What is 13/37 plus 9/13? (Answer: 502/481)

Exact Answer

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Problem: What is 13/37 plus 9/13?
Formula / Expression: 13/37 + 9/13
Final Answer: 1 21/481 (502/481)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 37 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 37 × 13 = 481.
Working: LCD(37, 13) = 481

Step 2: Convert to Equivalent Fractions with Common Denominator 481
Multiply the numerator and denominator of 13/37 by 13, and multiply the numerator and denominator of 9/13 by 37 so both fractions share the common base 481.
Working: 13 × 13/37 × 13 = 169/481 and 9 × 37/13 × 37 = 333/481

Step 3: Add the Numerators
Now add the numerators (169 + 333 = 502) and keep the common denominator 481 unchanged.
Working: 169 + 333/481 = 502/481

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 502 and 481 is 1, confirming that 502/481 cannot be reduced further—it is already in its simplest irreducible form.
Working: 502/481

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (502) is greater than the denominator (481), divide 502 by 481: it goes in 1 whole time(s) with a remainder of 21, giving the mixed number 1 21/481.
Working: 502/481 = 1 21/481

Step 6: Decimal & Percentage Representation
Dividing the numerator 502 by denominator 481 produces a repeating decimal (approximately 1.043659, or 104.3659%).
Working: 502 ÷ 481 = 1.043659 (104.3659%)

Key Values:
- Simplified Fraction: 502/481
- Mixed Number Form: 1 21/481
- Decimal Value: 1.043659
- Percentage: 104.3659%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-13-37-plus-9-13/
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13/37 + 9/13 = 502/481

Simplified Fraction

502/481

Mixed Number

1 21/481

Decimal Value

1.043659

Percentage

104.3659%

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Step-by-Step Solution: 13/37 + 9/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 37 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 37 × 13 = 481.

LCD(37, 13) = 481

Step 2

Convert to Equivalent Fractions with Common Denominator 481

Multiply the numerator and denominator of 13/37 by 13, and multiply the numerator and denominator of 9/13 by 37 so both fractions share the common base 481.

13 × 13/37 × 13 = 169/481 and 9 × 37/13 × 37 = 333/481

Step 3

Add the Numerators

Now add the numerators (169 + 333 = 502) and keep the common denominator 481 unchanged.

169 + 333/481 = 502/481

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 502 and 481 is 1, confirming that 502/481 cannot be reduced further—it is already in its simplest irreducible form.

502/481

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (502) is greater than the denominator (481), divide 502 by 481: it goes in 1 whole time(s) with a remainder of 21, giving the mixed number 1 21/481.

502/481 = 121/481

Step 6

Decimal & Percentage Representation

Dividing the numerator 502 by denominator 481 produces a repeating decimal (approximately 1.043659, or 104.3659%).

502 ÷ 481 = 1.043659 (104.3659%)

Visual Representation

The diagram below illustrates 13/37 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`502/481`
Mixed Number Form	`1 21/481`
Decimal Form	`1.043659`
Percentage	`104.3659%`

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Frequently Asked Questions

What is 13/37 plus 9/13 as a fraction?

13/37 + 9/13 in simplest fraction form is 502/481 (or 1 21/481 as a mixed number).

What is 13/37 plus 9/13 as a decimal?

13/37 + 9/13 converted to a decimal is 1.043659.

What is 13/37 plus 9/13 as a percentage?

13/37 + 9/13 expressed as a percentage is 104.3659%.

How do you write 13/37 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 502/481 can be written as the mixed number 1 21/481.

Does 13/37 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.043659...) because the denominator contains prime factors other than 2 and 5.