What is 2/17 plus 3/5? (Answer: 61/85)

Exact Answer

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Problem: What is 2/17 plus 3/5?
Formula / Expression: 2/17 + 3/5
Final Answer: 61/85
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 17 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 17 × 5 = 85.
Working: LCD(17, 5) = 85

Step 2: Convert to Equivalent Fractions with Common Denominator 85
Multiply the numerator and denominator of 2/17 by 5, and multiply the numerator and denominator of 3/5 by 17 so both fractions share the common base 85.
Working: 2 × 5/17 × 5 = 10/85 and 3 × 17/5 × 17 = 51/85

Step 3: Add the Numerators
Now add the numerators (10 + 51 = 61) and keep the common denominator 85 unchanged.
Working: 10 + 51/85 = 61/85

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 61 and 85 is 1, confirming that 61/85 cannot be reduced further—it is already in its simplest irreducible form.
Working: 61/85

Step 5: Decimal & Percentage Representation
Dividing the numerator 61 by denominator 85 produces a repeating decimal (approximately 0.717647, or 71.7647%).
Working: 61 ÷ 85 = 0.717647 (71.7647%)

Key Values:
- Simplified Fraction: 61/85
- Mixed Number Form: 61/85
- Decimal Value: 0.717647
- Percentage: 71.7647%

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Solved with FractionsCalc:
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2/17 + 3/5 = 61/85

Simplified Fraction

61/85

Mixed Number

Proper (61/85)

Decimal Value

0.717647

Percentage

71.7647%

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Step-by-Step Solution: 2/17 + 3/5

Step 1

Find the Least Common Denominator (LCD)

The denominators 17 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 17 × 5 = 85.

LCD(17, 5) = 85

Step 2

Convert to Equivalent Fractions with Common Denominator 85

Multiply the numerator and denominator of 2/17 by 5, and multiply the numerator and denominator of 3/5 by 17 so both fractions share the common base 85.

2 × 5/17 × 5 = 10/85 and 3 × 17/5 × 17 = 51/85

Step 3

Add the Numerators

Now add the numerators (10 + 51 = 61) and keep the common denominator 85 unchanged.

10 + 51/85 = 61/85

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 61 and 85 is 1, confirming that 61/85 cannot be reduced further—it is already in its simplest irreducible form.

61/85

Step 5

Decimal & Percentage Representation

Dividing the numerator 61 by denominator 85 produces a repeating decimal (approximately 0.717647, or 71.7647%).

61 ÷ 85 = 0.717647 (71.7647%)

Visual Representation

The diagram below illustrates 2/17 plus 3/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`61/85`
Mixed Number Form	`61/85`
Decimal Form	`0.717647`
Percentage	`71.7647%`

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Frequently Asked Questions

What is 2/17 plus 3/5 as a fraction?

2/17 + 3/5 in simplest fraction form is 61/85.

What is 2/17 plus 3/5 as a decimal?

2/17 + 3/5 converted to a decimal is 0.717647.

What is 2/17 plus 3/5 as a percentage?

2/17 + 3/5 expressed as a percentage is 71.7647%.

Does 2/17 plus 3/5 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.717647...) because the denominator contains prime factors other than 2 and 5.