What is 13/23 plus 9/13? (Answer: 376/299)

Exact Answer

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Problem: What is 13/23 plus 9/13?
Formula / Expression: 13/23 + 9/13
Final Answer: 1 77/299 (376/299)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 23 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 13 = 299.
Working: LCD(23, 13) = 299

Step 2: Convert to Equivalent Fractions with Common Denominator 299
Multiply the numerator and denominator of 13/23 by 13, and multiply the numerator and denominator of 9/13 by 23 so both fractions share the common base 299.
Working: 13 × 13/23 × 13 = 169/299 and 9 × 23/13 × 23 = 207/299

Step 3: Add the Numerators
Now add the numerators (169 + 207 = 376) and keep the common denominator 299 unchanged.
Working: 169 + 207/299 = 376/299

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 376 and 299 is 1, confirming that 376/299 cannot be reduced further—it is already in its simplest irreducible form.
Working: 376/299

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (376) is greater than the denominator (299), divide 376 by 299: it goes in 1 whole time(s) with a remainder of 77, giving the mixed number 1 77/299.
Working: 376/299 = 1 77/299

Step 6: Decimal & Percentage Representation
Dividing the numerator 376 by denominator 299 produces a repeating decimal (approximately 1.257525, or 125.7525%).
Working: 376 ÷ 299 = 1.257525 (125.7525%)

Key Values:
- Simplified Fraction: 376/299
- Mixed Number Form: 1 77/299
- Decimal Value: 1.257525
- Percentage: 125.7525%

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Solved with FractionsCalc:
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13/23 + 9/13 = 376/299

Simplified Fraction

376/299

Mixed Number

1 77/299

Decimal Value

1.257525

Percentage

125.7525%

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Step-by-Step Solution: 13/23 + 9/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 23 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 13 = 299.

LCD(23, 13) = 299

Step 2

Convert to Equivalent Fractions with Common Denominator 299

Multiply the numerator and denominator of 13/23 by 13, and multiply the numerator and denominator of 9/13 by 23 so both fractions share the common base 299.

13 × 13/23 × 13 = 169/299 and 9 × 23/13 × 23 = 207/299

Step 3

Add the Numerators

Now add the numerators (169 + 207 = 376) and keep the common denominator 299 unchanged.

169 + 207/299 = 376/299

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 376 and 299 is 1, confirming that 376/299 cannot be reduced further—it is already in its simplest irreducible form.

376/299

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (376) is greater than the denominator (299), divide 376 by 299: it goes in 1 whole time(s) with a remainder of 77, giving the mixed number 1 77/299.

376/299 = 177/299

Step 6

Decimal & Percentage Representation

Dividing the numerator 376 by denominator 299 produces a repeating decimal (approximately 1.257525, or 125.7525%).

376 ÷ 299 = 1.257525 (125.7525%)

Visual Representation

The diagram below illustrates 13/23 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`376/299`
Mixed Number Form	`1 77/299`
Decimal Form	`1.257525`
Percentage	`125.7525%`

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Frequently Asked Questions

What is 13/23 plus 9/13 as a fraction?

13/23 + 9/13 in simplest fraction form is 376/299 (or 1 77/299 as a mixed number).

What is 13/23 plus 9/13 as a decimal?

13/23 + 9/13 converted to a decimal is 1.257525.

What is 13/23 plus 9/13 as a percentage?

13/23 + 9/13 expressed as a percentage is 125.7525%.

How do you write 13/23 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 376/299 can be written as the mixed number 1 77/299.

Does 13/23 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.257525...) because the denominator contains prime factors other than 2 and 5.