What is 7/17 plus 1/2? (Answer: 31/34)

Exact Answer

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Problem: What is 7/17 plus 1/2?
Formula / Expression: 7/17 + 1/2
Final Answer: 31/34
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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 7/17 by 2, and multiply the numerator and denominator of 1/2 by 17 so both fractions share the common base 34.
Working: 7 × 2/17 × 2 = 14/34 and 1 × 17/2 × 17 = 17/34

Step 3: Add the Numerators
Now add the numerators (14 + 17 = 31) and keep the common denominator 34 unchanged.
Working: 14 + 17/34 = 31/34

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 31 and 34 is 1, confirming that 31/34 cannot be reduced further—it is already in its simplest irreducible form.
Working: 31/34

Step 5: Decimal & Percentage Representation
Dividing the numerator 31 by denominator 34 produces a repeating decimal (approximately 0.911765, or 91.1765%).
Working: 31 ÷ 34 = 0.911765 (91.1765%)

Key Values:
- Simplified Fraction: 31/34
- Mixed Number Form: 31/34
- Decimal Value: 0.911765
- Percentage: 91.1765%

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Solved with FractionsCalc:
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7/17 + 1/2 = 31/34

Simplified Fraction

31/34

Mixed Number

Proper (31/34)

Decimal Value

0.911765

Percentage

91.1765%

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Step-by-Step Solution: 7/17 + 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 7/17 by 2, and multiply the numerator and denominator of 1/2 by 17 so both fractions share the common base 34.

7 × 2/17 × 2 = 14/34 and 1 × 17/2 × 17 = 17/34

Step 3

Add the Numerators

Now add the numerators (14 + 17 = 31) and keep the common denominator 34 unchanged.

14 + 17/34 = 31/34

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 31 and 34 is 1, confirming that 31/34 cannot be reduced further—it is already in its simplest irreducible form.

31/34

Step 5

Decimal & Percentage Representation

Dividing the numerator 31 by denominator 34 produces a repeating decimal (approximately 0.911765, or 91.1765%).

31 ÷ 34 = 0.911765 (91.1765%)

Visual Representation

The diagram below illustrates 7/17 plus 1/2 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`31/34`
Mixed Number Form	`31/34`
Decimal Form	`0.911765`
Percentage	`91.1765%`

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Frequently Asked Questions

What is 7/17 plus 1/2 as a fraction?

7/17 + 1/2 in simplest fraction form is 31/34.

What is 7/17 plus 1/2 as a decimal?

7/17 + 1/2 converted to a decimal is 0.911765.

What is 7/17 plus 1/2 as a percentage?

7/17 + 1/2 expressed as a percentage is 91.1765%.

Does 7/17 plus 1/2 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.911765...) because the denominator contains prime factors other than 2 and 5.