What is 2/7 plus 12/22? (Answer: 64/77)

Exact Answer

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Problem: What is 2/7 plus 12/22?
Formula / Expression: 2/7 + 12/22
Final Answer: 64/77
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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 12/22 by 7 so both fractions share the common base 154.
Working: 2 × 22/7 × 22 = 44/154 and 12 × 7/22 × 7 = 84/154

Step 3: Add the Numerators
Now add the numerators (44 + 84 = 128) and keep the common denominator 154 unchanged.
Working: 44 + 84/154 = 128/154

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 128 and 154, which is 2. Divide both the numerator and denominator by 2.
Working: 128 ÷ 2/154 ÷ 2 = 64/77

Step 5: Decimal & Percentage Representation
Dividing the numerator 64 by denominator 77 produces a repeating decimal (approximately 0.831169, or 83.1169%).
Working: 64 ÷ 77 = 0.831169 (83.1169%)

Key Values:
- Simplified Fraction: 64/77
- Mixed Number Form: 64/77
- Decimal Value: 0.831169
- Percentage: 83.1169%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-7-plus-12-22/
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2/7 + 12/22 = 64/77

Simplified Fraction

64/77

Mixed Number

Proper (64/77)

Decimal Value

0.831169

Percentage

83.1169%

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Step-by-Step Solution: 2/7 + 12/22

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 12/22 by 7 so both fractions share the common base 154.

2 × 22/7 × 22 = 44/154 and 12 × 7/22 × 7 = 84/154

Step 3

Add the Numerators

Now add the numerators (44 + 84 = 128) and keep the common denominator 154 unchanged.

44 + 84/154 = 128/154

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 128 and 154, which is 2. Divide both the numerator and denominator by 2.

128 ÷ 2/154 ÷ 2 = 64/77

Step 5

Decimal & Percentage Representation

Dividing the numerator 64 by denominator 77 produces a repeating decimal (approximately 0.831169, or 83.1169%).

64 ÷ 77 = 0.831169 (83.1169%)

Visual Representation

The diagram below illustrates 2/7 plus 12/22 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`64/77`
Mixed Number Form	`64/77`
Decimal Form	`0.831169`
Percentage	`83.1169%`

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Frequently Asked Questions

What is 2/7 plus 12/22 as a fraction?

2/7 + 12/22 in simplest fraction form is 64/77.

What is 2/7 plus 12/22 as a decimal?

2/7 + 12/22 converted to a decimal is 0.831169.

What is 2/7 plus 12/22 as a percentage?

2/7 + 12/22 expressed as a percentage is 83.1169%.

Does 2/7 plus 12/22 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.831169...) because the denominator contains prime factors other than 2 and 5.