What is 1/22 plus 2/3? (Answer: 47/66)

Exact Answer

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Problem: What is 1/22 plus 2/3?
Formula / Expression: 1/22 + 2/3
Final Answer: 47/66
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 22 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 22 × 3 = 66.
Working: LCD(22, 3) = 66

Step 2: Convert to Equivalent Fractions with Common Denominator 66
Multiply the numerator and denominator of 1/22 by 3, and multiply the numerator and denominator of 2/3 by 22 so both fractions share the common base 66.
Working: 1 × 3/22 × 3 = 3/66 and 2 × 22/3 × 22 = 44/66

Step 3: Add the Numerators
Now add the numerators (3 + 44 = 47) and keep the common denominator 66 unchanged.
Working: 3 + 44/66 = 47/66

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 47 and 66 is 1, confirming that 47/66 cannot be reduced further—it is already in its simplest irreducible form.
Working: 47/66

Step 5: Decimal & Percentage Representation
Dividing the numerator 47 by denominator 66 produces a repeating decimal (approximately 0.712121, or 71.2121%).
Working: 47 ÷ 66 = 0.712121 (71.2121%)

Key Values:
- Simplified Fraction: 47/66
- Mixed Number Form: 47/66
- Decimal Value: 0.712121
- Percentage: 71.2121%

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Solved with FractionsCalc:
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1/22 + 2/3 = 47/66

Simplified Fraction

47/66

Mixed Number

Proper (47/66)

Decimal Value

0.712121

Percentage

71.2121%

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Step-by-Step Solution: 1/22 + 2/3

Step 1

Find the Least Common Denominator (LCD)

The denominators 22 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 22 × 3 = 66.

LCD(22, 3) = 66

Step 2

Convert to Equivalent Fractions with Common Denominator 66

Multiply the numerator and denominator of 1/22 by 3, and multiply the numerator and denominator of 2/3 by 22 so both fractions share the common base 66.

1 × 3/22 × 3 = 3/66 and 2 × 22/3 × 22 = 44/66

Step 3

Add the Numerators

Now add the numerators (3 + 44 = 47) and keep the common denominator 66 unchanged.

3 + 44/66 = 47/66

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 47 and 66 is 1, confirming that 47/66 cannot be reduced further—it is already in its simplest irreducible form.

47/66

Step 5

Decimal & Percentage Representation

Dividing the numerator 47 by denominator 66 produces a repeating decimal (approximately 0.712121, or 71.2121%).

47 ÷ 66 = 0.712121 (71.2121%)

Visual Representation

The diagram below illustrates 1/22 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`47/66`
Mixed Number Form	`47/66`
Decimal Form	`0.712121`
Percentage	`71.2121%`

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Frequently Asked Questions

What is 1/22 plus 2/3 as a fraction?

1/22 + 2/3 in simplest fraction form is 47/66.

What is 1/22 plus 2/3 as a decimal?

1/22 + 2/3 converted to a decimal is 0.712121.

What is 1/22 plus 2/3 as a percentage?

1/22 + 2/3 expressed as a percentage is 71.2121%.

Does 1/22 plus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.712121...) because the denominator contains prime factors other than 2 and 5.