What is 1/9 plus 5/22? (Answer: 67/198)

Exact Answer

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Problem: What is 1/9 plus 5/22?
Formula / Expression: 1/9 + 5/22
Final Answer: 67/198
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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 1/9 by 22, and multiply the numerator and denominator of 5/22 by 9 so both fractions share the common base 198.
Working: 1 × 22/9 × 22 = 22/198 and 5 × 9/22 × 9 = 45/198

Step 3: Add the Numerators
Now add the numerators (22 + 45 = 67) and keep the common denominator 198 unchanged.
Working: 22 + 45/198 = 67/198

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 67 and 198 is 1, confirming that 67/198 cannot be reduced further—it is already in its simplest irreducible form.
Working: 67/198

Step 5: Decimal & Percentage Representation
Dividing the numerator 67 by denominator 198 produces a repeating decimal (approximately 0.338384, or 33.8384%).
Working: 67 ÷ 198 = 0.338384 (33.8384%)

Key Values:
- Simplified Fraction: 67/198
- Mixed Number Form: 67/198
- Decimal Value: 0.338384
- Percentage: 33.8384%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-9-plus-5-22/
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1/9 + 5/22 = 67/198

Simplified Fraction

67/198

Mixed Number

Proper (67/198)

Decimal Value

0.338384

Percentage

33.8384%

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Step-by-Step Solution: 1/9 + 5/22

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 1/9 by 22, and multiply the numerator and denominator of 5/22 by 9 so both fractions share the common base 198.

1 × 22/9 × 22 = 22/198 and 5 × 9/22 × 9 = 45/198

Step 3

Add the Numerators

Now add the numerators (22 + 45 = 67) and keep the common denominator 198 unchanged.

22 + 45/198 = 67/198

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 67 and 198 is 1, confirming that 67/198 cannot be reduced further—it is already in its simplest irreducible form.

67/198

Step 5

Decimal & Percentage Representation

Dividing the numerator 67 by denominator 198 produces a repeating decimal (approximately 0.338384, or 33.8384%).

67 ÷ 198 = 0.338384 (33.8384%)

Visual Representation

The diagram below illustrates 1/9 plus 5/22 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`67/198`
Mixed Number Form	`67/198`
Decimal Form	`0.338384`
Percentage	`33.8384%`

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Frequently Asked Questions

What is 1/9 plus 5/22 as a fraction?

1/9 + 5/22 in simplest fraction form is 67/198.

What is 1/9 plus 5/22 as a decimal?

1/9 + 5/22 converted to a decimal is 0.338384.

What is 1/9 plus 5/22 as a percentage?

1/9 + 5/22 expressed as a percentage is 33.8384%.

Does 1/9 plus 5/22 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.338384...) because the denominator contains prime factors other than 2 and 5.