What is 3/29 plus 2/9? (Answer: 85/261)

Exact Answer

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Problem: What is 3/29 plus 2/9?
Formula / Expression: 3/29 + 2/9
Final Answer: 85/261
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 261
Multiply the numerator and denominator of 3/29 by 9, and multiply the numerator and denominator of 2/9 by 29 so both fractions share the common base 261.
Working: 3 × 9/29 × 9 = 27/261 and 2 × 29/9 × 29 = 58/261

Step 3: Add the Numerators
Now add the numerators (27 + 58 = 85) and keep the common denominator 261 unchanged.
Working: 27 + 58/261 = 85/261

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 85 and 261 is 1, confirming that 85/261 cannot be reduced further—it is already in its simplest irreducible form.
Working: 85/261

Step 5: Decimal & Percentage Representation
Dividing the numerator 85 by denominator 261 produces a repeating decimal (approximately 0.32567, or 32.567%).
Working: 85 ÷ 261 = 0.32567 (32.567%)

Key Values:
- Simplified Fraction: 85/261
- Mixed Number Form: 85/261
- Decimal Value: 0.32567
- Percentage: 32.567%

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Solved with FractionsCalc:
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3/29 + 2/9 = 85/261

Simplified Fraction

85/261

Mixed Number

Proper (85/261)

Decimal Value

0.32567

Percentage

32.567%

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Step-by-Step Solution: 3/29 + 2/9

Step 1

Find the Least Common Denominator (LCD)

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

LCD(29, 9) = 261

Step 2

Convert to Equivalent Fractions with Common Denominator 261

Multiply the numerator and denominator of 3/29 by 9, and multiply the numerator and denominator of 2/9 by 29 so both fractions share the common base 261.

3 × 9/29 × 9 = 27/261 and 2 × 29/9 × 29 = 58/261

Step 3

Add the Numerators

Now add the numerators (27 + 58 = 85) and keep the common denominator 261 unchanged.

27 + 58/261 = 85/261

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 85 and 261 is 1, confirming that 85/261 cannot be reduced further—it is already in its simplest irreducible form.

85/261

Step 5

Decimal & Percentage Representation

Dividing the numerator 85 by denominator 261 produces a repeating decimal (approximately 0.32567, or 32.567%).

85 ÷ 261 = 0.32567 (32.567%)

Visual Representation

The diagram below illustrates 3/29 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`85/261`
Mixed Number Form	`85/261`
Decimal Form	`0.32567`
Percentage	`32.567%`

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Frequently Asked Questions

What is 3/29 plus 2/9 as a fraction?

3/29 + 2/9 in simplest fraction form is 85/261.

What is 3/29 plus 2/9 as a decimal?

3/29 + 2/9 converted to a decimal is 0.32567.

What is 3/29 plus 2/9 as a percentage?

3/29 + 2/9 expressed as a percentage is 32.567%.

Does 3/29 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.32567...) because the denominator contains prime factors other than 2 and 5.