What is 2/11 plus 4/7? (Answer: 58/77)

Exact Answer

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Problem: What is 2/11 plus 4/7?
Formula / Expression: 2/11 + 4/7
Final Answer: 58/77
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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 4/7 by 11 so both fractions share the common base 77.
Working: 2 × 7/11 × 7 = 14/77 and 4 × 11/7 × 11 = 44/77

Step 3: Add the Numerators
Now add the numerators (14 + 44 = 58) and keep the common denominator 77 unchanged.
Working: 14 + 44/77 = 58/77

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 58 and 77 is 1, confirming that 58/77 cannot be reduced further—it is already in its simplest irreducible form.
Working: 58/77

Step 5: Decimal & Percentage Representation
Dividing the numerator 58 by denominator 77 produces a repeating decimal (approximately 0.753247, or 75.3247%).
Working: 58 ÷ 77 = 0.753247 (75.3247%)

Key Values:
- Simplified Fraction: 58/77
- Mixed Number Form: 58/77
- Decimal Value: 0.753247
- Percentage: 75.3247%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-11-plus-4-7/
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2/11 + 4/7 = 58/77

Simplified Fraction

58/77

Mixed Number

Proper (58/77)

Decimal Value

0.753247

Percentage

75.3247%

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Step-by-Step Solution: 2/11 + 4/7

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 4/7 by 11 so both fractions share the common base 77.

2 × 7/11 × 7 = 14/77 and 4 × 11/7 × 11 = 44/77

Step 3

Add the Numerators

Now add the numerators (14 + 44 = 58) and keep the common denominator 77 unchanged.

14 + 44/77 = 58/77

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 58 and 77 is 1, confirming that 58/77 cannot be reduced further—it is already in its simplest irreducible form.

58/77

Step 5

Decimal & Percentage Representation

Dividing the numerator 58 by denominator 77 produces a repeating decimal (approximately 0.753247, or 75.3247%).

58 ÷ 77 = 0.753247 (75.3247%)

Visual Representation

The diagram below illustrates 2/11 plus 4/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`58/77`
Mixed Number Form	`58/77`
Decimal Form	`0.753247`
Percentage	`75.3247%`

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Frequently Asked Questions

What is 2/11 plus 4/7 as a fraction?

2/11 + 4/7 in simplest fraction form is 58/77.

What is 2/11 plus 4/7 as a decimal?

2/11 + 4/7 converted to a decimal is 0.753247.

What is 2/11 plus 4/7 as a percentage?

2/11 + 4/7 expressed as a percentage is 75.3247%.

Does 2/11 plus 4/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.753247...) because the denominator contains prime factors other than 2 and 5.