What is 13/19 plus 9/13? (Answer: 340/247)

Exact Answer

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Problem: What is 13/19 plus 9/13?
Formula / Expression: 13/19 + 9/13
Final Answer: 1 93/247 (340/247)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 19 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 19 × 13 = 247.
Working: LCD(19, 13) = 247

Step 2: Convert to Equivalent Fractions with Common Denominator 247
Multiply the numerator and denominator of 13/19 by 13, and multiply the numerator and denominator of 9/13 by 19 so both fractions share the common base 247.
Working: 13 × 13/19 × 13 = 169/247 and 9 × 19/13 × 19 = 171/247

Step 3: Add the Numerators
Now add the numerators (169 + 171 = 340) and keep the common denominator 247 unchanged.
Working: 169 + 171/247 = 340/247

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 340 and 247 is 1, confirming that 340/247 cannot be reduced further—it is already in its simplest irreducible form.
Working: 340/247

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (340) is greater than the denominator (247), divide 340 by 247: it goes in 1 whole time(s) with a remainder of 93, giving the mixed number 1 93/247.
Working: 340/247 = 1 93/247

Step 6: Decimal & Percentage Representation
Dividing the numerator 340 by denominator 247 produces a repeating decimal (approximately 1.376518, or 137.6518%).
Working: 340 ÷ 247 = 1.376518 (137.6518%)

Key Values:
- Simplified Fraction: 340/247
- Mixed Number Form: 1 93/247
- Decimal Value: 1.376518
- Percentage: 137.6518%

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Solved with FractionsCalc:
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13/19 + 9/13 = 340/247

Simplified Fraction

340/247

Mixed Number

1 93/247

Decimal Value

1.376518

Percentage

137.6518%

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Step-by-Step Solution: 13/19 + 9/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 19 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 19 × 13 = 247.

LCD(19, 13) = 247

Step 2

Convert to Equivalent Fractions with Common Denominator 247

Multiply the numerator and denominator of 13/19 by 13, and multiply the numerator and denominator of 9/13 by 19 so both fractions share the common base 247.

13 × 13/19 × 13 = 169/247 and 9 × 19/13 × 19 = 171/247

Step 3

Add the Numerators

Now add the numerators (169 + 171 = 340) and keep the common denominator 247 unchanged.

169 + 171/247 = 340/247

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 340 and 247 is 1, confirming that 340/247 cannot be reduced further—it is already in its simplest irreducible form.

340/247

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (340) is greater than the denominator (247), divide 340 by 247: it goes in 1 whole time(s) with a remainder of 93, giving the mixed number 1 93/247.

340/247 = 193/247

Step 6

Decimal & Percentage Representation

Dividing the numerator 340 by denominator 247 produces a repeating decimal (approximately 1.376518, or 137.6518%).

340 ÷ 247 = 1.376518 (137.6518%)

Visual Representation

The diagram below illustrates 13/19 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`340/247`
Mixed Number Form	`1 93/247`
Decimal Form	`1.376518`
Percentage	`137.6518%`

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Frequently Asked Questions

What is 13/19 plus 9/13 as a fraction?

13/19 + 9/13 in simplest fraction form is 340/247 (or 1 93/247 as a mixed number).

What is 13/19 plus 9/13 as a decimal?

13/19 + 9/13 converted to a decimal is 1.376518.

What is 13/19 plus 9/13 as a percentage?

13/19 + 9/13 expressed as a percentage is 137.6518%.

How do you write 13/19 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 340/247 can be written as the mixed number 1 93/247.

Does 13/19 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.376518...) because the denominator contains prime factors other than 2 and 5.