What is 3/22 plus 2/6? (Answer: 31/66)

Exact Answer

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Problem: What is 3/22 plus 2/6?
Formula / Expression: 3/22 + 2/6
Final Answer: 31/66
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 22 and 6 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 66 (which is smaller than their product 22 × 6 = 132, keeping the calculation simpler).
Working: LCD(22, 6) = 66

Step 2: Convert to Equivalent Fractions with Common Denominator 66
Multiply the numerator and denominator of 3/22 by 3, and multiply the numerator and denominator of 2/6 by 11 so both fractions share the common base 66.
Working: 3 × 3/22 × 3 = 9/66 and 2 × 11/6 × 11 = 22/66

Step 3: Add the Numerators
Now add the numerators (9 + 22 = 31) and keep the common denominator 66 unchanged.
Working: 9 + 22/66 = 31/66

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 31 and 66 is 1, confirming that 31/66 cannot be reduced further—it is already in its simplest irreducible form.
Working: 31/66

Step 5: Decimal & Percentage Representation
Dividing the numerator 31 by denominator 66 produces a repeating decimal (approximately 0.469697, or 46.9697%).
Working: 31 ÷ 66 = 0.469697 (46.9697%)

Key Values:
- Simplified Fraction: 31/66
- Mixed Number Form: 31/66
- Decimal Value: 0.469697
- Percentage: 46.9697%

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Solved with FractionsCalc:
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3/22 + 2/6 = 31/66

Simplified Fraction

31/66

Mixed Number

Proper (31/66)

Decimal Value

0.469697

Percentage

46.9697%

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Step-by-Step Solution: 3/22 + 2/6

Step 1

Find the Least Common Denominator (LCD)

The denominators 22 and 6 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 66 (which is smaller than their product 22 × 6 = 132, keeping the calculation simpler).

LCD(22, 6) = 66

Step 2

Convert to Equivalent Fractions with Common Denominator 66

Multiply the numerator and denominator of 3/22 by 3, and multiply the numerator and denominator of 2/6 by 11 so both fractions share the common base 66.

3 × 3/22 × 3 = 9/66 and 2 × 11/6 × 11 = 22/66

Step 3

Add the Numerators

Now add the numerators (9 + 22 = 31) and keep the common denominator 66 unchanged.

9 + 22/66 = 31/66

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 31 and 66 is 1, confirming that 31/66 cannot be reduced further—it is already in its simplest irreducible form.

31/66

Step 5

Decimal & Percentage Representation

Dividing the numerator 31 by denominator 66 produces a repeating decimal (approximately 0.469697, or 46.9697%).

31 ÷ 66 = 0.469697 (46.9697%)

Visual Representation

The diagram below illustrates 3/22 plus 2/6 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`31/66`
Mixed Number Form	`31/66`
Decimal Form	`0.469697`
Percentage	`46.9697%`

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Frequently Asked Questions

What is 3/22 plus 2/6 as a fraction?

3/22 + 2/6 in simplest fraction form is 31/66.

What is 3/22 plus 2/6 as a decimal?

3/22 + 2/6 converted to a decimal is 0.469697.

What is 3/22 plus 2/6 as a percentage?

3/22 + 2/6 expressed as a percentage is 46.9697%.

Does 3/22 plus 2/6 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.469697...) because the denominator contains prime factors other than 2 and 5.