What is 2/9 plus 7/22? (Answer: 107/198)

Exact Answer

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Problem: What is 2/9 plus 7/22?
Formula / Expression: 2/9 + 7/22
Final Answer: 107/198
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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 2/9 by 22, and multiply the numerator and denominator of 7/22 by 9 so both fractions share the common base 198.
Working: 2 × 22/9 × 22 = 44/198 and 7 × 9/22 × 9 = 63/198

Step 3: Add the Numerators
Now add the numerators (44 + 63 = 107) and keep the common denominator 198 unchanged.
Working: 44 + 63/198 = 107/198

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 107 and 198 is 1, confirming that 107/198 cannot be reduced further—it is already in its simplest irreducible form.
Working: 107/198

Step 5: Decimal & Percentage Representation
Dividing the numerator 107 by denominator 198 produces a repeating decimal (approximately 0.540404, or 54.0404%).
Working: 107 ÷ 198 = 0.540404 (54.0404%)

Key Values:
- Simplified Fraction: 107/198
- Mixed Number Form: 107/198
- Decimal Value: 0.540404
- Percentage: 54.0404%

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Solved with FractionsCalc:
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2/9 + 7/22 = 107/198

Simplified Fraction

107/198

Mixed Number

Proper (107/198)

Decimal Value

0.540404

Percentage

54.0404%

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Step-by-Step Solution: 2/9 + 7/22

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 2/9 by 22, and multiply the numerator and denominator of 7/22 by 9 so both fractions share the common base 198.

2 × 22/9 × 22 = 44/198 and 7 × 9/22 × 9 = 63/198

Step 3

Add the Numerators

Now add the numerators (44 + 63 = 107) and keep the common denominator 198 unchanged.

44 + 63/198 = 107/198

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 107 and 198 is 1, confirming that 107/198 cannot be reduced further—it is already in its simplest irreducible form.

107/198

Step 5

Decimal & Percentage Representation

Dividing the numerator 107 by denominator 198 produces a repeating decimal (approximately 0.540404, or 54.0404%).

107 ÷ 198 = 0.540404 (54.0404%)

Visual Representation

The diagram below illustrates 2/9 plus 7/22 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`107/198`
Mixed Number Form	`107/198`
Decimal Form	`0.540404`
Percentage	`54.0404%`

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Frequently Asked Questions

What is 2/9 plus 7/22 as a fraction?

2/9 + 7/22 in simplest fraction form is 107/198.

What is 2/9 plus 7/22 as a decimal?

2/9 + 7/22 converted to a decimal is 0.540404.

What is 2/9 plus 7/22 as a percentage?

2/9 + 7/22 expressed as a percentage is 54.0404%.

Does 2/9 plus 7/22 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.540404...) because the denominator contains prime factors other than 2 and 5.