What is 3/11 plus 1/2? (Answer: 17/22)

Exact Answer

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Problem: What is 3/11 plus 1/2?
Formula / Expression: 3/11 + 1/2
Final Answer: 17/22
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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 3/11 by 2, and multiply the numerator and denominator of 1/2 by 11 so both fractions share the common base 22.
Working: 3 × 2/11 × 2 = 6/22 and 1 × 11/2 × 11 = 11/22

Step 3: Add the Numerators
Now add the numerators (6 + 11 = 17) and keep the common denominator 22 unchanged.
Working: 6 + 11/22 = 17/22

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 17 and 22 is 1, confirming that 17/22 cannot be reduced further—it is already in its simplest irreducible form.
Working: 17/22

Step 5: Decimal & Percentage Representation
Dividing the numerator 17 by denominator 22 produces a repeating decimal (approximately 0.772727, or 77.2727%).
Working: 17 ÷ 22 = 0.772727 (77.2727%)

Key Values:
- Simplified Fraction: 17/22
- Mixed Number Form: 17/22
- Decimal Value: 0.772727
- Percentage: 77.2727%

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3/11 + 1/2 = 17/22

Simplified Fraction

17/22

Mixed Number

Proper (17/22)

Decimal Value

0.772727

Percentage

77.2727%

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Step-by-Step Solution: 3/11 + 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 3/11 by 2, and multiply the numerator and denominator of 1/2 by 11 so both fractions share the common base 22.

3 × 2/11 × 2 = 6/22 and 1 × 11/2 × 11 = 11/22

Step 3

Add the Numerators

Now add the numerators (6 + 11 = 17) and keep the common denominator 22 unchanged.

6 + 11/22 = 17/22

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 17 and 22 is 1, confirming that 17/22 cannot be reduced further—it is already in its simplest irreducible form.

17/22

Step 5

Decimal & Percentage Representation

Dividing the numerator 17 by denominator 22 produces a repeating decimal (approximately 0.772727, or 77.2727%).

17 ÷ 22 = 0.772727 (77.2727%)

Visual Representation

The diagram below illustrates 3/11 plus 1/2 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`17/22`
Mixed Number Form	`17/22`
Decimal Form	`0.772727`
Percentage	`77.2727%`

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Frequently Asked Questions

What is 3/11 plus 1/2 as a fraction?

3/11 + 1/2 in simplest fraction form is 17/22.

What is 3/11 plus 1/2 as a decimal?

3/11 + 1/2 converted to a decimal is 0.772727.

What is 3/11 plus 1/2 as a percentage?

3/11 + 1/2 expressed as a percentage is 77.2727%.

Does 3/11 plus 1/2 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.772727...) because the denominator contains prime factors other than 2 and 5.