What is 3/11 plus 2/5? (Answer: 37/55)

Exact Answer

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Problem: What is 3/11 plus 2/5?
Formula / Expression: 3/11 + 2/5
Final Answer: 37/55
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 11 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 11 × 5 = 55.
Working: LCD(11, 5) = 55

Step 2: Convert to Equivalent Fractions with Common Denominator 55
Multiply the numerator and denominator of 3/11 by 5, and multiply the numerator and denominator of 2/5 by 11 so both fractions share the common base 55.
Working: 3 × 5/11 × 5 = 15/55 and 2 × 11/5 × 11 = 22/55

Step 3: Add the Numerators
Now add the numerators (15 + 22 = 37) and keep the common denominator 55 unchanged.
Working: 15 + 22/55 = 37/55

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 37 and 55 is 1, confirming that 37/55 cannot be reduced further—it is already in its simplest irreducible form.
Working: 37/55

Step 5: Decimal & Percentage Representation
Dividing the numerator 37 by denominator 55 produces a repeating decimal (approximately 0.672727, or 67.2727%).
Working: 37 ÷ 55 = 0.672727 (67.2727%)

Key Values:
- Simplified Fraction: 37/55
- Mixed Number Form: 37/55
- Decimal Value: 0.672727
- Percentage: 67.2727%

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Solved with FractionsCalc:
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3/11 + 2/5 = 37/55

Simplified Fraction

37/55

Mixed Number

Proper (37/55)

Decimal Value

0.672727

Percentage

67.2727%

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Step-by-Step Solution: 3/11 + 2/5

Step 1

Find the Least Common Denominator (LCD)

The denominators 11 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 11 × 5 = 55.

LCD(11, 5) = 55

Step 2

Convert to Equivalent Fractions with Common Denominator 55

Multiply the numerator and denominator of 3/11 by 5, and multiply the numerator and denominator of 2/5 by 11 so both fractions share the common base 55.

3 × 5/11 × 5 = 15/55 and 2 × 11/5 × 11 = 22/55

Step 3

Add the Numerators

Now add the numerators (15 + 22 = 37) and keep the common denominator 55 unchanged.

15 + 22/55 = 37/55

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 37 and 55 is 1, confirming that 37/55 cannot be reduced further—it is already in its simplest irreducible form.

37/55

Step 5

Decimal & Percentage Representation

Dividing the numerator 37 by denominator 55 produces a repeating decimal (approximately 0.672727, or 67.2727%).

37 ÷ 55 = 0.672727 (67.2727%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`37/55`
Mixed Number Form	`37/55`
Decimal Form	`0.672727`
Percentage	`67.2727%`

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Frequently Asked Questions

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

3/11 + 2/5 in simplest fraction form is 37/55.

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

3/11 + 2/5 converted to a decimal is 0.672727.

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

3/11 + 2/5 expressed as a percentage is 67.2727%.

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

It results in a repeating decimal (approximately 0.672727...) because the denominator contains prime factors other than 2 and 5.