What is 2/9 plus 8/29? (Answer: 130/261)

Exact Answer

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Problem: What is 2/9 plus 8/29?
Formula / Expression: 2/9 + 8/29
Final Answer: 130/261
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 29 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 29 = 261.
Working: LCD(9, 29) = 261

Step 2: Convert to Equivalent Fractions with Common Denominator 261
Multiply the numerator and denominator of 2/9 by 29, and multiply the numerator and denominator of 8/29 by 9 so both fractions share the common base 261.
Working: 2 × 29/9 × 29 = 58/261 and 8 × 9/29 × 9 = 72/261

Step 3: Add the Numerators
Now add the numerators (58 + 72 = 130) and keep the common denominator 261 unchanged.
Working: 58 + 72/261 = 130/261

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 130 and 261 is 1, confirming that 130/261 cannot be reduced further—it is already in its simplest irreducible form.
Working: 130/261

Step 5: Decimal & Percentage Representation
Dividing the numerator 130 by denominator 261 produces a repeating decimal (approximately 0.498084, or 49.8084%).
Working: 130 ÷ 261 = 0.498084 (49.8084%)

Key Values:
- Simplified Fraction: 130/261
- Mixed Number Form: 130/261
- Decimal Value: 0.498084
- Percentage: 49.8084%

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Solved with FractionsCalc:
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2/9 + 8/29 = 130/261

Simplified Fraction

130/261

Mixed Number

Proper (130/261)

Decimal Value

0.498084

Percentage

49.8084%

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Step-by-Step Solution: 2/9 + 8/29

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 29 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 29 = 261.

LCD(9, 29) = 261

Step 2

Convert to Equivalent Fractions with Common Denominator 261

Multiply the numerator and denominator of 2/9 by 29, and multiply the numerator and denominator of 8/29 by 9 so both fractions share the common base 261.

2 × 29/9 × 29 = 58/261 and 8 × 9/29 × 9 = 72/261

Step 3

Add the Numerators

Now add the numerators (58 + 72 = 130) and keep the common denominator 261 unchanged.

58 + 72/261 = 130/261

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 130 and 261 is 1, confirming that 130/261 cannot be reduced further—it is already in its simplest irreducible form.

130/261

Step 5

Decimal & Percentage Representation

Dividing the numerator 130 by denominator 261 produces a repeating decimal (approximately 0.498084, or 49.8084%).

130 ÷ 261 = 0.498084 (49.8084%)

Visual Representation

The diagram below illustrates 2/9 plus 8/29 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`130/261`
Mixed Number Form	`130/261`
Decimal Form	`0.498084`
Percentage	`49.8084%`

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Frequently Asked Questions

What is 2/9 plus 8/29 as a fraction?

2/9 + 8/29 in simplest fraction form is 130/261.

What is 2/9 plus 8/29 as a decimal?

2/9 + 8/29 converted to a decimal is 0.498084.

What is 2/9 plus 8/29 as a percentage?

2/9 + 8/29 expressed as a percentage is 49.8084%.

Does 2/9 plus 8/29 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.498084...) because the denominator contains prime factors other than 2 and 5.