What is 2/35 plus 2/17? (Answer: 104/595)

Exact Answer

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Problem: What is 2/35 plus 2/17?
Formula / Expression: 2/35 + 2/17
Final Answer: 104/595
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 35 and 17 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 35 × 17 = 595.
Working: LCD(35, 17) = 595

Step 2: Convert to Equivalent Fractions with Common Denominator 595
Multiply the numerator and denominator of 2/35 by 17, and multiply the numerator and denominator of 2/17 by 35 so both fractions share the common base 595.
Working: 2 × 17/35 × 17 = 34/595 and 2 × 35/17 × 35 = 70/595

Step 3: Add the Numerators
Now add the numerators (34 + 70 = 104) and keep the common denominator 595 unchanged.
Working: 34 + 70/595 = 104/595

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 104 and 595 is 1, confirming that 104/595 cannot be reduced further—it is already in its simplest irreducible form.
Working: 104/595

Step 5: Decimal & Percentage Representation
Dividing the numerator 104 by denominator 595 produces a repeating decimal (approximately 0.17479, or 17.479%).
Working: 104 ÷ 595 = 0.17479 (17.479%)

Key Values:
- Simplified Fraction: 104/595
- Mixed Number Form: 104/595
- Decimal Value: 0.17479
- Percentage: 17.479%

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Solved with FractionsCalc:
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2/35 + 2/17 = 104/595

Simplified Fraction

104/595

Mixed Number

Proper (104/595)

Decimal Value

0.17479

Percentage

17.479%

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Step-by-Step Solution: 2/35 + 2/17

Step 1

Find the Least Common Denominator (LCD)

The denominators 35 and 17 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 35 × 17 = 595.

LCD(35, 17) = 595

Step 2

Convert to Equivalent Fractions with Common Denominator 595

Multiply the numerator and denominator of 2/35 by 17, and multiply the numerator and denominator of 2/17 by 35 so both fractions share the common base 595.

2 × 17/35 × 17 = 34/595 and 2 × 35/17 × 35 = 70/595

Step 3

Add the Numerators

Now add the numerators (34 + 70 = 104) and keep the common denominator 595 unchanged.

34 + 70/595 = 104/595

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 104 and 595 is 1, confirming that 104/595 cannot be reduced further—it is already in its simplest irreducible form.

104/595

Step 5

Decimal & Percentage Representation

Dividing the numerator 104 by denominator 595 produces a repeating decimal (approximately 0.17479, or 17.479%).

104 ÷ 595 = 0.17479 (17.479%)

Visual Representation

The diagram below illustrates 2/35 plus 2/17 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`104/595`
Mixed Number Form	`104/595`
Decimal Form	`0.17479`
Percentage	`17.479%`

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Frequently Asked Questions

What is 2/35 plus 2/17 as a fraction?

2/35 + 2/17 in simplest fraction form is 104/595.

What is 2/35 plus 2/17 as a decimal?

2/35 + 2/17 converted to a decimal is 0.17479.

What is 2/35 plus 2/17 as a percentage?

2/35 + 2/17 expressed as a percentage is 17.479%.

Does 2/35 plus 2/17 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.17479...) because the denominator contains prime factors other than 2 and 5.