What is 13/47 plus 5/13? (Answer: 404/611)

Exact Answer

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Problem: What is 13/47 plus 5/13?
Formula / Expression: 13/47 + 5/13
Final Answer: 404/611
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 47 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 47 × 13 = 611.
Working: LCD(47, 13) = 611

Step 2: Convert to Equivalent Fractions with Common Denominator 611
Multiply the numerator and denominator of 13/47 by 13, and multiply the numerator and denominator of 5/13 by 47 so both fractions share the common base 611.
Working: 13 × 13/47 × 13 = 169/611 and 5 × 47/13 × 47 = 235/611

Step 3: Add the Numerators
Now add the numerators (169 + 235 = 404) and keep the common denominator 611 unchanged.
Working: 169 + 235/611 = 404/611

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 404 and 611 is 1, confirming that 404/611 cannot be reduced further—it is already in its simplest irreducible form.
Working: 404/611

Step 5: Decimal & Percentage Representation
Dividing the numerator 404 by denominator 611 produces a repeating decimal (approximately 0.661211, or 66.1211%).
Working: 404 ÷ 611 = 0.661211 (66.1211%)

Key Values:
- Simplified Fraction: 404/611
- Mixed Number Form: 404/611
- Decimal Value: 0.661211
- Percentage: 66.1211%

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Solved with FractionsCalc:
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13/47 + 5/13 = 404/611

Simplified Fraction

404/611

Mixed Number

Proper (404/611)

Decimal Value

0.661211

Percentage

66.1211%

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Step-by-Step Solution: 13/47 + 5/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 47 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 47 × 13 = 611.

LCD(47, 13) = 611

Step 2

Convert to Equivalent Fractions with Common Denominator 611

Multiply the numerator and denominator of 13/47 by 13, and multiply the numerator and denominator of 5/13 by 47 so both fractions share the common base 611.

13 × 13/47 × 13 = 169/611 and 5 × 47/13 × 47 = 235/611

Step 3

Add the Numerators

Now add the numerators (169 + 235 = 404) and keep the common denominator 611 unchanged.

169 + 235/611 = 404/611

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 404 and 611 is 1, confirming that 404/611 cannot be reduced further—it is already in its simplest irreducible form.

404/611

Step 5

Decimal & Percentage Representation

Dividing the numerator 404 by denominator 611 produces a repeating decimal (approximately 0.661211, or 66.1211%).

404 ÷ 611 = 0.661211 (66.1211%)

Visual Representation

The diagram below illustrates 13/47 plus 5/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`404/611`
Mixed Number Form	`404/611`
Decimal Form	`0.661211`
Percentage	`66.1211%`

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Frequently Asked Questions

What is 13/47 plus 5/13 as a fraction?

13/47 + 5/13 in simplest fraction form is 404/611.

What is 13/47 plus 5/13 as a decimal?

13/47 + 5/13 converted to a decimal is 0.661211.

What is 13/47 plus 5/13 as a percentage?

13/47 + 5/13 expressed as a percentage is 66.1211%.

Does 13/47 plus 5/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.661211...) because the denominator contains prime factors other than 2 and 5.