What is 2/37 plus 11/13? (Answer: 433/481)

Exact Answer

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Problem: What is 2/37 plus 11/13?
Formula / Expression: 2/37 + 11/13
Final Answer: 433/481
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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 2/37 by 13, and multiply the numerator and denominator of 11/13 by 37 so both fractions share the common base 481.
Working: 2 × 13/37 × 13 = 26/481 and 11 × 37/13 × 37 = 407/481

Step 3: Add the Numerators
Now add the numerators (26 + 407 = 433) and keep the common denominator 481 unchanged.
Working: 26 + 407/481 = 433/481

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 433 and 481 is 1, confirming that 433/481 cannot be reduced further—it is already in its simplest irreducible form.
Working: 433/481

Step 5: Decimal & Percentage Representation
Dividing the numerator 433 by denominator 481 produces a repeating decimal (approximately 0.900208, or 90.0208%).
Working: 433 ÷ 481 = 0.900208 (90.0208%)

Key Values:
- Simplified Fraction: 433/481
- Mixed Number Form: 433/481
- Decimal Value: 0.900208
- Percentage: 90.0208%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-37-plus-11-13/
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2/37 + 11/13 = 433/481

Simplified Fraction

433/481

Mixed Number

Proper (433/481)

Decimal Value

0.900208

Percentage

90.0208%

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Step-by-Step Solution: 2/37 + 11/13

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 2/37 by 13, and multiply the numerator and denominator of 11/13 by 37 so both fractions share the common base 481.

2 × 13/37 × 13 = 26/481 and 11 × 37/13 × 37 = 407/481

Step 3

Add the Numerators

Now add the numerators (26 + 407 = 433) and keep the common denominator 481 unchanged.

26 + 407/481 = 433/481

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 433 and 481 is 1, confirming that 433/481 cannot be reduced further—it is already in its simplest irreducible form.

433/481

Step 5

Decimal & Percentage Representation

Dividing the numerator 433 by denominator 481 produces a repeating decimal (approximately 0.900208, or 90.0208%).

433 ÷ 481 = 0.900208 (90.0208%)

Visual Representation

The diagram below illustrates 2/37 plus 11/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`433/481`
Mixed Number Form	`433/481`
Decimal Form	`0.900208`
Percentage	`90.0208%`

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Frequently Asked Questions

What is 2/37 plus 11/13 as a fraction?

2/37 + 11/13 in simplest fraction form is 433/481.

What is 2/37 plus 11/13 as a decimal?

2/37 + 11/13 converted to a decimal is 0.900208.

What is 2/37 plus 11/13 as a percentage?

2/37 + 11/13 expressed as a percentage is 90.0208%.

Does 2/37 plus 11/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.900208...) because the denominator contains prime factors other than 2 and 5.