What is 9/29 plus 9/13? (Answer: 378/377)

Exact Answer

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Problem: What is 9/29 plus 9/13?
Formula / Expression: 9/29 + 9/13
Final Answer: 1 1/377 (378/377)
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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 9/29 by 13, and multiply the numerator and denominator of 9/13 by 29 so both fractions share the common base 377.
Working: 9 × 13/29 × 13 = 117/377 and 9 × 29/13 × 29 = 261/377

Step 3: Add the Numerators
Now add the numerators (117 + 261 = 378) and keep the common denominator 377 unchanged.
Working: 117 + 261/377 = 378/377

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 378 and 377 is 1, confirming that 378/377 cannot be reduced further—it is already in its simplest irreducible form.
Working: 378/377

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (378) is greater than the denominator (377), divide 378 by 377: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/377.
Working: 378/377 = 1 1/377

Step 6: Decimal & Percentage Representation
Dividing the numerator 378 by denominator 377 produces a repeating decimal (approximately 1.002653, or 100.2653%).
Working: 378 ÷ 377 = 1.002653 (100.2653%)

Key Values:
- Simplified Fraction: 378/377
- Mixed Number Form: 1 1/377
- Decimal Value: 1.002653
- Percentage: 100.2653%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-9-29-plus-9-13/
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9/29 + 9/13 = 378/377

Simplified Fraction

378/377

Mixed Number

1 1/377

Decimal Value

1.002653

Percentage

100.2653%

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Step-by-Step Solution: 9/29 + 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 9/29 by 13, and multiply the numerator and denominator of 9/13 by 29 so both fractions share the common base 377.

9 × 13/29 × 13 = 117/377 and 9 × 29/13 × 29 = 261/377

Step 3

Add the Numerators

Now add the numerators (117 + 261 = 378) and keep the common denominator 377 unchanged.

117 + 261/377 = 378/377

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 378 and 377 is 1, confirming that 378/377 cannot be reduced further—it is already in its simplest irreducible form.

378/377

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (378) is greater than the denominator (377), divide 378 by 377: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/377.

378/377 = 11/377

Step 6

Decimal & Percentage Representation

Dividing the numerator 378 by denominator 377 produces a repeating decimal (approximately 1.002653, or 100.2653%).

378 ÷ 377 = 1.002653 (100.2653%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`378/377`
Mixed Number Form	`1 1/377`
Decimal Form	`1.002653`
Percentage	`100.2653%`

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Frequently Asked Questions

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

9/29 + 9/13 in simplest fraction form is 378/377 (or 1 1/377 as a mixed number).

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

9/29 + 9/13 converted to a decimal is 1.002653.

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

9/29 + 9/13 expressed as a percentage is 100.2653%.

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

Because the numerator is greater than the denominator, the improper fraction 378/377 can be written as the mixed number 1 1/377.

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

It results in a repeating decimal (approximately 1.002653...) because the denominator contains prime factors other than 2 and 5.