What is 3/29 plus 2/8? (Answer: 41/116)

Exact Answer

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Problem: What is 3/29 plus 2/8?
Formula / Expression: 3/29 + 2/8
Final Answer: 41/116
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 29 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 29 × 8 = 232.
Working: LCD(29, 8) = 232

Step 2: Convert to Equivalent Fractions with Common Denominator 232
Multiply the numerator and denominator of 3/29 by 8, and multiply the numerator and denominator of 2/8 by 29 so both fractions share the common base 232.
Working: 3 × 8/29 × 8 = 24/232 and 2 × 29/8 × 29 = 58/232

Step 3: Add the Numerators
Now add the numerators (24 + 58 = 82) and keep the common denominator 232 unchanged.
Working: 24 + 58/232 = 82/232

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 82 and 232, which is 2. Divide both the numerator and denominator by 2.
Working: 82 ÷ 2/232 ÷ 2 = 41/116

Step 5: Decimal & Percentage Representation
Dividing the numerator 41 by denominator 116 produces a repeating decimal (approximately 0.353448, or 35.3448%).
Working: 41 ÷ 116 = 0.353448 (35.3448%)

Key Values:
- Simplified Fraction: 41/116
- Mixed Number Form: 41/116
- Decimal Value: 0.353448
- Percentage: 35.3448%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-29-plus-2-8/
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3/29 + 2/8 = 41/116

Simplified Fraction

41/116

Mixed Number

Proper (41/116)

Decimal Value

0.353448

Percentage

35.3448%

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Step-by-Step Solution: 3/29 + 2/8

Step 1

Find the Least Common Denominator (LCD)

The denominators 29 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 29 × 8 = 232.

LCD(29, 8) = 232

Step 2

Convert to Equivalent Fractions with Common Denominator 232

Multiply the numerator and denominator of 3/29 by 8, and multiply the numerator and denominator of 2/8 by 29 so both fractions share the common base 232.

3 × 8/29 × 8 = 24/232 and 2 × 29/8 × 29 = 58/232

Step 3

Add the Numerators

Now add the numerators (24 + 58 = 82) and keep the common denominator 232 unchanged.

24 + 58/232 = 82/232

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 82 and 232, which is 2. Divide both the numerator and denominator by 2.

82 ÷ 2/232 ÷ 2 = 41/116

Step 5

Decimal & Percentage Representation

Dividing the numerator 41 by denominator 116 produces a repeating decimal (approximately 0.353448, or 35.3448%).

41 ÷ 116 = 0.353448 (35.3448%)

Visual Representation

The diagram below illustrates 3/29 plus 2/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`41/116`
Mixed Number Form	`41/116`
Decimal Form	`0.353448`
Percentage	`35.3448%`

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Frequently Asked Questions

What is 3/29 plus 2/8 as a fraction?

3/29 + 2/8 in simplest fraction form is 41/116.

What is 3/29 plus 2/8 as a decimal?

3/29 + 2/8 converted to a decimal is 0.353448.

What is 3/29 plus 2/8 as a percentage?

3/29 + 2/8 expressed as a percentage is 35.3448%.

Does 3/29 plus 2/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.353448...) because the denominator contains prime factors other than 2 and 5.