What is 2/17 plus 5/8? (Answer: 101/136)

Exact Answer

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Problem: What is 2/17 plus 5/8?
Formula / Expression: 2/17 + 5/8
Final Answer: 101/136
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 17 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 17 × 8 = 136.
Working: LCD(17, 8) = 136

Step 2: Convert to Equivalent Fractions with Common Denominator 136
Multiply the numerator and denominator of 2/17 by 8, and multiply the numerator and denominator of 5/8 by 17 so both fractions share the common base 136.
Working: 2 × 8/17 × 8 = 16/136 and 5 × 17/8 × 17 = 85/136

Step 3: Add the Numerators
Now add the numerators (16 + 85 = 101) and keep the common denominator 136 unchanged.
Working: 16 + 85/136 = 101/136

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 101 and 136 is 1, confirming that 101/136 cannot be reduced further—it is already in its simplest irreducible form.
Working: 101/136

Step 5: Decimal & Percentage Representation
Dividing the numerator 101 by denominator 136 produces a repeating decimal (approximately 0.742647, or 74.2647%).
Working: 101 ÷ 136 = 0.742647 (74.2647%)

Key Values:
- Simplified Fraction: 101/136
- Mixed Number Form: 101/136
- Decimal Value: 0.742647
- Percentage: 74.2647%

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2/17 + 5/8 = 101/136

Simplified Fraction

101/136

Mixed Number

Proper (101/136)

Decimal Value

0.742647

Percentage

74.2647%

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Step-by-Step Solution: 2/17 + 5/8

Step 1

Find the Least Common Denominator (LCD)

The denominators 17 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 17 × 8 = 136.

LCD(17, 8) = 136

Step 2

Convert to Equivalent Fractions with Common Denominator 136

Multiply the numerator and denominator of 2/17 by 8, and multiply the numerator and denominator of 5/8 by 17 so both fractions share the common base 136.

2 × 8/17 × 8 = 16/136 and 5 × 17/8 × 17 = 85/136

Step 3

Add the Numerators

Now add the numerators (16 + 85 = 101) and keep the common denominator 136 unchanged.

16 + 85/136 = 101/136

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 101 and 136 is 1, confirming that 101/136 cannot be reduced further—it is already in its simplest irreducible form.

101/136

Step 5

Decimal & Percentage Representation

Dividing the numerator 101 by denominator 136 produces a repeating decimal (approximately 0.742647, or 74.2647%).

101 ÷ 136 = 0.742647 (74.2647%)

Visual Representation

The diagram below illustrates 2/17 plus 5/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`101/136`
Mixed Number Form	`101/136`
Decimal Form	`0.742647`
Percentage	`74.2647%`

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Frequently Asked Questions

What is 2/17 plus 5/8 as a fraction?

2/17 + 5/8 in simplest fraction form is 101/136.

What is 2/17 plus 5/8 as a decimal?

2/17 + 5/8 converted to a decimal is 0.742647.

What is 2/17 plus 5/8 as a percentage?

2/17 + 5/8 expressed as a percentage is 74.2647%.

Does 2/17 plus 5/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.742647...) because the denominator contains prime factors other than 2 and 5.