What is 8/22 plus 2/3? (Answer: 34/33)

Exact Answer

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Problem: What is 8/22 plus 2/3?
Formula / Expression: 8/22 + 2/3
Final Answer: 1 1/33 (34/33)
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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 8/22 by 3, and multiply the numerator and denominator of 2/3 by 22 so both fractions share the common base 66.
Working: 8 × 3/22 × 3 = 24/66 and 2 × 22/3 × 22 = 44/66

Step 3: Add the Numerators
Now add the numerators (24 + 44 = 68) and keep the common denominator 66 unchanged.
Working: 24 + 44/66 = 68/66

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 68 and 66, which is 2. Divide both the numerator and denominator by 2.
Working: 68 ÷ 2/66 ÷ 2 = 34/33

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (34) is greater than the denominator (33), divide 34 by 33: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/33.
Working: 34/33 = 1 1/33

Step 6: Decimal & Percentage Representation
Dividing the numerator 34 by denominator 33 produces a repeating decimal (approximately 1.030303, or 103.0303%).
Working: 34 ÷ 33 = 1.030303 (103.0303%)

Key Values:
- Simplified Fraction: 34/33
- Mixed Number Form: 1 1/33
- Decimal Value: 1.030303
- Percentage: 103.0303%

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Solved with FractionsCalc:
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8/22 + 2/3 = 34/33

Simplified Fraction

34/33

Mixed Number

1 1/33

Decimal Value

1.030303

Percentage

103.0303%

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Step-by-Step Solution: 8/22 + 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 8/22 by 3, and multiply the numerator and denominator of 2/3 by 22 so both fractions share the common base 66.

8 × 3/22 × 3 = 24/66 and 2 × 22/3 × 22 = 44/66

Step 3

Add the Numerators

Now add the numerators (24 + 44 = 68) and keep the common denominator 66 unchanged.

24 + 44/66 = 68/66

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 68 and 66, which is 2. Divide both the numerator and denominator by 2.

68 ÷ 2/66 ÷ 2 = 34/33

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (34) is greater than the denominator (33), divide 34 by 33: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/33.

34/33 = 11/33

Step 6

Decimal & Percentage Representation

Dividing the numerator 34 by denominator 33 produces a repeating decimal (approximately 1.030303, or 103.0303%).

34 ÷ 33 = 1.030303 (103.0303%)

Visual Representation

The diagram below illustrates 8/22 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`34/33`
Mixed Number Form	`1 1/33`
Decimal Form	`1.030303`
Percentage	`103.0303%`

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Frequently Asked Questions

What is 8/22 plus 2/3 as a fraction?

8/22 + 2/3 in simplest fraction form is 34/33 (or 1 1/33 as a mixed number).

What is 8/22 plus 2/3 as a decimal?

8/22 + 2/3 converted to a decimal is 1.030303.

What is 8/22 plus 2/3 as a percentage?

8/22 + 2/3 expressed as a percentage is 103.0303%.

How do you write 8/22 plus 2/3 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 34/33 can be written as the mixed number 1 1/33.

Does 8/22 plus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.030303...) because the denominator contains prime factors other than 2 and 5.