What is 2/6 plus 8/22? (Answer: 23/33)

Exact Answer

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Problem: What is 2/6 plus 8/22?
Formula / Expression: 2/6 + 8/22
Final Answer: 23/33
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 66
Multiply the numerator and denominator of 2/6 by 11, and multiply the numerator and denominator of 8/22 by 3 so both fractions share the common base 66.
Working: 2 × 11/6 × 11 = 22/66 and 8 × 3/22 × 3 = 24/66

Step 3: Add the Numerators
Now add the numerators (22 + 24 = 46) and keep the common denominator 66 unchanged.
Working: 22 + 24/66 = 46/66

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 46 and 66, which is 2. Divide both the numerator and denominator by 2.
Working: 46 ÷ 2/66 ÷ 2 = 23/33

Step 5: Decimal & Percentage Representation
Dividing the numerator 23 by denominator 33 produces a repeating decimal (approximately 0.69697, or 69.697%).
Working: 23 ÷ 33 = 0.69697 (69.697%)

Key Values:
- Simplified Fraction: 23/33
- Mixed Number Form: 23/33
- Decimal Value: 0.69697
- Percentage: 69.697%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-6-plus-8-22/
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2/6 + 8/22 = 23/33

Simplified Fraction

23/33

Mixed Number

Proper (23/33)

Decimal Value

0.69697

Percentage

69.697%

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Step-by-Step Solution: 2/6 + 8/22

Step 1

Find the Least Common Denominator (LCD)

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

LCD(6, 22) = 66

Step 2

Convert to Equivalent Fractions with Common Denominator 66

Multiply the numerator and denominator of 2/6 by 11, and multiply the numerator and denominator of 8/22 by 3 so both fractions share the common base 66.

2 × 11/6 × 11 = 22/66 and 8 × 3/22 × 3 = 24/66

Step 3

Add the Numerators

Now add the numerators (22 + 24 = 46) and keep the common denominator 66 unchanged.

22 + 24/66 = 46/66

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 46 and 66, which is 2. Divide both the numerator and denominator by 2.

46 ÷ 2/66 ÷ 2 = 23/33

Step 5

Decimal & Percentage Representation

Dividing the numerator 23 by denominator 33 produces a repeating decimal (approximately 0.69697, or 69.697%).

23 ÷ 33 = 0.69697 (69.697%)

Visual Representation

The diagram below illustrates 2/6 plus 8/22 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`23/33`
Mixed Number Form	`23/33`
Decimal Form	`0.69697`
Percentage	`69.697%`

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Frequently Asked Questions

What is 2/6 plus 8/22 as a fraction?

2/6 + 8/22 in simplest fraction form is 23/33.

What is 2/6 plus 8/22 as a decimal?

2/6 + 8/22 converted to a decimal is 0.69697.

What is 2/6 plus 8/22 as a percentage?

2/6 + 8/22 expressed as a percentage is 69.697%.

Does 2/6 plus 8/22 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.69697...) because the denominator contains prime factors other than 2 and 5.