What is 3/9 plus 8/22? (Answer: 23/33)

Exact Answer

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Problem: What is 3/9 plus 8/22?
Formula / Expression: 3/9 + 8/22
Final Answer: 23/33
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 22 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 22 = 198.
Working: LCD(9, 22) = 198

Step 2: Convert to Equivalent Fractions with Common Denominator 198
Multiply the numerator and denominator of 3/9 by 22, and multiply the numerator and denominator of 8/22 by 9 so both fractions share the common base 198.
Working: 3 × 22/9 × 22 = 66/198 and 8 × 9/22 × 9 = 72/198

Step 3: Add the Numerators
Now add the numerators (66 + 72 = 138) and keep the common denominator 198 unchanged.
Working: 66 + 72/198 = 138/198

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 138 and 198, which is 6. Divide both the numerator and denominator by 6.
Working: 138 ÷ 6/198 ÷ 6 = 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:
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3/9 + 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: 3/9 + 8/22

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 22 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 22 = 198.

LCD(9, 22) = 198

Step 2

Convert to Equivalent Fractions with Common Denominator 198

Multiply the numerator and denominator of 3/9 by 22, and multiply the numerator and denominator of 8/22 by 9 so both fractions share the common base 198.

3 × 22/9 × 22 = 66/198 and 8 × 9/22 × 9 = 72/198

Step 3

Add the Numerators

Now add the numerators (66 + 72 = 138) and keep the common denominator 198 unchanged.

66 + 72/198 = 138/198

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 138 and 198, which is 6. Divide both the numerator and denominator by 6.

138 ÷ 6/198 ÷ 6 = 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 3/9 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 3/9 plus 8/22 as a fraction?

3/9 + 8/22 in simplest fraction form is 23/33.

What is 3/9 plus 8/22 as a decimal?

3/9 + 8/22 converted to a decimal is 0.69697.

What is 3/9 plus 8/22 as a percentage?

3/9 + 8/22 expressed as a percentage is 69.697%.

Does 3/9 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.