What is 2/17 plus 11/13? (Answer: 213/221)

Exact Answer

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Problem: What is 2/17 plus 11/13?
Formula / Expression: 2/17 + 11/13
Final Answer: 213/221
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 17 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 17 × 13 = 221.
Working: LCD(17, 13) = 221

Step 2: Convert to Equivalent Fractions with Common Denominator 221
Multiply the numerator and denominator of 2/17 by 13, and multiply the numerator and denominator of 11/13 by 17 so both fractions share the common base 221.
Working: 2 × 13/17 × 13 = 26/221 and 11 × 17/13 × 17 = 187/221

Step 3: Add the Numerators
Now add the numerators (26 + 187 = 213) and keep the common denominator 221 unchanged.
Working: 26 + 187/221 = 213/221

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 213 and 221 is 1, confirming that 213/221 cannot be reduced further—it is already in its simplest irreducible form.
Working: 213/221

Step 5: Decimal & Percentage Representation
Dividing the numerator 213 by denominator 221 produces a repeating decimal (approximately 0.963801, or 96.3801%).
Working: 213 ÷ 221 = 0.963801 (96.3801%)

Key Values:
- Simplified Fraction: 213/221
- Mixed Number Form: 213/221
- Decimal Value: 0.963801
- Percentage: 96.3801%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-17-plus-11-13/
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2/17 + 11/13 = 213/221

Simplified Fraction

213/221

Mixed Number

Proper (213/221)

Decimal Value

0.963801

Percentage

96.3801%

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Step-by-Step Solution: 2/17 + 11/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 17 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 17 × 13 = 221.

LCD(17, 13) = 221

Step 2

Convert to Equivalent Fractions with Common Denominator 221

Multiply the numerator and denominator of 2/17 by 13, and multiply the numerator and denominator of 11/13 by 17 so both fractions share the common base 221.

2 × 13/17 × 13 = 26/221 and 11 × 17/13 × 17 = 187/221

Step 3

Add the Numerators

Now add the numerators (26 + 187 = 213) and keep the common denominator 221 unchanged.

26 + 187/221 = 213/221

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 213 and 221 is 1, confirming that 213/221 cannot be reduced further—it is already in its simplest irreducible form.

213/221

Step 5

Decimal & Percentage Representation

Dividing the numerator 213 by denominator 221 produces a repeating decimal (approximately 0.963801, or 96.3801%).

213 ÷ 221 = 0.963801 (96.3801%)

Visual Representation

The diagram below illustrates 2/17 plus 11/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`213/221`
Mixed Number Form	`213/221`
Decimal Form	`0.963801`
Percentage	`96.3801%`

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Frequently Asked Questions

What is 2/17 plus 11/13 as a fraction?

2/17 + 11/13 in simplest fraction form is 213/221.

What is 2/17 plus 11/13 as a decimal?

2/17 + 11/13 converted to a decimal is 0.963801.

What is 2/17 plus 11/13 as a percentage?

2/17 + 11/13 expressed as a percentage is 96.3801%.

Does 2/17 plus 11/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.963801...) because the denominator contains prime factors other than 2 and 5.