What is 2/7 plus 5/17? (Answer: 69/119)

Exact Answer

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Problem: What is 2/7 plus 5/17?
Formula / Expression: 2/7 + 5/17
Final Answer: 69/119
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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 5/17 by 7 so both fractions share the common base 119.
Working: 2 × 17/7 × 17 = 34/119 and 5 × 7/17 × 7 = 35/119

Step 3: Add the Numerators
Now add the numerators (34 + 35 = 69) and keep the common denominator 119 unchanged.
Working: 34 + 35/119 = 69/119

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 69 and 119 is 1, confirming that 69/119 cannot be reduced further—it is already in its simplest irreducible form.
Working: 69/119

Step 5: Decimal & Percentage Representation
Dividing the numerator 69 by denominator 119 produces a repeating decimal (approximately 0.579832, or 57.9832%).
Working: 69 ÷ 119 = 0.579832 (57.9832%)

Key Values:
- Simplified Fraction: 69/119
- Mixed Number Form: 69/119
- Decimal Value: 0.579832
- Percentage: 57.9832%

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Solved with FractionsCalc:
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2/7 + 5/17 = 69/119

Simplified Fraction

69/119

Mixed Number

Proper (69/119)

Decimal Value

0.579832

Percentage

57.9832%

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Step-by-Step Solution: 2/7 + 5/17

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 5/17 by 7 so both fractions share the common base 119.

2 × 17/7 × 17 = 34/119 and 5 × 7/17 × 7 = 35/119

Step 3

Add the Numerators

Now add the numerators (34 + 35 = 69) and keep the common denominator 119 unchanged.

34 + 35/119 = 69/119

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 69 and 119 is 1, confirming that 69/119 cannot be reduced further—it is already in its simplest irreducible form.

69/119

Step 5

Decimal & Percentage Representation

Dividing the numerator 69 by denominator 119 produces a repeating decimal (approximately 0.579832, or 57.9832%).

69 ÷ 119 = 0.579832 (57.9832%)

Visual Representation

The diagram below illustrates 2/7 plus 5/17 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`69/119`
Mixed Number Form	`69/119`
Decimal Form	`0.579832`
Percentage	`57.9832%`

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Frequently Asked Questions

What is 2/7 plus 5/17 as a fraction?

2/7 + 5/17 in simplest fraction form is 69/119.

What is 2/7 plus 5/17 as a decimal?

2/7 + 5/17 converted to a decimal is 0.579832.

What is 2/7 plus 5/17 as a percentage?

2/7 + 5/17 expressed as a percentage is 57.9832%.

Does 2/7 plus 5/17 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.579832...) because the denominator contains prime factors other than 2 and 5.