Fraction

511/494

Mixed Number

1 17/494

Decimal Value

1.034413

Percentage

103.4413%

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Step-by-Step Solution: 13/38 + 9/13

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 13/38 by 13, and multiply the numerator and denominator of 9/13 by 38 so both fractions share the common base 494.

13 × 13/38 × 13 = 169/494 and 9 × 38/13 × 38 = 342/494

Step 3

Add the Numerators

Now add the numerators (169 + 342 = 511) and keep the common denominator 494 unchanged.

169 + 342/494 = 511/494

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 511 and 494 is 1, confirming that 511/494 cannot be reduced further—it is already in its simplest irreducible form.

511/494

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (511) is greater than the denominator (494), divide 511 by 494: it goes in 1 whole time(s) with a remainder of 17, giving the mixed number 1 17/494.

511/494 = 117/494

Step 6

Decimal & Percentage Representation

Dividing the numerator 511 by denominator 494 produces a repeating decimal (approximately 1.034413, or 103.4413%).

511 ÷ 494 = 1.034413 (103.4413%)

Visual Representation

The diagram below illustrates 13/38 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`511/494`
Mixed Number Form	`1 17/494`
Decimal Form	`1.034413`
Percentage	`103.4413%`

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Frequently Asked Questions

What is 13/38 plus 9/13 as a fraction?

13/38 + 9/13 in simplest fraction form is 511/494 (or 1 17/494 as a mixed number).

What is 13/38 plus 9/13 as a decimal?

13/38 + 9/13 converted to a decimal is 1.034413.

What is 13/38 plus 9/13 as a percentage?

13/38 + 9/13 expressed as a percentage is 103.4413%.

How do you write 13/38 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 511/494 can be written as the mixed number 1 17/494.

Does 13/38 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.034413...) because the denominator contains prime factors other than 2 and 5.