What is 2/7 plus 11/22? (Answer: 11/14)

Exact Answer

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Problem: What is 2/7 plus 11/22?
Formula / Expression: 2/7 + 11/22
Final Answer: 11/14
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 7 and 22 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 22 = 154.
Working: LCD(7, 22) = 154

Step 2: Convert to Equivalent Fractions with Common Denominator 154
Multiply the numerator and denominator of 2/7 by 22, and multiply the numerator and denominator of 11/22 by 7 so both fractions share the common base 154.
Working: 2 × 22/7 × 22 = 44/154 and 11 × 7/22 × 7 = 77/154

Step 3: Add the Numerators
Now add the numerators (44 + 77 = 121) and keep the common denominator 154 unchanged.
Working: 44 + 77/154 = 121/154

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 121 and 154, which is 11. Divide both the numerator and denominator by 11.
Working: 121 ÷ 11/154 ÷ 11 = 11/14

Step 5: Decimal & Percentage Representation
Dividing the numerator 11 by denominator 14 produces a repeating decimal (approximately 0.785714, or 78.5714%).
Working: 11 ÷ 14 = 0.785714 (78.5714%)

Key Values:
- Simplified Fraction: 11/14
- Mixed Number Form: 11/14
- Decimal Value: 0.785714
- Percentage: 78.5714%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-7-plus-11-22/
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2/7 + 11/22 = 11/14

Simplified Fraction

11/14

Mixed Number

Proper (11/14)

Decimal Value

0.785714

Percentage

78.5714%

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Step-by-Step Solution: 2/7 + 11/22

Step 1

Find the Least Common Denominator (LCD)

The denominators 7 and 22 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 22 = 154.

LCD(7, 22) = 154

Step 2

Convert to Equivalent Fractions with Common Denominator 154

Multiply the numerator and denominator of 2/7 by 22, and multiply the numerator and denominator of 11/22 by 7 so both fractions share the common base 154.

2 × 22/7 × 22 = 44/154 and 11 × 7/22 × 7 = 77/154

Step 3

Add the Numerators

Now add the numerators (44 + 77 = 121) and keep the common denominator 154 unchanged.

44 + 77/154 = 121/154

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 121 and 154, which is 11. Divide both the numerator and denominator by 11.

121 ÷ 11/154 ÷ 11 = 11/14

Step 5

Decimal & Percentage Representation

Dividing the numerator 11 by denominator 14 produces a repeating decimal (approximately 0.785714, or 78.5714%).

11 ÷ 14 = 0.785714 (78.5714%)

Visual Representation

The diagram below illustrates 2/7 plus 11/22 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`11/14`
Mixed Number Form	`11/14`
Decimal Form	`0.785714`
Percentage	`78.5714%`

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Frequently Asked Questions

What is 2/7 plus 11/22 as a fraction?

2/7 + 11/22 in simplest fraction form is 11/14.

What is 2/7 plus 11/22 as a decimal?

2/7 + 11/22 converted to a decimal is 0.785714.

What is 2/7 plus 11/22 as a percentage?

2/7 + 11/22 expressed as a percentage is 78.5714%.

Does 2/7 plus 11/22 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.785714...) because the denominator contains prime factors other than 2 and 5.