What is 2/5 plus 9/17? (Answer: 79/85)

Exact Answer

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Problem: What is 2/5 plus 9/17?
Formula / Expression: 2/5 + 9/17
Final Answer: 79/85
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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 9/17 by 5 so both fractions share the common base 85.
Working: 2 × 17/5 × 17 = 34/85 and 9 × 5/17 × 5 = 45/85

Step 3: Add the Numerators
Now add the numerators (34 + 45 = 79) and keep the common denominator 85 unchanged.
Working: 34 + 45/85 = 79/85

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 79 and 85 is 1, confirming that 79/85 cannot be reduced further—it is already in its simplest irreducible form.
Working: 79/85

Step 5: Decimal & Percentage Representation
Dividing the numerator 79 by denominator 85 produces a repeating decimal (approximately 0.929412, or 92.9412%).
Working: 79 ÷ 85 = 0.929412 (92.9412%)

Key Values:
- Simplified Fraction: 79/85
- Mixed Number Form: 79/85
- Decimal Value: 0.929412
- Percentage: 92.9412%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-5-plus-9-17/
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2/5 + 9/17 = 79/85

Simplified Fraction

79/85

Mixed Number

Proper (79/85)

Decimal Value

0.929412

Percentage

92.9412%

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Step-by-Step Solution: 2/5 + 9/17

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 9/17 by 5 so both fractions share the common base 85.

2 × 17/5 × 17 = 34/85 and 9 × 5/17 × 5 = 45/85

Step 3

Add the Numerators

Now add the numerators (34 + 45 = 79) and keep the common denominator 85 unchanged.

34 + 45/85 = 79/85

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 79 and 85 is 1, confirming that 79/85 cannot be reduced further—it is already in its simplest irreducible form.

79/85

Step 5

Decimal & Percentage Representation

Dividing the numerator 79 by denominator 85 produces a repeating decimal (approximately 0.929412, or 92.9412%).

79 ÷ 85 = 0.929412 (92.9412%)

Visual Representation

The diagram below illustrates 2/5 plus 9/17 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`79/85`
Mixed Number Form	`79/85`
Decimal Form	`0.929412`
Percentage	`92.9412%`

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Frequently Asked Questions

What is 2/5 plus 9/17 as a fraction?

2/5 + 9/17 in simplest fraction form is 79/85.

What is 2/5 plus 9/17 as a decimal?

2/5 + 9/17 converted to a decimal is 0.929412.

What is 2/5 plus 9/17 as a percentage?

2/5 + 9/17 expressed as a percentage is 92.9412%.

Does 2/5 plus 9/17 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.929412...) because the denominator contains prime factors other than 2 and 5.