What is 2/5 plus 7/17? (Answer: 69/85)

Exact Answer

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Problem: What is 2/5 plus 7/17?
Formula / Expression: 2/5 + 7/17
Final Answer: 69/85
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 85
Multiply the numerator and denominator of 2/5 by 17, and multiply the numerator and denominator of 7/17 by 5 so both fractions share the common base 85.
Working: 2 × 17/5 × 17 = 34/85 and 7 × 5/17 × 5 = 35/85

Step 3: Add the Numerators
Now add the numerators (34 + 35 = 69) and keep the common denominator 85 unchanged.
Working: 34 + 35/85 = 69/85

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 69 and 85 is 1, confirming that 69/85 cannot be reduced further—it is already in its simplest irreducible form.
Working: 69/85

Step 5: Decimal & Percentage Representation
Dividing the numerator 69 by denominator 85 produces a repeating decimal (approximately 0.811765, or 81.1765%).
Working: 69 ÷ 85 = 0.811765 (81.1765%)

Key Values:
- Simplified Fraction: 69/85
- Mixed Number Form: 69/85
- Decimal Value: 0.811765
- Percentage: 81.1765%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-5-plus-7-17/
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2/5 + 7/17 = 69/85

Simplified Fraction

69/85

Mixed Number

Proper (69/85)

Decimal Value

0.811765

Percentage

81.1765%

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Step-by-Step Solution: 2/5 + 7/17

Step 1

Find the Least Common Denominator (LCD)

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

LCD(5, 17) = 85

Step 2

Convert to Equivalent Fractions with Common Denominator 85

Multiply the numerator and denominator of 2/5 by 17, and multiply the numerator and denominator of 7/17 by 5 so both fractions share the common base 85.

2 × 17/5 × 17 = 34/85 and 7 × 5/17 × 5 = 35/85

Step 3

Add the Numerators

Now add the numerators (34 + 35 = 69) and keep the common denominator 85 unchanged.

34 + 35/85 = 69/85

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 69 and 85 is 1, confirming that 69/85 cannot be reduced further—it is already in its simplest irreducible form.

69/85

Step 5

Decimal & Percentage Representation

Dividing the numerator 69 by denominator 85 produces a repeating decimal (approximately 0.811765, or 81.1765%).

69 ÷ 85 = 0.811765 (81.1765%)

Visual Representation

The diagram below illustrates 2/5 plus 7/17 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`69/85`
Mixed Number Form	`69/85`
Decimal Form	`0.811765`
Percentage	`81.1765%`

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Frequently Asked Questions

What is 2/5 plus 7/17 as a fraction?

2/5 + 7/17 in simplest fraction form is 69/85.

What is 2/5 plus 7/17 as a decimal?

2/5 + 7/17 converted to a decimal is 0.811765.

What is 2/5 plus 7/17 as a percentage?

2/5 + 7/17 expressed as a percentage is 81.1765%.

Does 2/5 plus 7/17 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.811765...) because the denominator contains prime factors other than 2 and 5.