What is 1/9 plus 9/29? (Answer: 110/261)

Exact Answer

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Problem: What is 1/9 plus 9/29?
Formula / Expression: 1/9 + 9/29
Final Answer: 110/261
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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 1/9 by 29, and multiply the numerator and denominator of 9/29 by 9 so both fractions share the common base 261.
Working: 1 × 29/9 × 29 = 29/261 and 9 × 9/29 × 9 = 81/261

Step 3: Add the Numerators
Now add the numerators (29 + 81 = 110) and keep the common denominator 261 unchanged.
Working: 29 + 81/261 = 110/261

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 110 and 261 is 1, confirming that 110/261 cannot be reduced further—it is already in its simplest irreducible form.
Working: 110/261

Step 5: Decimal & Percentage Representation
Dividing the numerator 110 by denominator 261 produces a repeating decimal (approximately 0.421456, or 42.1456%).
Working: 110 ÷ 261 = 0.421456 (42.1456%)

Key Values:
- Simplified Fraction: 110/261
- Mixed Number Form: 110/261
- Decimal Value: 0.421456
- Percentage: 42.1456%

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Solved with FractionsCalc:
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1/9 + 9/29 = 110/261

Simplified Fraction

110/261

Mixed Number

Proper (110/261)

Decimal Value

0.421456

Percentage

42.1456%

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Step-by-Step Solution: 1/9 + 9/29

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 1/9 by 29, and multiply the numerator and denominator of 9/29 by 9 so both fractions share the common base 261.

1 × 29/9 × 29 = 29/261 and 9 × 9/29 × 9 = 81/261

Step 3

Add the Numerators

Now add the numerators (29 + 81 = 110) and keep the common denominator 261 unchanged.

29 + 81/261 = 110/261

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 110 and 261 is 1, confirming that 110/261 cannot be reduced further—it is already in its simplest irreducible form.

110/261

Step 5

Decimal & Percentage Representation

Dividing the numerator 110 by denominator 261 produces a repeating decimal (approximately 0.421456, or 42.1456%).

110 ÷ 261 = 0.421456 (42.1456%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`110/261`
Mixed Number Form	`110/261`
Decimal Form	`0.421456`
Percentage	`42.1456%`

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Frequently Asked Questions

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

1/9 + 9/29 in simplest fraction form is 110/261.

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

1/9 + 9/29 converted to a decimal is 0.421456.

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

1/9 + 9/29 expressed as a percentage is 42.1456%.

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

It results in a repeating decimal (approximately 0.421456...) because the denominator contains prime factors other than 2 and 5.