What is 2/7 plus 8/17? (Answer: 90/119)

Exact Answer

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Problem: What is 2/7 plus 8/17?
Formula / Expression: 2/7 + 8/17
Final Answer: 90/119
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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 8/17 by 7 so both fractions share the common base 119.
Working: 2 × 17/7 × 17 = 34/119 and 8 × 7/17 × 7 = 56/119

Step 3: Add the Numerators
Now add the numerators (34 + 56 = 90) and keep the common denominator 119 unchanged.
Working: 34 + 56/119 = 90/119

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 90 and 119 is 1, confirming that 90/119 cannot be reduced further—it is already in its simplest irreducible form.
Working: 90/119

Step 5: Decimal & Percentage Representation
Dividing the numerator 90 by denominator 119 produces a repeating decimal (approximately 0.756303, or 75.6303%).
Working: 90 ÷ 119 = 0.756303 (75.6303%)

Key Values:
- Simplified Fraction: 90/119
- Mixed Number Form: 90/119
- Decimal Value: 0.756303
- Percentage: 75.6303%

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Solved with FractionsCalc:
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2/7 + 8/17 = 90/119

Simplified Fraction

90/119

Mixed Number

Proper (90/119)

Decimal Value

0.756303

Percentage

75.6303%

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Step-by-Step Solution: 2/7 + 8/17

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 8/17 by 7 so both fractions share the common base 119.

2 × 17/7 × 17 = 34/119 and 8 × 7/17 × 7 = 56/119

Step 3

Add the Numerators

Now add the numerators (34 + 56 = 90) and keep the common denominator 119 unchanged.

34 + 56/119 = 90/119

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 90 and 119 is 1, confirming that 90/119 cannot be reduced further—it is already in its simplest irreducible form.

90/119

Step 5

Decimal & Percentage Representation

Dividing the numerator 90 by denominator 119 produces a repeating decimal (approximately 0.756303, or 75.6303%).

90 ÷ 119 = 0.756303 (75.6303%)

Visual Representation

The diagram below illustrates 2/7 plus 8/17 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`90/119`
Mixed Number Form	`90/119`
Decimal Form	`0.756303`
Percentage	`75.6303%`

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Frequently Asked Questions

What is 2/7 plus 8/17 as a fraction?

2/7 + 8/17 in simplest fraction form is 90/119.

What is 2/7 plus 8/17 as a decimal?

2/7 + 8/17 converted to a decimal is 0.756303.

What is 2/7 plus 8/17 as a percentage?

2/7 + 8/17 expressed as a percentage is 75.6303%.

Does 2/7 plus 8/17 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.756303...) because the denominator contains prime factors other than 2 and 5.