What is 3/9 plus 4/11? (Answer: 23/33)

Exact Answer

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Problem: What is 3/9 plus 4/11?
Formula / Expression: 3/9 + 4/11
Final Answer: 23/33
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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 4/11 by 9 so both fractions share the common base 99.
Working: 3 × 11/9 × 11 = 33/99 and 4 × 9/11 × 9 = 36/99

Step 3: Add the Numerators
Now add the numerators (33 + 36 = 69) and keep the common denominator 99 unchanged.
Working: 33 + 36/99 = 69/99

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 69 and 99, which is 3. Divide both the numerator and denominator by 3.
Working: 69 ÷ 3/99 ÷ 3 = 23/33

Step 5: Decimal & Percentage Representation
Dividing the numerator 23 by denominator 33 produces a repeating decimal (approximately 0.69697, or 69.697%).
Working: 23 ÷ 33 = 0.69697 (69.697%)

Key Values:
- Simplified Fraction: 23/33
- Mixed Number Form: 23/33
- Decimal Value: 0.69697
- Percentage: 69.697%

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Solved with FractionsCalc:
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3/9 + 4/11 = 23/33

Simplified Fraction

23/33

Mixed Number

Proper (23/33)

Decimal Value

0.69697

Percentage

69.697%

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Step-by-Step Solution: 3/9 + 4/11

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 4/11 by 9 so both fractions share the common base 99.

3 × 11/9 × 11 = 33/99 and 4 × 9/11 × 9 = 36/99

Step 3

Add the Numerators

Now add the numerators (33 + 36 = 69) and keep the common denominator 99 unchanged.

33 + 36/99 = 69/99

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 69 and 99, which is 3. Divide both the numerator and denominator by 3.

69 ÷ 3/99 ÷ 3 = 23/33

Step 5

Decimal & Percentage Representation

Dividing the numerator 23 by denominator 33 produces a repeating decimal (approximately 0.69697, or 69.697%).

23 ÷ 33 = 0.69697 (69.697%)

Visual Representation

The diagram below illustrates 3/9 plus 4/11 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`23/33`
Mixed Number Form	`23/33`
Decimal Form	`0.69697`
Percentage	`69.697%`

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Frequently Asked Questions

What is 3/9 plus 4/11 as a fraction?

3/9 + 4/11 in simplest fraction form is 23/33.

What is 3/9 plus 4/11 as a decimal?

3/9 + 4/11 converted to a decimal is 0.69697.

What is 3/9 plus 4/11 as a percentage?

3/9 + 4/11 expressed as a percentage is 69.697%.

Does 3/9 plus 4/11 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.69697...) because the denominator contains prime factors other than 2 and 5.