What is 9/37 plus 10/13? (Answer: 487/481)

Exact Answer

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Problem: What is 9/37 plus 10/13?
Formula / Expression: 9/37 + 10/13
Final Answer: 1 6/481 (487/481)
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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 9/37 by 13, and multiply the numerator and denominator of 10/13 by 37 so both fractions share the common base 481.
Working: 9 × 13/37 × 13 = 117/481 and 10 × 37/13 × 37 = 370/481

Step 3: Add the Numerators
Now add the numerators (117 + 370 = 487) and keep the common denominator 481 unchanged.
Working: 117 + 370/481 = 487/481

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 487 and 481 is 1, confirming that 487/481 cannot be reduced further—it is already in its simplest irreducible form.
Working: 487/481

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (487) is greater than the denominator (481), divide 487 by 481: it goes in 1 whole time(s) with a remainder of 6, giving the mixed number 1 6/481.
Working: 487/481 = 1 6/481

Step 6: Decimal & Percentage Representation
Dividing the numerator 487 by denominator 481 produces a repeating decimal (approximately 1.012474, or 101.2474%).
Working: 487 ÷ 481 = 1.012474 (101.2474%)

Key Values:
- Simplified Fraction: 487/481
- Mixed Number Form: 1 6/481
- Decimal Value: 1.012474
- Percentage: 101.2474%

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Solved with FractionsCalc:
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9/37 + 10/13 = 487/481

Simplified Fraction

487/481

Mixed Number

1 6/481

Decimal Value

1.012474

Percentage

101.2474%

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Step-by-Step Solution: 9/37 + 10/13

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 9/37 by 13, and multiply the numerator and denominator of 10/13 by 37 so both fractions share the common base 481.

9 × 13/37 × 13 = 117/481 and 10 × 37/13 × 37 = 370/481

Step 3

Add the Numerators

Now add the numerators (117 + 370 = 487) and keep the common denominator 481 unchanged.

117 + 370/481 = 487/481

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 487 and 481 is 1, confirming that 487/481 cannot be reduced further—it is already in its simplest irreducible form.

487/481

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (487) is greater than the denominator (481), divide 487 by 481: it goes in 1 whole time(s) with a remainder of 6, giving the mixed number 1 6/481.

487/481 = 16/481

Step 6

Decimal & Percentage Representation

Dividing the numerator 487 by denominator 481 produces a repeating decimal (approximately 1.012474, or 101.2474%).

487 ÷ 481 = 1.012474 (101.2474%)

Visual Representation

The diagram below illustrates 9/37 plus 10/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`487/481`
Mixed Number Form	`1 6/481`
Decimal Form	`1.012474`
Percentage	`101.2474%`

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Frequently Asked Questions

What is 9/37 plus 10/13 as a fraction?

9/37 + 10/13 in simplest fraction form is 487/481 (or 1 6/481 as a mixed number).

What is 9/37 plus 10/13 as a decimal?

9/37 + 10/13 converted to a decimal is 1.012474.

What is 9/37 plus 10/13 as a percentage?

9/37 + 10/13 expressed as a percentage is 101.2474%.

How do you write 9/37 plus 10/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 487/481 can be written as the mixed number 1 6/481.

Does 9/37 plus 10/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.012474...) because the denominator contains prime factors other than 2 and 5.