What is 2/11 plus 3/7? (Answer: 47/77)

Exact Answer

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Problem: What is 2/11 plus 3/7?
Formula / Expression: 2/11 + 3/7
Final Answer: 47/77
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 11 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 11 × 7 = 77.
Working: LCD(11, 7) = 77

Step 2: Convert to Equivalent Fractions with Common Denominator 77
Multiply the numerator and denominator of 2/11 by 7, and multiply the numerator and denominator of 3/7 by 11 so both fractions share the common base 77.
Working: 2 × 7/11 × 7 = 14/77 and 3 × 11/7 × 11 = 33/77

Step 3: Add the Numerators
Now add the numerators (14 + 33 = 47) and keep the common denominator 77 unchanged.
Working: 14 + 33/77 = 47/77

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 47 and 77 is 1, confirming that 47/77 cannot be reduced further—it is already in its simplest irreducible form.
Working: 47/77

Step 5: Decimal & Percentage Representation
Dividing the numerator 47 by denominator 77 produces a repeating decimal (approximately 0.61039, or 61.039%).
Working: 47 ÷ 77 = 0.61039 (61.039%)

Key Values:
- Simplified Fraction: 47/77
- Mixed Number Form: 47/77
- Decimal Value: 0.61039
- Percentage: 61.039%

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Solved with FractionsCalc:
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2/11 + 3/7 = 47/77

Simplified Fraction

47/77

Mixed Number

Proper (47/77)

Decimal Value

0.61039

Percentage

61.039%

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Step-by-Step Solution: 2/11 + 3/7

Step 1

Find the Least Common Denominator (LCD)

The denominators 11 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 11 × 7 = 77.

LCD(11, 7) = 77

Step 2

Convert to Equivalent Fractions with Common Denominator 77

Multiply the numerator and denominator of 2/11 by 7, and multiply the numerator and denominator of 3/7 by 11 so both fractions share the common base 77.

2 × 7/11 × 7 = 14/77 and 3 × 11/7 × 11 = 33/77

Step 3

Add the Numerators

Now add the numerators (14 + 33 = 47) and keep the common denominator 77 unchanged.

14 + 33/77 = 47/77

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 47 and 77 is 1, confirming that 47/77 cannot be reduced further—it is already in its simplest irreducible form.

47/77

Step 5

Decimal & Percentage Representation

Dividing the numerator 47 by denominator 77 produces a repeating decimal (approximately 0.61039, or 61.039%).

47 ÷ 77 = 0.61039 (61.039%)

Visual Representation

The diagram below illustrates 2/11 plus 3/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`47/77`
Mixed Number Form	`47/77`
Decimal Form	`0.61039`
Percentage	`61.039%`

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Frequently Asked Questions

What is 2/11 plus 3/7 as a fraction?

2/11 + 3/7 in simplest fraction form is 47/77.

What is 2/11 plus 3/7 as a decimal?

2/11 + 3/7 converted to a decimal is 0.61039.

What is 2/11 plus 3/7 as a percentage?

2/11 + 3/7 expressed as a percentage is 61.039%.

Does 2/11 plus 3/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.61039...) because the denominator contains prime factors other than 2 and 5.