What is 3/22 plus 3/9? (Answer: 31/66)

Exact Answer

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Problem: What is 3/22 plus 3/9?
Formula / Expression: 3/22 + 3/9
Final Answer: 31/66
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 198
Multiply the numerator and denominator of 3/22 by 9, and multiply the numerator and denominator of 3/9 by 22 so both fractions share the common base 198.
Working: 3 × 9/22 × 9 = 27/198 and 3 × 22/9 × 22 = 66/198

Step 3: Add the Numerators
Now add the numerators (27 + 66 = 93) and keep the common denominator 198 unchanged.
Working: 27 + 66/198 = 93/198

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 93 and 198, which is 3. Divide both the numerator and denominator by 3.
Working: 93 ÷ 3/198 ÷ 3 = 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 + 3/9 = 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 + 3/9

Step 1

Find the Least Common Denominator (LCD)

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

LCD(22, 9) = 198

Step 2

Convert to Equivalent Fractions with Common Denominator 198

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

3 × 9/22 × 9 = 27/198 and 3 × 22/9 × 22 = 66/198

Step 3

Add the Numerators

Now add the numerators (27 + 66 = 93) and keep the common denominator 198 unchanged.

27 + 66/198 = 93/198

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 93 and 198, which is 3. Divide both the numerator and denominator by 3.

93 ÷ 3/198 ÷ 3 = 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 3/9 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 3/9 as a fraction?

3/22 + 3/9 in simplest fraction form is 31/66.

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

3/22 + 3/9 converted to a decimal is 0.469697.

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

3/22 + 3/9 expressed as a percentage is 46.9697%.

Does 3/22 plus 3/9 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.