What is 13/29 plus 9/13? (Answer: 430/377)

Exact Answer

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Problem: What is 13/29 plus 9/13?
Formula / Expression: 13/29 + 9/13
Final Answer: 1 53/377 (430/377)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 29 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 29 × 13 = 377.
Working: LCD(29, 13) = 377

Step 2: Convert to Equivalent Fractions with Common Denominator 377
Multiply the numerator and denominator of 13/29 by 13, and multiply the numerator and denominator of 9/13 by 29 so both fractions share the common base 377.
Working: 13 × 13/29 × 13 = 169/377 and 9 × 29/13 × 29 = 261/377

Step 3: Add the Numerators
Now add the numerators (169 + 261 = 430) and keep the common denominator 377 unchanged.
Working: 169 + 261/377 = 430/377

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 430 and 377 is 1, confirming that 430/377 cannot be reduced further—it is already in its simplest irreducible form.
Working: 430/377

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (430) is greater than the denominator (377), divide 430 by 377: it goes in 1 whole time(s) with a remainder of 53, giving the mixed number 1 53/377.
Working: 430/377 = 1 53/377

Step 6: Decimal & Percentage Representation
Dividing the numerator 430 by denominator 377 produces a repeating decimal (approximately 1.140584, or 114.0584%).
Working: 430 ÷ 377 = 1.140584 (114.0584%)

Key Values:
- Simplified Fraction: 430/377
- Mixed Number Form: 1 53/377
- Decimal Value: 1.140584
- Percentage: 114.0584%

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Solved with FractionsCalc:
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13/29 + 9/13 = 430/377

Simplified Fraction

430/377

Mixed Number

1 53/377

Decimal Value

1.140584

Percentage

114.0584%

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Step-by-Step Solution: 13/29 + 9/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 29 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 29 × 13 = 377.

LCD(29, 13) = 377

Step 2

Convert to Equivalent Fractions with Common Denominator 377

Multiply the numerator and denominator of 13/29 by 13, and multiply the numerator and denominator of 9/13 by 29 so both fractions share the common base 377.

13 × 13/29 × 13 = 169/377 and 9 × 29/13 × 29 = 261/377

Step 3

Add the Numerators

Now add the numerators (169 + 261 = 430) and keep the common denominator 377 unchanged.

169 + 261/377 = 430/377

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 430 and 377 is 1, confirming that 430/377 cannot be reduced further—it is already in its simplest irreducible form.

430/377

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (430) is greater than the denominator (377), divide 430 by 377: it goes in 1 whole time(s) with a remainder of 53, giving the mixed number 1 53/377.

430/377 = 153/377

Step 6

Decimal & Percentage Representation

Dividing the numerator 430 by denominator 377 produces a repeating decimal (approximately 1.140584, or 114.0584%).

430 ÷ 377 = 1.140584 (114.0584%)

Visual Representation

The diagram below illustrates 13/29 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`430/377`
Mixed Number Form	`1 53/377`
Decimal Form	`1.140584`
Percentage	`114.0584%`

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Frequently Asked Questions

What is 13/29 plus 9/13 as a fraction?

13/29 + 9/13 in simplest fraction form is 430/377 (or 1 53/377 as a mixed number).

What is 13/29 plus 9/13 as a decimal?

13/29 + 9/13 converted to a decimal is 1.140584.

What is 13/29 plus 9/13 as a percentage?

13/29 + 9/13 expressed as a percentage is 114.0584%.

How do you write 13/29 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 430/377 can be written as the mixed number 1 53/377.

Does 13/29 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.140584...) because the denominator contains prime factors other than 2 and 5.