What is 1/11 plus 2/9? (Answer: 31/99)

Exact Answer

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Problem: What is 1/11 plus 2/9?
Formula / Expression: 1/11 + 2/9
Final Answer: 31/99
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 11 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 11 × 9 = 99.
Working: LCD(11, 9) = 99

Step 2: Convert to Equivalent Fractions with Common Denominator 99
Multiply the numerator and denominator of 1/11 by 9, and multiply the numerator and denominator of 2/9 by 11 so both fractions share the common base 99.
Working: 1 × 9/11 × 9 = 9/99 and 2 × 11/9 × 11 = 22/99

Step 3: Add the Numerators
Now add the numerators (9 + 22 = 31) and keep the common denominator 99 unchanged.
Working: 9 + 22/99 = 31/99

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 31 and 99 is 1, confirming that 31/99 cannot be reduced further—it is already in its simplest irreducible form.
Working: 31/99

Step 5: Decimal & Percentage Representation
Dividing the numerator 31 by denominator 99 produces a repeating decimal (approximately 0.313131, or 31.3131%).
Working: 31 ÷ 99 = 0.313131 (31.3131%)

Key Values:
- Simplified Fraction: 31/99
- Mixed Number Form: 31/99
- Decimal Value: 0.313131
- Percentage: 31.3131%

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Solved with FractionsCalc:
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1/11 + 2/9 = 31/99

Simplified Fraction

31/99

Mixed Number

Proper (31/99)

Decimal Value

0.313131

Percentage

31.3131%

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Step-by-Step Solution: 1/11 + 2/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 11 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 11 × 9 = 99.

LCD(11, 9) = 99

Step 2

Convert to Equivalent Fractions with Common Denominator 99

Multiply the numerator and denominator of 1/11 by 9, and multiply the numerator and denominator of 2/9 by 11 so both fractions share the common base 99.

1 × 9/11 × 9 = 9/99 and 2 × 11/9 × 11 = 22/99

Step 3

Add the Numerators

Now add the numerators (9 + 22 = 31) and keep the common denominator 99 unchanged.

9 + 22/99 = 31/99

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 31 and 99 is 1, confirming that 31/99 cannot be reduced further—it is already in its simplest irreducible form.

31/99

Step 5

Decimal & Percentage Representation

Dividing the numerator 31 by denominator 99 produces a repeating decimal (approximately 0.313131, or 31.3131%).

31 ÷ 99 = 0.313131 (31.3131%)

Visual Representation

The diagram below illustrates 1/11 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`31/99`
Mixed Number Form	`31/99`
Decimal Form	`0.313131`
Percentage	`31.3131%`

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Frequently Asked Questions

What is 1/11 plus 2/9 as a fraction?

1/11 + 2/9 in simplest fraction form is 31/99.

What is 1/11 plus 2/9 as a decimal?

1/11 + 2/9 converted to a decimal is 0.313131.

What is 1/11 plus 2/9 as a percentage?

1/11 + 2/9 expressed as a percentage is 31.3131%.

Does 1/11 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.313131...) because the denominator contains prime factors other than 2 and 5.