What is 3/22 plus 5/9? (Answer: 137/198)

Exact Answer

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Problem: What is 3/22 plus 5/9?
Formula / Expression: 3/22 + 5/9
Final Answer: 137/198
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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 5/9 by 22 so both fractions share the common base 198.
Working: 3 × 9/22 × 9 = 27/198 and 5 × 22/9 × 22 = 110/198

Step 3: Add the Numerators
Now add the numerators (27 + 110 = 137) and keep the common denominator 198 unchanged.
Working: 27 + 110/198 = 137/198

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 137 and 198 is 1, confirming that 137/198 cannot be reduced further—it is already in its simplest irreducible form.
Working: 137/198

Step 5: Decimal & Percentage Representation
Dividing the numerator 137 by denominator 198 produces a repeating decimal (approximately 0.691919, or 69.1919%).
Working: 137 ÷ 198 = 0.691919 (69.1919%)

Key Values:
- Simplified Fraction: 137/198
- Mixed Number Form: 137/198
- Decimal Value: 0.691919
- Percentage: 69.1919%

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Solved with FractionsCalc:
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3/22 + 5/9 = 137/198

Simplified Fraction

137/198

Mixed Number

Proper (137/198)

Decimal Value

0.691919

Percentage

69.1919%

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Step-by-Step Solution: 3/22 + 5/9

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 5/9 by 22 so both fractions share the common base 198.

3 × 9/22 × 9 = 27/198 and 5 × 22/9 × 22 = 110/198

Step 3

Add the Numerators

Now add the numerators (27 + 110 = 137) and keep the common denominator 198 unchanged.

27 + 110/198 = 137/198

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 137 and 198 is 1, confirming that 137/198 cannot be reduced further—it is already in its simplest irreducible form.

137/198

Step 5

Decimal & Percentage Representation

Dividing the numerator 137 by denominator 198 produces a repeating decimal (approximately 0.691919, or 69.1919%).

137 ÷ 198 = 0.691919 (69.1919%)

Visual Representation

The diagram below illustrates 3/22 plus 5/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`137/198`
Mixed Number Form	`137/198`
Decimal Form	`0.691919`
Percentage	`69.1919%`

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Frequently Asked Questions

What is 3/22 plus 5/9 as a fraction?

3/22 + 5/9 in simplest fraction form is 137/198.

What is 3/22 plus 5/9 as a decimal?

3/22 + 5/9 converted to a decimal is 0.691919.

What is 3/22 plus 5/9 as a percentage?

3/22 + 5/9 expressed as a percentage is 69.1919%.

Does 3/22 plus 5/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.691919...) because the denominator contains prime factors other than 2 and 5.