What is 1/17 plus 2/7? (Answer: 41/119)

Exact Answer

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Problem: What is 1/17 plus 2/7?
Formula / Expression: 1/17 + 2/7
Final Answer: 41/119
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 17 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 17 × 7 = 119.
Working: LCD(17, 7) = 119

Step 2: Convert to Equivalent Fractions with Common Denominator 119
Multiply the numerator and denominator of 1/17 by 7, and multiply the numerator and denominator of 2/7 by 17 so both fractions share the common base 119.
Working: 1 × 7/17 × 7 = 7/119 and 2 × 17/7 × 17 = 34/119

Step 3: Add the Numerators
Now add the numerators (7 + 34 = 41) and keep the common denominator 119 unchanged.
Working: 7 + 34/119 = 41/119

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 41 and 119 is 1, confirming that 41/119 cannot be reduced further—it is already in its simplest irreducible form.
Working: 41/119

Step 5: Decimal & Percentage Representation
Dividing the numerator 41 by denominator 119 produces a repeating decimal (approximately 0.344538, or 34.4538%).
Working: 41 ÷ 119 = 0.344538 (34.4538%)

Key Values:
- Simplified Fraction: 41/119
- Mixed Number Form: 41/119
- Decimal Value: 0.344538
- Percentage: 34.4538%

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Solved with FractionsCalc:
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1/17 + 2/7 = 41/119

Simplified Fraction

41/119

Mixed Number

Proper (41/119)

Decimal Value

0.344538

Percentage

34.4538%

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Step-by-Step Solution: 1/17 + 2/7

Step 1

Find the Least Common Denominator (LCD)

The denominators 17 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 17 × 7 = 119.

LCD(17, 7) = 119

Step 2

Convert to Equivalent Fractions with Common Denominator 119

Multiply the numerator and denominator of 1/17 by 7, and multiply the numerator and denominator of 2/7 by 17 so both fractions share the common base 119.

1 × 7/17 × 7 = 7/119 and 2 × 17/7 × 17 = 34/119

Step 3

Add the Numerators

Now add the numerators (7 + 34 = 41) and keep the common denominator 119 unchanged.

7 + 34/119 = 41/119

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 41 and 119 is 1, confirming that 41/119 cannot be reduced further—it is already in its simplest irreducible form.

41/119

Step 5

Decimal & Percentage Representation

Dividing the numerator 41 by denominator 119 produces a repeating decimal (approximately 0.344538, or 34.4538%).

41 ÷ 119 = 0.344538 (34.4538%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`41/119`
Mixed Number Form	`41/119`
Decimal Form	`0.344538`
Percentage	`34.4538%`

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Frequently Asked Questions

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

1/17 + 2/7 in simplest fraction form is 41/119.

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

1/17 + 2/7 converted to a decimal is 0.344538.

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

1/17 + 2/7 expressed as a percentage is 34.4538%.

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

It results in a repeating decimal (approximately 0.344538...) because the denominator contains prime factors other than 2 and 5.