What is 3/9 plus 9/22? (Answer: 49/66)

Exact Answer

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Problem: What is 3/9 plus 9/22?
Formula / Expression: 3/9 + 9/22
Final Answer: 49/66
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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 9/22 by 9 so both fractions share the common base 198.
Working: 3 × 22/9 × 22 = 66/198 and 9 × 9/22 × 9 = 81/198

Step 3: Add the Numerators
Now add the numerators (66 + 81 = 147) and keep the common denominator 198 unchanged.
Working: 66 + 81/198 = 147/198

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 147 and 198, which is 3. Divide both the numerator and denominator by 3.
Working: 147 ÷ 3/198 ÷ 3 = 49/66

Step 5: Decimal & Percentage Representation
Dividing the numerator 49 by denominator 66 produces a repeating decimal (approximately 0.742424, or 74.2424%).
Working: 49 ÷ 66 = 0.742424 (74.2424%)

Key Values:
- Simplified Fraction: 49/66
- Mixed Number Form: 49/66
- Decimal Value: 0.742424
- Percentage: 74.2424%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-9-plus-9-22/
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3/9 + 9/22 = 49/66

Simplified Fraction

49/66

Mixed Number

Proper (49/66)

Decimal Value

0.742424

Percentage

74.2424%

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Step-by-Step Solution: 3/9 + 9/22

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 9/22 by 9 so both fractions share the common base 198.

3 × 22/9 × 22 = 66/198 and 9 × 9/22 × 9 = 81/198

Step 3

Add the Numerators

Now add the numerators (66 + 81 = 147) and keep the common denominator 198 unchanged.

66 + 81/198 = 147/198

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 147 and 198, which is 3. Divide both the numerator and denominator by 3.

147 ÷ 3/198 ÷ 3 = 49/66

Step 5

Decimal & Percentage Representation

Dividing the numerator 49 by denominator 66 produces a repeating decimal (approximately 0.742424, or 74.2424%).

49 ÷ 66 = 0.742424 (74.2424%)

Visual Representation

The diagram below illustrates 3/9 plus 9/22 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`49/66`
Mixed Number Form	`49/66`
Decimal Form	`0.742424`
Percentage	`74.2424%`

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Frequently Asked Questions

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

3/9 + 9/22 in simplest fraction form is 49/66.

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

3/9 + 9/22 converted to a decimal is 0.742424.

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

3/9 + 9/22 expressed as a percentage is 74.2424%.

Does 3/9 plus 9/22 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.742424...) because the denominator contains prime factors other than 2 and 5.