What is 5/22 plus 4/9? (Answer: 133/198)

Exact Answer

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Problem: What is 5/22 plus 4/9?
Formula / Expression: 5/22 + 4/9
Final Answer: 133/198
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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 5/22 by 9, and multiply the numerator and denominator of 4/9 by 22 so both fractions share the common base 198.
Working: 5 × 9/22 × 9 = 45/198 and 4 × 22/9 × 22 = 88/198

Step 3: Add the Numerators
Now add the numerators (45 + 88 = 133) and keep the common denominator 198 unchanged.
Working: 45 + 88/198 = 133/198

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 133 and 198 is 1, confirming that 133/198 cannot be reduced further—it is already in its simplest irreducible form.
Working: 133/198

Step 5: Decimal & Percentage Representation
Dividing the numerator 133 by denominator 198 produces a repeating decimal (approximately 0.671717, or 67.1717%).
Working: 133 ÷ 198 = 0.671717 (67.1717%)

Key Values:
- Simplified Fraction: 133/198
- Mixed Number Form: 133/198
- Decimal Value: 0.671717
- Percentage: 67.1717%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-22-plus-4-9/
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5/22 + 4/9 = 133/198

Simplified Fraction

133/198

Mixed Number

Proper (133/198)

Decimal Value

0.671717

Percentage

67.1717%

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Step-by-Step Solution: 5/22 + 4/9

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 5/22 by 9, and multiply the numerator and denominator of 4/9 by 22 so both fractions share the common base 198.

5 × 9/22 × 9 = 45/198 and 4 × 22/9 × 22 = 88/198

Step 3

Add the Numerators

Now add the numerators (45 + 88 = 133) and keep the common denominator 198 unchanged.

45 + 88/198 = 133/198

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 133 and 198 is 1, confirming that 133/198 cannot be reduced further—it is already in its simplest irreducible form.

133/198

Step 5

Decimal & Percentage Representation

Dividing the numerator 133 by denominator 198 produces a repeating decimal (approximately 0.671717, or 67.1717%).

133 ÷ 198 = 0.671717 (67.1717%)

Visual Representation

The diagram below illustrates 5/22 plus 4/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`133/198`
Mixed Number Form	`133/198`
Decimal Form	`0.671717`
Percentage	`67.1717%`

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Frequently Asked Questions

What is 5/22 plus 4/9 as a fraction?

5/22 + 4/9 in simplest fraction form is 133/198.

What is 5/22 plus 4/9 as a decimal?

5/22 + 4/9 converted to a decimal is 0.671717.

What is 5/22 plus 4/9 as a percentage?

5/22 + 4/9 expressed as a percentage is 67.1717%.

Does 5/22 plus 4/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.671717...) because the denominator contains prime factors other than 2 and 5.