What is 13/36 plus 9/13? (Answer: 493/468)

Exact Answer

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Problem: What is 13/36 plus 9/13?
Formula / Expression: 13/36 + 9/13
Final Answer: 1 25/468 (493/468)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 36 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 36 × 13 = 468.
Working: LCD(36, 13) = 468

Step 2: Convert to Equivalent Fractions with Common Denominator 468
Multiply the numerator and denominator of 13/36 by 13, and multiply the numerator and denominator of 9/13 by 36 so both fractions share the common base 468.
Working: 13 × 13/36 × 13 = 169/468 and 9 × 36/13 × 36 = 324/468

Step 3: Add the Numerators
Now add the numerators (169 + 324 = 493) and keep the common denominator 468 unchanged.
Working: 169 + 324/468 = 493/468

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 493 and 468 is 1, confirming that 493/468 cannot be reduced further—it is already in its simplest irreducible form.
Working: 493/468

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (493) is greater than the denominator (468), divide 493 by 468: it goes in 1 whole time(s) with a remainder of 25, giving the mixed number 1 25/468.
Working: 493/468 = 1 25/468

Step 6: Decimal & Percentage Representation
Dividing the numerator 493 by denominator 468 produces a repeating decimal (approximately 1.053419, or 105.3419%).
Working: 493 ÷ 468 = 1.053419 (105.3419%)

Key Values:
- Simplified Fraction: 493/468
- Mixed Number Form: 1 25/468
- Decimal Value: 1.053419
- Percentage: 105.3419%

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Solved with FractionsCalc:
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13/36 + 9/13 = 493/468

Simplified Fraction

493/468

Mixed Number

1 25/468

Decimal Value

1.053419

Percentage

105.3419%

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Step-by-Step Solution: 13/36 + 9/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 36 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 36 × 13 = 468.

LCD(36, 13) = 468

Step 2

Convert to Equivalent Fractions with Common Denominator 468

Multiply the numerator and denominator of 13/36 by 13, and multiply the numerator and denominator of 9/13 by 36 so both fractions share the common base 468.

13 × 13/36 × 13 = 169/468 and 9 × 36/13 × 36 = 324/468

Step 3

Add the Numerators

Now add the numerators (169 + 324 = 493) and keep the common denominator 468 unchanged.

169 + 324/468 = 493/468

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 493 and 468 is 1, confirming that 493/468 cannot be reduced further—it is already in its simplest irreducible form.

493/468

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (493) is greater than the denominator (468), divide 493 by 468: it goes in 1 whole time(s) with a remainder of 25, giving the mixed number 1 25/468.

493/468 = 125/468

Step 6

Decimal & Percentage Representation

Dividing the numerator 493 by denominator 468 produces a repeating decimal (approximately 1.053419, or 105.3419%).

493 ÷ 468 = 1.053419 (105.3419%)

Visual Representation

The diagram below illustrates 13/36 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`493/468`
Mixed Number Form	`1 25/468`
Decimal Form	`1.053419`
Percentage	`105.3419%`

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Frequently Asked Questions

What is 13/36 plus 9/13 as a fraction?

13/36 + 9/13 in simplest fraction form is 493/468 (or 1 25/468 as a mixed number).

What is 13/36 plus 9/13 as a decimal?

13/36 + 9/13 converted to a decimal is 1.053419.

What is 13/36 plus 9/13 as a percentage?

13/36 + 9/13 expressed as a percentage is 105.3419%.

How do you write 13/36 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 493/468 can be written as the mixed number 1 25/468.

Does 13/36 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.053419...) because the denominator contains prime factors other than 2 and 5.