What is 2/11 plus 2/7? (Answer: 36/77)

Exact Answer

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Problem: What is 2/11 plus 2/7?
Formula / Expression: 2/11 + 2/7
Final Answer: 36/77
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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 2/7 by 11 so both fractions share the common base 77.
Working: 2 × 7/11 × 7 = 14/77 and 2 × 11/7 × 11 = 22/77

Step 3: Add the Numerators
Now add the numerators (14 + 22 = 36) and keep the common denominator 77 unchanged.
Working: 14 + 22/77 = 36/77

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 36 and 77 is 1, confirming that 36/77 cannot be reduced further—it is already in its simplest irreducible form.
Working: 36/77

Step 5: Decimal & Percentage Representation
Dividing the numerator 36 by denominator 77 produces a repeating decimal (approximately 0.467532, or 46.7532%).
Working: 36 ÷ 77 = 0.467532 (46.7532%)

Key Values:
- Simplified Fraction: 36/77
- Mixed Number Form: 36/77
- Decimal Value: 0.467532
- Percentage: 46.7532%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-11-plus-2-7/
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2/11 + 2/7 = 36/77

Simplified Fraction

36/77

Mixed Number

Proper (36/77)

Decimal Value

0.467532

Percentage

46.7532%

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

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 2/7 by 11 so both fractions share the common base 77.

2 × 7/11 × 7 = 14/77 and 2 × 11/7 × 11 = 22/77

Step 3

Add the Numerators

Now add the numerators (14 + 22 = 36) and keep the common denominator 77 unchanged.

14 + 22/77 = 36/77

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 36 and 77 is 1, confirming that 36/77 cannot be reduced further—it is already in its simplest irreducible form.

36/77

Step 5

Decimal & Percentage Representation

Dividing the numerator 36 by denominator 77 produces a repeating decimal (approximately 0.467532, or 46.7532%).

36 ÷ 77 = 0.467532 (46.7532%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`36/77`
Mixed Number Form	`36/77`
Decimal Form	`0.467532`
Percentage	`46.7532%`

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Frequently Asked Questions

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

2/11 + 2/7 in simplest fraction form is 36/77.

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

2/11 + 2/7 converted to a decimal is 0.467532.

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

2/11 + 2/7 expressed as a percentage is 46.7532%.

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

It results in a repeating decimal (approximately 0.467532...) because the denominator contains prime factors other than 2 and 5.