What is 2/17 plus 2/15? (Answer: 64/255)

Exact Answer

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Problem: What is 2/17 plus 2/15?
Formula / Expression: 2/17 + 2/15
Final Answer: 64/255
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 17 and 15 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 17 × 15 = 255.
Working: LCD(17, 15) = 255

Step 2: Convert to Equivalent Fractions with Common Denominator 255
Multiply the numerator and denominator of 2/17 by 15, and multiply the numerator and denominator of 2/15 by 17 so both fractions share the common base 255.
Working: 2 × 15/17 × 15 = 30/255 and 2 × 17/15 × 17 = 34/255

Step 3: Add the Numerators
Now add the numerators (30 + 34 = 64) and keep the common denominator 255 unchanged.
Working: 30 + 34/255 = 64/255

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 64 and 255 is 1, confirming that 64/255 cannot be reduced further—it is already in its simplest irreducible form.
Working: 64/255

Step 5: Decimal & Percentage Representation
Dividing the numerator 64 by denominator 255 produces a repeating decimal (approximately 0.25098, or 25.098%).
Working: 64 ÷ 255 = 0.25098 (25.098%)

Key Values:
- Simplified Fraction: 64/255
- Mixed Number Form: 64/255
- Decimal Value: 0.25098
- Percentage: 25.098%

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Solved with FractionsCalc:
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2/17 + 2/15 = 64/255

Simplified Fraction

64/255

Mixed Number

Proper (64/255)

Decimal Value

0.25098

Percentage

25.098%

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Step-by-Step Solution: 2/17 + 2/15

Step 1

Find the Least Common Denominator (LCD)

The denominators 17 and 15 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 17 × 15 = 255.

LCD(17, 15) = 255

Step 2

Convert to Equivalent Fractions with Common Denominator 255

Multiply the numerator and denominator of 2/17 by 15, and multiply the numerator and denominator of 2/15 by 17 so both fractions share the common base 255.

2 × 15/17 × 15 = 30/255 and 2 × 17/15 × 17 = 34/255

Step 3

Add the Numerators

Now add the numerators (30 + 34 = 64) and keep the common denominator 255 unchanged.

30 + 34/255 = 64/255

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 64 and 255 is 1, confirming that 64/255 cannot be reduced further—it is already in its simplest irreducible form.

64/255

Step 5

Decimal & Percentage Representation

Dividing the numerator 64 by denominator 255 produces a repeating decimal (approximately 0.25098, or 25.098%).

64 ÷ 255 = 0.25098 (25.098%)

Visual Representation

The diagram below illustrates 2/17 plus 2/15 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`64/255`
Mixed Number Form	`64/255`
Decimal Form	`0.25098`
Percentage	`25.098%`

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Frequently Asked Questions

What is 2/17 plus 2/15 as a fraction?

2/17 + 2/15 in simplest fraction form is 64/255.

What is 2/17 plus 2/15 as a decimal?

2/17 + 2/15 converted to a decimal is 0.25098.

What is 2/17 plus 2/15 as a percentage?

2/17 + 2/15 expressed as a percentage is 25.098%.

Does 2/17 plus 2/15 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.25098...) because the denominator contains prime factors other than 2 and 5.