What is 13/20 plus 9/13? (Answer: 349/260)

Exact Answer

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Problem: What is 13/20 plus 9/13?
Formula / Expression: 13/20 + 9/13
Final Answer: 1 89/260 (349/260)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 20 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 20 × 13 = 260.
Working: LCD(20, 13) = 260

Step 2: Convert to Equivalent Fractions with Common Denominator 260
Multiply the numerator and denominator of 13/20 by 13, and multiply the numerator and denominator of 9/13 by 20 so both fractions share the common base 260.
Working: 13 × 13/20 × 13 = 169/260 and 9 × 20/13 × 20 = 180/260

Step 3: Add the Numerators
Now add the numerators (169 + 180 = 349) and keep the common denominator 260 unchanged.
Working: 169 + 180/260 = 349/260

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 349 and 260 is 1, confirming that 349/260 cannot be reduced further—it is already in its simplest irreducible form.
Working: 349/260

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (349) is greater than the denominator (260), divide 349 by 260: it goes in 1 whole time(s) with a remainder of 89, giving the mixed number 1 89/260.
Working: 349/260 = 1 89/260

Step 6: Decimal & Percentage Representation
Dividing the numerator 349 by denominator 260 produces a repeating decimal (approximately 1.342308, or 134.2308%).
Working: 349 ÷ 260 = 1.342308 (134.2308%)

Key Values:
- Simplified Fraction: 349/260
- Mixed Number Form: 1 89/260
- Decimal Value: 1.342308
- Percentage: 134.2308%

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Solved with FractionsCalc:
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13/20 + 9/13 = 349/260

Simplified Fraction

349/260

Mixed Number

1 89/260

Decimal Value

1.342308

Percentage

134.2308%

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Step-by-Step Solution: 13/20 + 9/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 20 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 20 × 13 = 260.

LCD(20, 13) = 260

Step 2

Convert to Equivalent Fractions with Common Denominator 260

Multiply the numerator and denominator of 13/20 by 13, and multiply the numerator and denominator of 9/13 by 20 so both fractions share the common base 260.

13 × 13/20 × 13 = 169/260 and 9 × 20/13 × 20 = 180/260

Step 3

Add the Numerators

Now add the numerators (169 + 180 = 349) and keep the common denominator 260 unchanged.

169 + 180/260 = 349/260

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 349 and 260 is 1, confirming that 349/260 cannot be reduced further—it is already in its simplest irreducible form.

349/260

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (349) is greater than the denominator (260), divide 349 by 260: it goes in 1 whole time(s) with a remainder of 89, giving the mixed number 1 89/260.

349/260 = 189/260

Step 6

Decimal & Percentage Representation

Dividing the numerator 349 by denominator 260 produces a repeating decimal (approximately 1.342308, or 134.2308%).

349 ÷ 260 = 1.342308 (134.2308%)

Visual Representation

The diagram below illustrates 13/20 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`349/260`
Mixed Number Form	`1 89/260`
Decimal Form	`1.342308`
Percentage	`134.2308%`

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Frequently Asked Questions

What is 13/20 plus 9/13 as a fraction?

13/20 + 9/13 in simplest fraction form is 349/260 (or 1 89/260 as a mixed number).

What is 13/20 plus 9/13 as a decimal?

13/20 + 9/13 converted to a decimal is 1.342308.

What is 13/20 plus 9/13 as a percentage?

13/20 + 9/13 expressed as a percentage is 134.2308%.

How do you write 13/20 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 349/260 can be written as the mixed number 1 89/260.

Does 13/20 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.342308...) because the denominator contains prime factors other than 2 and 5.