What is 2/5 plus 5/11? (Answer: 47/55)

Exact Answer

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Problem: What is 2/5 plus 5/11?
Formula / Expression: 2/5 + 5/11
Final Answer: 47/55
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 55
Multiply the numerator and denominator of 2/5 by 11, and multiply the numerator and denominator of 5/11 by 5 so both fractions share the common base 55.
Working: 2 × 11/5 × 11 = 22/55 and 5 × 5/11 × 5 = 25/55

Step 3: Add the Numerators
Now add the numerators (22 + 25 = 47) and keep the common denominator 55 unchanged.
Working: 22 + 25/55 = 47/55

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 47 and 55 is 1, confirming that 47/55 cannot be reduced further—it is already in its simplest irreducible form.
Working: 47/55

Step 5: Decimal & Percentage Representation
Dividing the numerator 47 by denominator 55 produces a repeating decimal (approximately 0.854545, or 85.4545%).
Working: 47 ÷ 55 = 0.854545 (85.4545%)

Key Values:
- Simplified Fraction: 47/55
- Mixed Number Form: 47/55
- Decimal Value: 0.854545
- Percentage: 85.4545%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-5-plus-5-11/
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2/5 + 5/11 = 47/55

Simplified Fraction

47/55

Mixed Number

Proper (47/55)

Decimal Value

0.854545

Percentage

85.4545%

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

Step 1

Find the Least Common Denominator (LCD)

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

LCD(5, 11) = 55

Step 2

Convert to Equivalent Fractions with Common Denominator 55

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

2 × 11/5 × 11 = 22/55 and 5 × 5/11 × 5 = 25/55

Step 3

Add the Numerators

Now add the numerators (22 + 25 = 47) and keep the common denominator 55 unchanged.

22 + 25/55 = 47/55

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 47 and 55 is 1, confirming that 47/55 cannot be reduced further—it is already in its simplest irreducible form.

47/55

Step 5

Decimal & Percentage Representation

Dividing the numerator 47 by denominator 55 produces a repeating decimal (approximately 0.854545, or 85.4545%).

47 ÷ 55 = 0.854545 (85.4545%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`47/55`
Mixed Number Form	`47/55`
Decimal Form	`0.854545`
Percentage	`85.4545%`

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Frequently Asked Questions

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

2/5 + 5/11 in simplest fraction form is 47/55.

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

2/5 + 5/11 converted to a decimal is 0.854545.

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

2/5 + 5/11 expressed as a percentage is 85.4545%.

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

It results in a repeating decimal (approximately 0.854545...) because the denominator contains prime factors other than 2 and 5.