What is 2/6 plus 9/11? (Answer: 38/33)

Exact Answer

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Problem: What is 2/6 plus 9/11?
Formula / Expression: 2/6 + 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 6 and 11 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 6 × 11 = 66.
Working: LCD(6, 11) = 66

Step 2: Convert to Equivalent Fractions with Common Denominator 66
Multiply the numerator and denominator of 2/6 by 11, and multiply the numerator and denominator of 9/11 by 6 so both fractions share the common base 66.
Working: 2 × 11/6 × 11 = 22/66 and 9 × 6/11 × 6 = 54/66

Step 3: Add the Numerators
Now add the numerators (22 + 54 = 76) and keep the common denominator 66 unchanged.
Working: 22 + 54/66 = 76/66

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 76 and 66, which is 2. Divide both the numerator and denominator by 2.
Working: 76 ÷ 2/66 ÷ 2 = 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:
https://fractionscalc.com/what-is-2-6-plus-9-11/
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2/6 + 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: 2/6 + 9/11

Step 1

Find the Least Common Denominator (LCD)

The denominators 6 and 11 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 6 × 11 = 66.

LCD(6, 11) = 66

Step 2

Convert to Equivalent Fractions with Common Denominator 66

Multiply the numerator and denominator of 2/6 by 11, and multiply the numerator and denominator of 9/11 by 6 so both fractions share the common base 66.

2 × 11/6 × 11 = 22/66 and 9 × 6/11 × 6 = 54/66

Step 3

Add the Numerators

Now add the numerators (22 + 54 = 76) and keep the common denominator 66 unchanged.

22 + 54/66 = 76/66

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 76 and 66, which is 2. Divide both the numerator and denominator by 2.

76 ÷ 2/66 ÷ 2 = 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 2/6 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 2/6 plus 9/11 as a fraction?

2/6 + 9/11 in simplest fraction form is 38/33 (or 1 5/33 as a mixed number).

What is 2/6 plus 9/11 as a decimal?

2/6 + 9/11 converted to a decimal is 1.151515.

What is 2/6 plus 9/11 as a percentage?

2/6 + 9/11 expressed as a percentage is 115.1515%.

How do you write 2/6 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 2/6 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.