What is 3/37 plus 5/13? (Answer: 224/481)

Exact Answer

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Problem: What is 3/37 plus 5/13?
Formula / Expression: 3/37 + 5/13
Final Answer: 224/481
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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 3/37 by 13, and multiply the numerator and denominator of 5/13 by 37 so both fractions share the common base 481.
Working: 3 × 13/37 × 13 = 39/481 and 5 × 37/13 × 37 = 185/481

Step 3: Add the Numerators
Now add the numerators (39 + 185 = 224) and keep the common denominator 481 unchanged.
Working: 39 + 185/481 = 224/481

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 224 and 481 is 1, confirming that 224/481 cannot be reduced further—it is already in its simplest irreducible form.
Working: 224/481

Step 5: Decimal & Percentage Representation
Dividing the numerator 224 by denominator 481 produces a repeating decimal (approximately 0.465696, or 46.5696%).
Working: 224 ÷ 481 = 0.465696 (46.5696%)

Key Values:
- Simplified Fraction: 224/481
- Mixed Number Form: 224/481
- Decimal Value: 0.465696
- Percentage: 46.5696%

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Solved with FractionsCalc:
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3/37 + 5/13 = 224/481

Simplified Fraction

224/481

Mixed Number

Proper (224/481)

Decimal Value

0.465696

Percentage

46.5696%

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Step-by-Step Solution: 3/37 + 5/13

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 3/37 by 13, and multiply the numerator and denominator of 5/13 by 37 so both fractions share the common base 481.

3 × 13/37 × 13 = 39/481 and 5 × 37/13 × 37 = 185/481

Step 3

Add the Numerators

Now add the numerators (39 + 185 = 224) and keep the common denominator 481 unchanged.

39 + 185/481 = 224/481

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 224 and 481 is 1, confirming that 224/481 cannot be reduced further—it is already in its simplest irreducible form.

224/481

Step 5

Decimal & Percentage Representation

Dividing the numerator 224 by denominator 481 produces a repeating decimal (approximately 0.465696, or 46.5696%).

224 ÷ 481 = 0.465696 (46.5696%)

Visual Representation

The diagram below illustrates 3/37 plus 5/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`224/481`
Mixed Number Form	`224/481`
Decimal Form	`0.465696`
Percentage	`46.5696%`

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Frequently Asked Questions

What is 3/37 plus 5/13 as a fraction?

3/37 + 5/13 in simplest fraction form is 224/481.

What is 3/37 plus 5/13 as a decimal?

3/37 + 5/13 converted to a decimal is 0.465696.

What is 3/37 plus 5/13 as a percentage?

3/37 + 5/13 expressed as a percentage is 46.5696%.

Does 3/37 plus 5/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.465696...) because the denominator contains prime factors other than 2 and 5.