What is 1/11 plus 2/3? (Answer: 25/33)

Exact Answer

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Problem: What is 1/11 plus 2/3?
Formula / Expression: 1/11 + 2/3
Final Answer: 25/33
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 11 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 11 × 3 = 33.
Working: LCD(11, 3) = 33

Step 2: Convert to Equivalent Fractions with Common Denominator 33
Multiply the numerator and denominator of 1/11 by 3, and multiply the numerator and denominator of 2/3 by 11 so both fractions share the common base 33.
Working: 1 × 3/11 × 3 = 3/33 and 2 × 11/3 × 11 = 22/33

Step 3: Add the Numerators
Now add the numerators (3 + 22 = 25) and keep the common denominator 33 unchanged.
Working: 3 + 22/33 = 25/33

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 25 and 33 is 1, confirming that 25/33 cannot be reduced further—it is already in its simplest irreducible form.
Working: 25/33

Step 5: Decimal & Percentage Representation
Dividing the numerator 25 by denominator 33 produces a repeating decimal (approximately 0.757576, or 75.7576%).
Working: 25 ÷ 33 = 0.757576 (75.7576%)

Key Values:
- Simplified Fraction: 25/33
- Mixed Number Form: 25/33
- Decimal Value: 0.757576
- Percentage: 75.7576%

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Solved with FractionsCalc:
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1/11 + 2/3 = 25/33

Simplified Fraction

25/33

Mixed Number

Proper (25/33)

Decimal Value

0.757576

Percentage

75.7576%

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Step-by-Step Solution: 1/11 + 2/3

Step 1

Find the Least Common Denominator (LCD)

The denominators 11 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 11 × 3 = 33.

LCD(11, 3) = 33

Step 2

Convert to Equivalent Fractions with Common Denominator 33

Multiply the numerator and denominator of 1/11 by 3, and multiply the numerator and denominator of 2/3 by 11 so both fractions share the common base 33.

1 × 3/11 × 3 = 3/33 and 2 × 11/3 × 11 = 22/33

Step 3

Add the Numerators

Now add the numerators (3 + 22 = 25) and keep the common denominator 33 unchanged.

3 + 22/33 = 25/33

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 25 and 33 is 1, confirming that 25/33 cannot be reduced further—it is already in its simplest irreducible form.

25/33

Step 5

Decimal & Percentage Representation

Dividing the numerator 25 by denominator 33 produces a repeating decimal (approximately 0.757576, or 75.7576%).

25 ÷ 33 = 0.757576 (75.7576%)

Visual Representation

The diagram below illustrates 1/11 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`25/33`
Mixed Number Form	`25/33`
Decimal Form	`0.757576`
Percentage	`75.7576%`

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Frequently Asked Questions

What is 1/11 plus 2/3 as a fraction?

1/11 + 2/3 in simplest fraction form is 25/33.

What is 1/11 plus 2/3 as a decimal?

1/11 + 2/3 converted to a decimal is 0.757576.

What is 1/11 plus 2/3 as a percentage?

1/11 + 2/3 expressed as a percentage is 75.7576%.

Does 1/11 plus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.757576...) because the denominator contains prime factors other than 2 and 5.