What is 2/7 plus 7/17? (Answer: 83/119)

Exact Answer

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Problem: What is 2/7 plus 7/17?
Formula / Expression: 2/7 + 7/17
Final Answer: 83/119
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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 7/17 by 7 so both fractions share the common base 119.
Working: 2 × 17/7 × 17 = 34/119 and 7 × 7/17 × 7 = 49/119

Step 3: Add the Numerators
Now add the numerators (34 + 49 = 83) and keep the common denominator 119 unchanged.
Working: 34 + 49/119 = 83/119

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 83 and 119 is 1, confirming that 83/119 cannot be reduced further—it is already in its simplest irreducible form.
Working: 83/119

Step 5: Decimal & Percentage Representation
Dividing the numerator 83 by denominator 119 produces a repeating decimal (approximately 0.697479, or 69.7479%).
Working: 83 ÷ 119 = 0.697479 (69.7479%)

Key Values:
- Simplified Fraction: 83/119
- Mixed Number Form: 83/119
- Decimal Value: 0.697479
- Percentage: 69.7479%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-7-plus-7-17/
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2/7 + 7/17 = 83/119

Simplified Fraction

83/119

Mixed Number

Proper (83/119)

Decimal Value

0.697479

Percentage

69.7479%

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

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 7/17 by 7 so both fractions share the common base 119.

2 × 17/7 × 17 = 34/119 and 7 × 7/17 × 7 = 49/119

Step 3

Add the Numerators

Now add the numerators (34 + 49 = 83) and keep the common denominator 119 unchanged.

34 + 49/119 = 83/119

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 83 and 119 is 1, confirming that 83/119 cannot be reduced further—it is already in its simplest irreducible form.

83/119

Step 5

Decimal & Percentage Representation

Dividing the numerator 83 by denominator 119 produces a repeating decimal (approximately 0.697479, or 69.7479%).

83 ÷ 119 = 0.697479 (69.7479%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`83/119`
Mixed Number Form	`83/119`
Decimal Form	`0.697479`
Percentage	`69.7479%`

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Frequently Asked Questions

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

2/7 + 7/17 in simplest fraction form is 83/119.

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

2/7 + 7/17 converted to a decimal is 0.697479.

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

2/7 + 7/17 expressed as a percentage is 69.7479%.

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

It results in a repeating decimal (approximately 0.697479...) because the denominator contains prime factors other than 2 and 5.