What is 2/17 plus 4/7? (Answer: 82/119)

Exact Answer

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Problem: What is 2/17 plus 4/7?
Formula / Expression: 2/17 + 4/7
Final Answer: 82/119
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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 2/17 by 7, and multiply the numerator and denominator of 4/7 by 17 so both fractions share the common base 119.
Working: 2 × 7/17 × 7 = 14/119 and 4 × 17/7 × 17 = 68/119

Step 3: Add the Numerators
Now add the numerators (14 + 68 = 82) and keep the common denominator 119 unchanged.
Working: 14 + 68/119 = 82/119

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 82 and 119 is 1, confirming that 82/119 cannot be reduced further—it is already in its simplest irreducible form.
Working: 82/119

Step 5: Decimal & Percentage Representation
Dividing the numerator 82 by denominator 119 produces a repeating decimal (approximately 0.689076, or 68.9076%).
Working: 82 ÷ 119 = 0.689076 (68.9076%)

Key Values:
- Simplified Fraction: 82/119
- Mixed Number Form: 82/119
- Decimal Value: 0.689076
- Percentage: 68.9076%

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Solved with FractionsCalc:
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2/17 + 4/7 = 82/119

Simplified Fraction

82/119

Mixed Number

Proper (82/119)

Decimal Value

0.689076

Percentage

68.9076%

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Step-by-Step Solution: 2/17 + 4/7

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 2/17 by 7, and multiply the numerator and denominator of 4/7 by 17 so both fractions share the common base 119.

2 × 7/17 × 7 = 14/119 and 4 × 17/7 × 17 = 68/119

Step 3

Add the Numerators

Now add the numerators (14 + 68 = 82) and keep the common denominator 119 unchanged.

14 + 68/119 = 82/119

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 82 and 119 is 1, confirming that 82/119 cannot be reduced further—it is already in its simplest irreducible form.

82/119

Step 5

Decimal & Percentage Representation

Dividing the numerator 82 by denominator 119 produces a repeating decimal (approximately 0.689076, or 68.9076%).

82 ÷ 119 = 0.689076 (68.9076%)

Visual Representation

The diagram below illustrates 2/17 plus 4/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`82/119`
Mixed Number Form	`82/119`
Decimal Form	`0.689076`
Percentage	`68.9076%`

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Frequently Asked Questions

What is 2/17 plus 4/7 as a fraction?

2/17 + 4/7 in simplest fraction form is 82/119.

What is 2/17 plus 4/7 as a decimal?

2/17 + 4/7 converted to a decimal is 0.689076.

What is 2/17 plus 4/7 as a percentage?

2/17 + 4/7 expressed as a percentage is 68.9076%.

Does 2/17 plus 4/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.689076...) because the denominator contains prime factors other than 2 and 5.