What is 2/55 plus 2/9? (Answer: 128/495)

Exact Answer

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Problem: What is 2/55 plus 2/9?
Formula / Expression: 2/55 + 2/9
Final Answer: 128/495
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 55 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 55 × 9 = 495.
Working: LCD(55, 9) = 495

Step 2: Convert to Equivalent Fractions with Common Denominator 495
Multiply the numerator and denominator of 2/55 by 9, and multiply the numerator and denominator of 2/9 by 55 so both fractions share the common base 495.
Working: 2 × 9/55 × 9 = 18/495 and 2 × 55/9 × 55 = 110/495

Step 3: Add the Numerators
Now add the numerators (18 + 110 = 128) and keep the common denominator 495 unchanged.
Working: 18 + 110/495 = 128/495

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 128 and 495 is 1, confirming that 128/495 cannot be reduced further—it is already in its simplest irreducible form.
Working: 128/495

Step 5: Decimal & Percentage Representation
Dividing the numerator 128 by denominator 495 produces a repeating decimal (approximately 0.258586, or 25.8586%).
Working: 128 ÷ 495 = 0.258586 (25.8586%)

Key Values:
- Simplified Fraction: 128/495
- Mixed Number Form: 128/495
- Decimal Value: 0.258586
- Percentage: 25.8586%

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2/55 + 2/9 = 128/495

Simplified Fraction

128/495

Mixed Number

Proper (128/495)

Decimal Value

0.258586

Percentage

25.8586%

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Step-by-Step Solution: 2/55 + 2/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 55 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 55 × 9 = 495.

LCD(55, 9) = 495

Step 2

Convert to Equivalent Fractions with Common Denominator 495

Multiply the numerator and denominator of 2/55 by 9, and multiply the numerator and denominator of 2/9 by 55 so both fractions share the common base 495.

2 × 9/55 × 9 = 18/495 and 2 × 55/9 × 55 = 110/495

Step 3

Add the Numerators

Now add the numerators (18 + 110 = 128) and keep the common denominator 495 unchanged.

18 + 110/495 = 128/495

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 128 and 495 is 1, confirming that 128/495 cannot be reduced further—it is already in its simplest irreducible form.

128/495

Step 5

Decimal & Percentage Representation

Dividing the numerator 128 by denominator 495 produces a repeating decimal (approximately 0.258586, or 25.8586%).

128 ÷ 495 = 0.258586 (25.8586%)

Visual Representation

The diagram below illustrates 2/55 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`128/495`
Mixed Number Form	`128/495`
Decimal Form	`0.258586`
Percentage	`25.8586%`

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Frequently Asked Questions

What is 2/55 plus 2/9 as a fraction?

2/55 + 2/9 in simplest fraction form is 128/495.

What is 2/55 plus 2/9 as a decimal?

2/55 + 2/9 converted to a decimal is 0.258586.

What is 2/55 plus 2/9 as a percentage?

2/55 + 2/9 expressed as a percentage is 25.8586%.

Does 2/55 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.258586...) because the denominator contains prime factors other than 2 and 5.