What is 1/29 plus 2/9? (Answer: 67/261)

Exact Answer

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Problem: What is 1/29 plus 2/9?
Formula / Expression: 1/29 + 2/9
Final Answer: 67/261
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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 1/29 by 9, and multiply the numerator and denominator of 2/9 by 29 so both fractions share the common base 261.
Working: 1 × 9/29 × 9 = 9/261 and 2 × 29/9 × 29 = 58/261

Step 3: Add the Numerators
Now add the numerators (9 + 58 = 67) and keep the common denominator 261 unchanged.
Working: 9 + 58/261 = 67/261

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 67 and 261 is 1, confirming that 67/261 cannot be reduced further—it is already in its simplest irreducible form.
Working: 67/261

Step 5: Decimal & Percentage Representation
Dividing the numerator 67 by denominator 261 produces a repeating decimal (approximately 0.256705, or 25.6705%).
Working: 67 ÷ 261 = 0.256705 (25.6705%)

Key Values:
- Simplified Fraction: 67/261
- Mixed Number Form: 67/261
- Decimal Value: 0.256705
- Percentage: 25.6705%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-29-plus-2-9/
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1/29 + 2/9 = 67/261

Simplified Fraction

67/261

Mixed Number

Proper (67/261)

Decimal Value

0.256705

Percentage

25.6705%

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Step-by-Step Solution: 1/29 + 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 1/29 by 9, and multiply the numerator and denominator of 2/9 by 29 so both fractions share the common base 261.

1 × 9/29 × 9 = 9/261 and 2 × 29/9 × 29 = 58/261

Step 3

Add the Numerators

Now add the numerators (9 + 58 = 67) and keep the common denominator 261 unchanged.

9 + 58/261 = 67/261

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 67 and 261 is 1, confirming that 67/261 cannot be reduced further—it is already in its simplest irreducible form.

67/261

Step 5

Decimal & Percentage Representation

Dividing the numerator 67 by denominator 261 produces a repeating decimal (approximately 0.256705, or 25.6705%).

67 ÷ 261 = 0.256705 (25.6705%)

Visual Representation

The diagram below illustrates 1/29 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`67/261`
Mixed Number Form	`67/261`
Decimal Form	`0.256705`
Percentage	`25.6705%`

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Frequently Asked Questions

What is 1/29 plus 2/9 as a fraction?

1/29 + 2/9 in simplest fraction form is 67/261.

What is 1/29 plus 2/9 as a decimal?

1/29 + 2/9 converted to a decimal is 0.256705.

What is 1/29 plus 2/9 as a percentage?

1/29 + 2/9 expressed as a percentage is 25.6705%.

Does 1/29 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.256705...) because the denominator contains prime factors other than 2 and 5.