What is 2/17 plus 1/2? (Answer: 21/34)

Exact Answer

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Problem: What is 2/17 plus 1/2?
Formula / Expression: 2/17 + 1/2
Final Answer: 21/34
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 17 and 2 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 17 × 2 = 34.
Working: LCD(17, 2) = 34

Step 2: Convert to Equivalent Fractions with Common Denominator 34
Multiply the numerator and denominator of 2/17 by 2, and multiply the numerator and denominator of 1/2 by 17 so both fractions share the common base 34.
Working: 2 × 2/17 × 2 = 4/34 and 1 × 17/2 × 17 = 17/34

Step 3: Add the Numerators
Now add the numerators (4 + 17 = 21) and keep the common denominator 34 unchanged.
Working: 4 + 17/34 = 21/34

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 21 and 34 is 1, confirming that 21/34 cannot be reduced further—it is already in its simplest irreducible form.
Working: 21/34

Step 5: Decimal & Percentage Representation
Dividing the numerator 21 by denominator 34 produces a repeating decimal (approximately 0.617647, or 61.7647%).
Working: 21 ÷ 34 = 0.617647 (61.7647%)

Key Values:
- Simplified Fraction: 21/34
- Mixed Number Form: 21/34
- Decimal Value: 0.617647
- Percentage: 61.7647%

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Solved with FractionsCalc:
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2/17 + 1/2 = 21/34

Simplified Fraction

21/34

Mixed Number

Proper (21/34)

Decimal Value

0.617647

Percentage

61.7647%

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Step-by-Step Solution: 2/17 + 1/2

Step 1

Find the Least Common Denominator (LCD)

The denominators 17 and 2 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 17 × 2 = 34.

LCD(17, 2) = 34

Step 2

Convert to Equivalent Fractions with Common Denominator 34

Multiply the numerator and denominator of 2/17 by 2, and multiply the numerator and denominator of 1/2 by 17 so both fractions share the common base 34.

2 × 2/17 × 2 = 4/34 and 1 × 17/2 × 17 = 17/34

Step 3

Add the Numerators

Now add the numerators (4 + 17 = 21) and keep the common denominator 34 unchanged.

4 + 17/34 = 21/34

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 21 and 34 is 1, confirming that 21/34 cannot be reduced further—it is already in its simplest irreducible form.

21/34

Step 5

Decimal & Percentage Representation

Dividing the numerator 21 by denominator 34 produces a repeating decimal (approximately 0.617647, or 61.7647%).

21 ÷ 34 = 0.617647 (61.7647%)

Visual Representation

The diagram below illustrates 2/17 plus 1/2 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`21/34`
Mixed Number Form	`21/34`
Decimal Form	`0.617647`
Percentage	`61.7647%`

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Frequently Asked Questions

What is 2/17 plus 1/2 as a fraction?

2/17 + 1/2 in simplest fraction form is 21/34.

What is 2/17 plus 1/2 as a decimal?

2/17 + 1/2 converted to a decimal is 0.617647.

What is 2/17 plus 1/2 as a percentage?

2/17 + 1/2 expressed as a percentage is 61.7647%.

Does 2/17 plus 1/2 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.617647...) because the denominator contains prime factors other than 2 and 5.