What is 5/11 plus 2/3? (Answer: 37/33)

Exact Answer

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Problem: What is 5/11 plus 2/3?
Formula / Expression: 5/11 + 2/3
Final Answer: 1 4/33 (37/33)
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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 5/11 by 3, and multiply the numerator and denominator of 2/3 by 11 so both fractions share the common base 33.
Working: 5 × 3/11 × 3 = 15/33 and 2 × 11/3 × 11 = 22/33

Step 3: Add the Numerators
Now add the numerators (15 + 22 = 37) and keep the common denominator 33 unchanged.
Working: 15 + 22/33 = 37/33

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 37 and 33 is 1, confirming that 37/33 cannot be reduced further—it is already in its simplest irreducible form.
Working: 37/33

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (37) is greater than the denominator (33), divide 37 by 33: it goes in 1 whole time(s) with a remainder of 4, giving the mixed number 1 4/33.
Working: 37/33 = 1 4/33

Step 6: Decimal & Percentage Representation
Dividing the numerator 37 by denominator 33 produces a repeating decimal (approximately 1.121212, or 112.1212%).
Working: 37 ÷ 33 = 1.121212 (112.1212%)

Key Values:
- Simplified Fraction: 37/33
- Mixed Number Form: 1 4/33
- Decimal Value: 1.121212
- Percentage: 112.1212%

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Solved with FractionsCalc:
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5/11 + 2/3 = 37/33

Simplified Fraction

37/33

Mixed Number

1 4/33

Decimal Value

1.121212

Percentage

112.1212%

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Step-by-Step Solution: 5/11 + 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 5/11 by 3, and multiply the numerator and denominator of 2/3 by 11 so both fractions share the common base 33.

5 × 3/11 × 3 = 15/33 and 2 × 11/3 × 11 = 22/33

Step 3

Add the Numerators

Now add the numerators (15 + 22 = 37) and keep the common denominator 33 unchanged.

15 + 22/33 = 37/33

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 37 and 33 is 1, confirming that 37/33 cannot be reduced further—it is already in its simplest irreducible form.

37/33

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (37) is greater than the denominator (33), divide 37 by 33: it goes in 1 whole time(s) with a remainder of 4, giving the mixed number 1 4/33.

37/33 = 14/33

Step 6

Decimal & Percentage Representation

Dividing the numerator 37 by denominator 33 produces a repeating decimal (approximately 1.121212, or 112.1212%).

37 ÷ 33 = 1.121212 (112.1212%)

Visual Representation

The diagram below illustrates 5/11 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`37/33`
Mixed Number Form	`1 4/33`
Decimal Form	`1.121212`
Percentage	`112.1212%`

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Frequently Asked Questions

What is 5/11 plus 2/3 as a fraction?

5/11 + 2/3 in simplest fraction form is 37/33 (or 1 4/33 as a mixed number).

What is 5/11 plus 2/3 as a decimal?

5/11 + 2/3 converted to a decimal is 1.121212.

What is 5/11 plus 2/3 as a percentage?

5/11 + 2/3 expressed as a percentage is 112.1212%.

How do you write 5/11 plus 2/3 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 37/33 can be written as the mixed number 1 4/33.

Does 5/11 plus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.121212...) because the denominator contains prime factors other than 2 and 5.