What is 3/17 plus 2/8? (Answer: 29/68)

Exact Answer

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Problem: What is 3/17 plus 2/8?
Formula / Expression: 3/17 + 2/8
Final Answer: 29/68
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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 3/17 by 8, and multiply the numerator and denominator of 2/8 by 17 so both fractions share the common base 136.
Working: 3 × 8/17 × 8 = 24/136 and 2 × 17/8 × 17 = 34/136

Step 3: Add the Numerators
Now add the numerators (24 + 34 = 58) and keep the common denominator 136 unchanged.
Working: 24 + 34/136 = 58/136

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 58 and 136, which is 2. Divide both the numerator and denominator by 2.
Working: 58 ÷ 2/136 ÷ 2 = 29/68

Step 5: Decimal & Percentage Representation
Dividing the numerator 29 by denominator 68 produces a repeating decimal (approximately 0.426471, or 42.6471%).
Working: 29 ÷ 68 = 0.426471 (42.6471%)

Key Values:
- Simplified Fraction: 29/68
- Mixed Number Form: 29/68
- Decimal Value: 0.426471
- Percentage: 42.6471%

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Solved with FractionsCalc:
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3/17 + 2/8 = 29/68

Simplified Fraction

29/68

Mixed Number

Proper (29/68)

Decimal Value

0.426471

Percentage

42.6471%

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Step-by-Step Solution: 3/17 + 2/8

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 3/17 by 8, and multiply the numerator and denominator of 2/8 by 17 so both fractions share the common base 136.

3 × 8/17 × 8 = 24/136 and 2 × 17/8 × 17 = 34/136

Step 3

Add the Numerators

Now add the numerators (24 + 34 = 58) and keep the common denominator 136 unchanged.

24 + 34/136 = 58/136

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 58 and 136, which is 2. Divide both the numerator and denominator by 2.

58 ÷ 2/136 ÷ 2 = 29/68

Step 5

Decimal & Percentage Representation

Dividing the numerator 29 by denominator 68 produces a repeating decimal (approximately 0.426471, or 42.6471%).

29 ÷ 68 = 0.426471 (42.6471%)

Visual Representation

The diagram below illustrates 3/17 plus 2/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`29/68`
Mixed Number Form	`29/68`
Decimal Form	`0.426471`
Percentage	`42.6471%`

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Frequently Asked Questions

What is 3/17 plus 2/8 as a fraction?

3/17 + 2/8 in simplest fraction form is 29/68.

What is 3/17 plus 2/8 as a decimal?

3/17 + 2/8 converted to a decimal is 0.426471.

What is 3/17 plus 2/8 as a percentage?

3/17 + 2/8 expressed as a percentage is 42.6471%.

Does 3/17 plus 2/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.426471...) because the denominator contains prime factors other than 2 and 5.