What is 5/11 plus 1/2? (Answer: 21/22)

Exact Answer

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Problem: What is 5/11 plus 1/2?
Formula / Expression: 5/11 + 1/2
Final Answer: 21/22
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 11 and 2 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 11 × 2 = 22.
Working: LCD(11, 2) = 22

Step 2: Convert to Equivalent Fractions with Common Denominator 22
Multiply the numerator and denominator of 5/11 by 2, and multiply the numerator and denominator of 1/2 by 11 so both fractions share the common base 22.
Working: 5 × 2/11 × 2 = 10/22 and 1 × 11/2 × 11 = 11/22

Step 3: Add the Numerators
Now add the numerators (10 + 11 = 21) and keep the common denominator 22 unchanged.
Working: 10 + 11/22 = 21/22

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 21 and 22 is 1, confirming that 21/22 cannot be reduced further—it is already in its simplest irreducible form.
Working: 21/22

Step 5: Decimal & Percentage Representation
Dividing the numerator 21 by denominator 22 produces a repeating decimal (approximately 0.954545, or 95.4545%).
Working: 21 ÷ 22 = 0.954545 (95.4545%)

Key Values:
- Simplified Fraction: 21/22
- Mixed Number Form: 21/22
- Decimal Value: 0.954545
- Percentage: 95.4545%

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5/11 + 1/2 = 21/22

Simplified Fraction

21/22

Mixed Number

Proper (21/22)

Decimal Value

0.954545

Percentage

95.4545%

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

Step 1

Find the Least Common Denominator (LCD)

The denominators 11 and 2 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 11 × 2 = 22.

LCD(11, 2) = 22

Step 2

Convert to Equivalent Fractions with Common Denominator 22

Multiply the numerator and denominator of 5/11 by 2, and multiply the numerator and denominator of 1/2 by 11 so both fractions share the common base 22.

5 × 2/11 × 2 = 10/22 and 1 × 11/2 × 11 = 11/22

Step 3

Add the Numerators

Now add the numerators (10 + 11 = 21) and keep the common denominator 22 unchanged.

10 + 11/22 = 21/22

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 21 and 22 is 1, confirming that 21/22 cannot be reduced further—it is already in its simplest irreducible form.

21/22

Step 5

Decimal & Percentage Representation

Dividing the numerator 21 by denominator 22 produces a repeating decimal (approximately 0.954545, or 95.4545%).

21 ÷ 22 = 0.954545 (95.4545%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`21/22`
Mixed Number Form	`21/22`
Decimal Form	`0.954545`
Percentage	`95.4545%`

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Frequently Asked Questions

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

5/11 + 1/2 in simplest fraction form is 21/22.

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

5/11 + 1/2 converted to a decimal is 0.954545.

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

5/11 + 1/2 expressed as a percentage is 95.4545%.

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

It results in a repeating decimal (approximately 0.954545...) because the denominator contains prime factors other than 2 and 5.