What is 2/11 plus 1/5? (Answer: 21/55)

Exact Answer

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Problem: What is 2/11 plus 1/5?
Formula / Expression: 2/11 + 1/5
Final Answer: 21/55
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 11 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 11 × 5 = 55.
Working: LCD(11, 5) = 55

Step 2: Convert to Equivalent Fractions with Common Denominator 55
Multiply the numerator and denominator of 2/11 by 5, and multiply the numerator and denominator of 1/5 by 11 so both fractions share the common base 55.
Working: 2 × 5/11 × 5 = 10/55 and 1 × 11/5 × 11 = 11/55

Step 3: Add the Numerators
Now add the numerators (10 + 11 = 21) and keep the common denominator 55 unchanged.
Working: 10 + 11/55 = 21/55

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 21 and 55 is 1, confirming that 21/55 cannot be reduced further—it is already in its simplest irreducible form.
Working: 21/55

Step 5: Decimal & Percentage Representation
Dividing the numerator 21 by denominator 55 produces a repeating decimal (approximately 0.381818, or 38.1818%).
Working: 21 ÷ 55 = 0.381818 (38.1818%)

Key Values:
- Simplified Fraction: 21/55
- Mixed Number Form: 21/55
- Decimal Value: 0.381818
- Percentage: 38.1818%

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Solved with FractionsCalc:
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2/11 + 1/5 = 21/55

Simplified Fraction

21/55

Mixed Number

Proper (21/55)

Decimal Value

0.381818

Percentage

38.1818%

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Step-by-Step Solution: 2/11 + 1/5

Step 1

Find the Least Common Denominator (LCD)

The denominators 11 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 11 × 5 = 55.

LCD(11, 5) = 55

Step 2

Convert to Equivalent Fractions with Common Denominator 55

Multiply the numerator and denominator of 2/11 by 5, and multiply the numerator and denominator of 1/5 by 11 so both fractions share the common base 55.

2 × 5/11 × 5 = 10/55 and 1 × 11/5 × 11 = 11/55

Step 3

Add the Numerators

Now add the numerators (10 + 11 = 21) and keep the common denominator 55 unchanged.

10 + 11/55 = 21/55

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 21 and 55 is 1, confirming that 21/55 cannot be reduced further—it is already in its simplest irreducible form.

21/55

Step 5

Decimal & Percentage Representation

Dividing the numerator 21 by denominator 55 produces a repeating decimal (approximately 0.381818, or 38.1818%).

21 ÷ 55 = 0.381818 (38.1818%)

Visual Representation

The diagram below illustrates 2/11 plus 1/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`21/55`
Mixed Number Form	`21/55`
Decimal Form	`0.381818`
Percentage	`38.1818%`

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Frequently Asked Questions

What is 2/11 plus 1/5 as a fraction?

2/11 + 1/5 in simplest fraction form is 21/55.

What is 2/11 plus 1/5 as a decimal?

2/11 + 1/5 converted to a decimal is 0.381818.

What is 2/11 plus 1/5 as a percentage?

2/11 + 1/5 expressed as a percentage is 38.1818%.

Does 2/11 plus 1/5 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.381818...) because the denominator contains prime factors other than 2 and 5.