What is 13/25 plus 9/13? (Answer: 394/325)

Exact Answer

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Problem: What is 13/25 plus 9/13?
Formula / Expression: 13/25 + 9/13
Final Answer: 1 69/325 (394/325)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 25 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 25 × 13 = 325.
Working: LCD(25, 13) = 325

Step 2: Convert to Equivalent Fractions with Common Denominator 325
Multiply the numerator and denominator of 13/25 by 13, and multiply the numerator and denominator of 9/13 by 25 so both fractions share the common base 325.
Working: 13 × 13/25 × 13 = 169/325 and 9 × 25/13 × 25 = 225/325

Step 3: Add the Numerators
Now add the numerators (169 + 225 = 394) and keep the common denominator 325 unchanged.
Working: 169 + 225/325 = 394/325

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 394 and 325 is 1, confirming that 394/325 cannot be reduced further—it is already in its simplest irreducible form.
Working: 394/325

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (394) is greater than the denominator (325), divide 394 by 325: it goes in 1 whole time(s) with a remainder of 69, giving the mixed number 1 69/325.
Working: 394/325 = 1 69/325

Step 6: Decimal & Percentage Representation
Dividing the numerator 394 by denominator 325 produces a repeating decimal (approximately 1.212308, or 121.2308%).
Working: 394 ÷ 325 = 1.212308 (121.2308%)

Key Values:
- Simplified Fraction: 394/325
- Mixed Number Form: 1 69/325
- Decimal Value: 1.212308
- Percentage: 121.2308%

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Solved with FractionsCalc:
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13/25 + 9/13 = 394/325

Simplified Fraction

394/325

Mixed Number

1 69/325

Decimal Value

1.212308

Percentage

121.2308%

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Step-by-Step Solution: 13/25 + 9/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 25 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 25 × 13 = 325.

LCD(25, 13) = 325

Step 2

Convert to Equivalent Fractions with Common Denominator 325

Multiply the numerator and denominator of 13/25 by 13, and multiply the numerator and denominator of 9/13 by 25 so both fractions share the common base 325.

13 × 13/25 × 13 = 169/325 and 9 × 25/13 × 25 = 225/325

Step 3

Add the Numerators

Now add the numerators (169 + 225 = 394) and keep the common denominator 325 unchanged.

169 + 225/325 = 394/325

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 394 and 325 is 1, confirming that 394/325 cannot be reduced further—it is already in its simplest irreducible form.

394/325

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (394) is greater than the denominator (325), divide 394 by 325: it goes in 1 whole time(s) with a remainder of 69, giving the mixed number 1 69/325.

394/325 = 169/325

Step 6

Decimal & Percentage Representation

Dividing the numerator 394 by denominator 325 produces a repeating decimal (approximately 1.212308, or 121.2308%).

394 ÷ 325 = 1.212308 (121.2308%)

Visual Representation

The diagram below illustrates 13/25 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`394/325`
Mixed Number Form	`1 69/325`
Decimal Form	`1.212308`
Percentage	`121.2308%`

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Frequently Asked Questions

What is 13/25 plus 9/13 as a fraction?

13/25 + 9/13 in simplest fraction form is 394/325 (or 1 69/325 as a mixed number).

What is 13/25 plus 9/13 as a decimal?

13/25 + 9/13 converted to a decimal is 1.212308.

What is 13/25 plus 9/13 as a percentage?

13/25 + 9/13 expressed as a percentage is 121.2308%.

How do you write 13/25 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 394/325 can be written as the mixed number 1 69/325.

Does 13/25 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.212308...) because the denominator contains prime factors other than 2 and 5.