What is 5/17 plus 2/5? (Answer: 59/85)

Exact Answer

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Problem: What is 5/17 plus 2/5?
Formula / Expression: 5/17 + 2/5
Final Answer: 59/85
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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 5/17 by 5, and multiply the numerator and denominator of 2/5 by 17 so both fractions share the common base 85.
Working: 5 × 5/17 × 5 = 25/85 and 2 × 17/5 × 17 = 34/85

Step 3: Add the Numerators
Now add the numerators (25 + 34 = 59) and keep the common denominator 85 unchanged.
Working: 25 + 34/85 = 59/85

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 59 and 85 is 1, confirming that 59/85 cannot be reduced further—it is already in its simplest irreducible form.
Working: 59/85

Step 5: Decimal & Percentage Representation
Dividing the numerator 59 by denominator 85 produces a repeating decimal (approximately 0.694118, or 69.4118%).
Working: 59 ÷ 85 = 0.694118 (69.4118%)

Key Values:
- Simplified Fraction: 59/85
- Mixed Number Form: 59/85
- Decimal Value: 0.694118
- Percentage: 69.4118%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-17-plus-2-5/
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5/17 + 2/5 = 59/85

Simplified Fraction

59/85

Mixed Number

Proper (59/85)

Decimal Value

0.694118

Percentage

69.4118%

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

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

5 × 5/17 × 5 = 25/85 and 2 × 17/5 × 17 = 34/85

Step 3

Add the Numerators

Now add the numerators (25 + 34 = 59) and keep the common denominator 85 unchanged.

25 + 34/85 = 59/85

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 59 and 85 is 1, confirming that 59/85 cannot be reduced further—it is already in its simplest irreducible form.

59/85

Step 5

Decimal & Percentage Representation

Dividing the numerator 59 by denominator 85 produces a repeating decimal (approximately 0.694118, or 69.4118%).

59 ÷ 85 = 0.694118 (69.4118%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`59/85`
Mixed Number Form	`59/85`
Decimal Form	`0.694118`
Percentage	`69.4118%`

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Frequently Asked Questions

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

5/17 + 2/5 in simplest fraction form is 59/85.

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

5/17 + 2/5 converted to a decimal is 0.694118.

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

5/17 + 2/5 expressed as a percentage is 69.4118%.

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

It results in a repeating decimal (approximately 0.694118...) because the denominator contains prime factors other than 2 and 5.