What is 3/47 plus 2/13? (Answer: 133/611)

Exact Answer

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Problem: What is 3/47 plus 2/13?
Formula / Expression: 3/47 + 2/13
Final Answer: 133/611
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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 3/47 by 13, and multiply the numerator and denominator of 2/13 by 47 so both fractions share the common base 611.
Working: 3 × 13/47 × 13 = 39/611 and 2 × 47/13 × 47 = 94/611

Step 3: Add the Numerators
Now add the numerators (39 + 94 = 133) and keep the common denominator 611 unchanged.
Working: 39 + 94/611 = 133/611

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 133 and 611 is 1, confirming that 133/611 cannot be reduced further—it is already in its simplest irreducible form.
Working: 133/611

Step 5: Decimal & Percentage Representation
Dividing the numerator 133 by denominator 611 produces a repeating decimal (approximately 0.217676, or 21.7676%).
Working: 133 ÷ 611 = 0.217676 (21.7676%)

Key Values:
- Simplified Fraction: 133/611
- Mixed Number Form: 133/611
- Decimal Value: 0.217676
- Percentage: 21.7676%

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Solved with FractionsCalc:
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3/47 + 2/13 = 133/611

Simplified Fraction

133/611

Mixed Number

Proper (133/611)

Decimal Value

0.217676

Percentage

21.7676%

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Step-by-Step Solution: 3/47 + 2/13

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 3/47 by 13, and multiply the numerator and denominator of 2/13 by 47 so both fractions share the common base 611.

3 × 13/47 × 13 = 39/611 and 2 × 47/13 × 47 = 94/611

Step 3

Add the Numerators

Now add the numerators (39 + 94 = 133) and keep the common denominator 611 unchanged.

39 + 94/611 = 133/611

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 133 and 611 is 1, confirming that 133/611 cannot be reduced further—it is already in its simplest irreducible form.

133/611

Step 5

Decimal & Percentage Representation

Dividing the numerator 133 by denominator 611 produces a repeating decimal (approximately 0.217676, or 21.7676%).

133 ÷ 611 = 0.217676 (21.7676%)

Visual Representation

The diagram below illustrates 3/47 plus 2/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`133/611`
Mixed Number Form	`133/611`
Decimal Form	`0.217676`
Percentage	`21.7676%`

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Frequently Asked Questions

What is 3/47 plus 2/13 as a fraction?

3/47 + 2/13 in simplest fraction form is 133/611.

What is 3/47 plus 2/13 as a decimal?

3/47 + 2/13 converted to a decimal is 0.217676.

What is 3/47 plus 2/13 as a percentage?

3/47 + 2/13 expressed as a percentage is 21.7676%.

Does 3/47 plus 2/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.217676...) because the denominator contains prime factors other than 2 and 5.