What is 12/37 plus 9/13? (Answer: 489/481)

Exact Answer

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Problem: What is 12/37 plus 9/13?
Formula / Expression: 12/37 + 9/13
Final Answer: 1 8/481 (489/481)
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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 12/37 by 13, and multiply the numerator and denominator of 9/13 by 37 so both fractions share the common base 481.
Working: 12 × 13/37 × 13 = 156/481 and 9 × 37/13 × 37 = 333/481

Step 3: Add the Numerators
Now add the numerators (156 + 333 = 489) and keep the common denominator 481 unchanged.
Working: 156 + 333/481 = 489/481

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 489 and 481 is 1, confirming that 489/481 cannot be reduced further—it is already in its simplest irreducible form.
Working: 489/481

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (489) is greater than the denominator (481), divide 489 by 481: it goes in 1 whole time(s) with a remainder of 8, giving the mixed number 1 8/481.
Working: 489/481 = 1 8/481

Step 6: Decimal & Percentage Representation
Dividing the numerator 489 by denominator 481 produces a repeating decimal (approximately 1.016632, or 101.6632%).
Working: 489 ÷ 481 = 1.016632 (101.6632%)

Key Values:
- Simplified Fraction: 489/481
- Mixed Number Form: 1 8/481
- Decimal Value: 1.016632
- Percentage: 101.6632%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-12-37-plus-9-13/
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12/37 + 9/13 = 489/481

Simplified Fraction

489/481

Mixed Number

1 8/481

Decimal Value

1.016632

Percentage

101.6632%

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Step-by-Step Solution: 12/37 + 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 12/37 by 13, and multiply the numerator and denominator of 9/13 by 37 so both fractions share the common base 481.

12 × 13/37 × 13 = 156/481 and 9 × 37/13 × 37 = 333/481

Step 3

Add the Numerators

Now add the numerators (156 + 333 = 489) and keep the common denominator 481 unchanged.

156 + 333/481 = 489/481

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 489 and 481 is 1, confirming that 489/481 cannot be reduced further—it is already in its simplest irreducible form.

489/481

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (489) is greater than the denominator (481), divide 489 by 481: it goes in 1 whole time(s) with a remainder of 8, giving the mixed number 1 8/481.

489/481 = 18/481

Step 6

Decimal & Percentage Representation

Dividing the numerator 489 by denominator 481 produces a repeating decimal (approximately 1.016632, or 101.6632%).

489 ÷ 481 = 1.016632 (101.6632%)

Visual Representation

The diagram below illustrates 12/37 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`489/481`
Mixed Number Form	`1 8/481`
Decimal Form	`1.016632`
Percentage	`101.6632%`

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Frequently Asked Questions

What is 12/37 plus 9/13 as a fraction?

12/37 + 9/13 in simplest fraction form is 489/481 (or 1 8/481 as a mixed number).

What is 12/37 plus 9/13 as a decimal?

12/37 + 9/13 converted to a decimal is 1.016632.

What is 12/37 plus 9/13 as a percentage?

12/37 + 9/13 expressed as a percentage is 101.6632%.

How do you write 12/37 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 489/481 can be written as the mixed number 1 8/481.

Does 12/37 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.016632...) because the denominator contains prime factors other than 2 and 5.