What is 13/22 plus 9/13? (Answer: 367/286)

Exact Answer

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Problem: What is 13/22 plus 9/13?
Formula / Expression: 13/22 + 9/13
Final Answer: 1 81/286 (367/286)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 22 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 22 × 13 = 286.
Working: LCD(22, 13) = 286

Step 2: Convert to Equivalent Fractions with Common Denominator 286
Multiply the numerator and denominator of 13/22 by 13, and multiply the numerator and denominator of 9/13 by 22 so both fractions share the common base 286.
Working: 13 × 13/22 × 13 = 169/286 and 9 × 22/13 × 22 = 198/286

Step 3: Add the Numerators
Now add the numerators (169 + 198 = 367) and keep the common denominator 286 unchanged.
Working: 169 + 198/286 = 367/286

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 367 and 286 is 1, confirming that 367/286 cannot be reduced further—it is already in its simplest irreducible form.
Working: 367/286

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (367) is greater than the denominator (286), divide 367 by 286: it goes in 1 whole time(s) with a remainder of 81, giving the mixed number 1 81/286.
Working: 367/286 = 1 81/286

Step 6: Decimal & Percentage Representation
Dividing the numerator 367 by denominator 286 produces a repeating decimal (approximately 1.283217, or 128.3217%).
Working: 367 ÷ 286 = 1.283217 (128.3217%)

Key Values:
- Simplified Fraction: 367/286
- Mixed Number Form: 1 81/286
- Decimal Value: 1.283217
- Percentage: 128.3217%

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Solved with FractionsCalc:
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13/22 + 9/13 = 367/286

Simplified Fraction

367/286

Mixed Number

1 81/286

Decimal Value

1.283217

Percentage

128.3217%

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Step-by-Step Solution: 13/22 + 9/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 22 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 22 × 13 = 286.

LCD(22, 13) = 286

Step 2

Convert to Equivalent Fractions with Common Denominator 286

Multiply the numerator and denominator of 13/22 by 13, and multiply the numerator and denominator of 9/13 by 22 so both fractions share the common base 286.

13 × 13/22 × 13 = 169/286 and 9 × 22/13 × 22 = 198/286

Step 3

Add the Numerators

Now add the numerators (169 + 198 = 367) and keep the common denominator 286 unchanged.

169 + 198/286 = 367/286

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 367 and 286 is 1, confirming that 367/286 cannot be reduced further—it is already in its simplest irreducible form.

367/286

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (367) is greater than the denominator (286), divide 367 by 286: it goes in 1 whole time(s) with a remainder of 81, giving the mixed number 1 81/286.

367/286 = 181/286

Step 6

Decimal & Percentage Representation

Dividing the numerator 367 by denominator 286 produces a repeating decimal (approximately 1.283217, or 128.3217%).

367 ÷ 286 = 1.283217 (128.3217%)

Visual Representation

The diagram below illustrates 13/22 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`367/286`
Mixed Number Form	`1 81/286`
Decimal Form	`1.283217`
Percentage	`128.3217%`

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Frequently Asked Questions

What is 13/22 plus 9/13 as a fraction?

13/22 + 9/13 in simplest fraction form is 367/286 (or 1 81/286 as a mixed number).

What is 13/22 plus 9/13 as a decimal?

13/22 + 9/13 converted to a decimal is 1.283217.

What is 13/22 plus 9/13 as a percentage?

13/22 + 9/13 expressed as a percentage is 128.3217%.

How do you write 13/22 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 367/286 can be written as the mixed number 1 81/286.

Does 13/22 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.283217...) because the denominator contains prime factors other than 2 and 5.