What is 3/9 plus 9/11? (Answer: 38/33)

Exact Answer

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Problem: What is 3/9 plus 9/11?
Formula / Expression: 3/9 + 9/11
Final Answer: 1 5/33 (38/33)
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 99
Multiply the numerator and denominator of 3/9 by 11, and multiply the numerator and denominator of 9/11 by 9 so both fractions share the common base 99.
Working: 3 × 11/9 × 11 = 33/99 and 9 × 9/11 × 9 = 81/99

Step 3: Add the Numerators
Now add the numerators (33 + 81 = 114) and keep the common denominator 99 unchanged.
Working: 33 + 81/99 = 114/99

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 114 and 99, which is 3. Divide both the numerator and denominator by 3.
Working: 114 ÷ 3/99 ÷ 3 = 38/33

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (38) is greater than the denominator (33), divide 38 by 33: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/33.
Working: 38/33 = 1 5/33

Step 6: Decimal & Percentage Representation
Dividing the numerator 38 by denominator 33 produces a repeating decimal (approximately 1.151515, or 115.1515%).
Working: 38 ÷ 33 = 1.151515 (115.1515%)

Key Values:
- Simplified Fraction: 38/33
- Mixed Number Form: 1 5/33
- Decimal Value: 1.151515
- Percentage: 115.1515%

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Solved with FractionsCalc:
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3/9 + 9/11 = 38/33

Simplified Fraction

38/33

Mixed Number

1 5/33

Decimal Value

1.151515

Percentage

115.1515%

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Step-by-Step Solution: 3/9 + 9/11

Step 1

Find the Least Common Denominator (LCD)

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

LCD(9, 11) = 99

Step 2

Convert to Equivalent Fractions with Common Denominator 99

Multiply the numerator and denominator of 3/9 by 11, and multiply the numerator and denominator of 9/11 by 9 so both fractions share the common base 99.

3 × 11/9 × 11 = 33/99 and 9 × 9/11 × 9 = 81/99

Step 3

Add the Numerators

Now add the numerators (33 + 81 = 114) and keep the common denominator 99 unchanged.

33 + 81/99 = 114/99

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 114 and 99, which is 3. Divide both the numerator and denominator by 3.

114 ÷ 3/99 ÷ 3 = 38/33

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (38) is greater than the denominator (33), divide 38 by 33: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/33.

38/33 = 15/33

Step 6

Decimal & Percentage Representation

Dividing the numerator 38 by denominator 33 produces a repeating decimal (approximately 1.151515, or 115.1515%).

38 ÷ 33 = 1.151515 (115.1515%)

Visual Representation

The diagram below illustrates 3/9 plus 9/11 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`38/33`
Mixed Number Form	`1 5/33`
Decimal Form	`1.151515`
Percentage	`115.1515%`

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Frequently Asked Questions

What is 3/9 plus 9/11 as a fraction?

3/9 + 9/11 in simplest fraction form is 38/33 (or 1 5/33 as a mixed number).

What is 3/9 plus 9/11 as a decimal?

3/9 + 9/11 converted to a decimal is 1.151515.

What is 3/9 plus 9/11 as a percentage?

3/9 + 9/11 expressed as a percentage is 115.1515%.

How do you write 3/9 plus 9/11 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 38/33 can be written as the mixed number 1 5/33.

Does 3/9 plus 9/11 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.151515...) because the denominator contains prime factors other than 2 and 5.