What is 2/7 plus 9/17? (Answer: 97/119)

Exact Answer

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Problem: What is 2/7 plus 9/17?
Formula / Expression: 2/7 + 9/17
Final Answer: 97/119
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 119
Multiply the numerator and denominator of 2/7 by 17, and multiply the numerator and denominator of 9/17 by 7 so both fractions share the common base 119.
Working: 2 × 17/7 × 17 = 34/119 and 9 × 7/17 × 7 = 63/119

Step 3: Add the Numerators
Now add the numerators (34 + 63 = 97) and keep the common denominator 119 unchanged.
Working: 34 + 63/119 = 97/119

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 97 and 119 is 1, confirming that 97/119 cannot be reduced further—it is already in its simplest irreducible form.
Working: 97/119

Step 5: Decimal & Percentage Representation
Dividing the numerator 97 by denominator 119 produces a repeating decimal (approximately 0.815126, or 81.5126%).
Working: 97 ÷ 119 = 0.815126 (81.5126%)

Key Values:
- Simplified Fraction: 97/119
- Mixed Number Form: 97/119
- Decimal Value: 0.815126
- Percentage: 81.5126%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-7-plus-9-17/
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2/7 + 9/17 = 97/119

Simplified Fraction

97/119

Mixed Number

Proper (97/119)

Decimal Value

0.815126

Percentage

81.5126%

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Step-by-Step Solution: 2/7 + 9/17

Step 1

Find the Least Common Denominator (LCD)

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

LCD(7, 17) = 119

Step 2

Convert to Equivalent Fractions with Common Denominator 119

Multiply the numerator and denominator of 2/7 by 17, and multiply the numerator and denominator of 9/17 by 7 so both fractions share the common base 119.

2 × 17/7 × 17 = 34/119 and 9 × 7/17 × 7 = 63/119

Step 3

Add the Numerators

Now add the numerators (34 + 63 = 97) and keep the common denominator 119 unchanged.

34 + 63/119 = 97/119

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 97 and 119 is 1, confirming that 97/119 cannot be reduced further—it is already in its simplest irreducible form.

97/119

Step 5

Decimal & Percentage Representation

Dividing the numerator 97 by denominator 119 produces a repeating decimal (approximately 0.815126, or 81.5126%).

97 ÷ 119 = 0.815126 (81.5126%)

Visual Representation

The diagram below illustrates 2/7 plus 9/17 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`97/119`
Mixed Number Form	`97/119`
Decimal Form	`0.815126`
Percentage	`81.5126%`

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Frequently Asked Questions

What is 2/7 plus 9/17 as a fraction?

2/7 + 9/17 in simplest fraction form is 97/119.

What is 2/7 plus 9/17 as a decimal?

2/7 + 9/17 converted to a decimal is 0.815126.

What is 2/7 plus 9/17 as a percentage?

2/7 + 9/17 expressed as a percentage is 81.5126%.

Does 2/7 plus 9/17 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.815126...) because the denominator contains prime factors other than 2 and 5.