What is 2/9 plus 8/25? (Answer: 122/225)

Exact Answer

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Problem: What is 2/9 plus 8/25?
Formula / Expression: 2/9 + 8/25
Final Answer: 122/225
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 25 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 25 = 225.
Working: LCD(9, 25) = 225

Step 2: Convert to Equivalent Fractions with Common Denominator 225
Multiply the numerator and denominator of 2/9 by 25, and multiply the numerator and denominator of 8/25 by 9 so both fractions share the common base 225.
Working: 2 × 25/9 × 25 = 50/225 and 8 × 9/25 × 9 = 72/225

Step 3: Add the Numerators
Now add the numerators (50 + 72 = 122) and keep the common denominator 225 unchanged.
Working: 50 + 72/225 = 122/225

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 122 and 225 is 1, confirming that 122/225 cannot be reduced further—it is already in its simplest irreducible form.
Working: 122/225

Step 5: Decimal & Percentage Representation
Dividing the numerator 122 by denominator 225 produces a repeating decimal (approximately 0.542222, or 54.2222%).
Working: 122 ÷ 225 = 0.542222 (54.2222%)

Key Values:
- Simplified Fraction: 122/225
- Mixed Number Form: 122/225
- Decimal Value: 0.542222
- Percentage: 54.2222%

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Solved with FractionsCalc:
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2/9 + 8/25 = 122/225

Simplified Fraction

122/225

Mixed Number

Proper (122/225)

Decimal Value

0.542222

Percentage

54.2222%

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Step-by-Step Solution: 2/9 + 8/25

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 25 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 25 = 225.

LCD(9, 25) = 225

Step 2

Convert to Equivalent Fractions with Common Denominator 225

Multiply the numerator and denominator of 2/9 by 25, and multiply the numerator and denominator of 8/25 by 9 so both fractions share the common base 225.

2 × 25/9 × 25 = 50/225 and 8 × 9/25 × 9 = 72/225

Step 3

Add the Numerators

Now add the numerators (50 + 72 = 122) and keep the common denominator 225 unchanged.

50 + 72/225 = 122/225

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 122 and 225 is 1, confirming that 122/225 cannot be reduced further—it is already in its simplest irreducible form.

122/225

Step 5

Decimal & Percentage Representation

Dividing the numerator 122 by denominator 225 produces a repeating decimal (approximately 0.542222, or 54.2222%).

122 ÷ 225 = 0.542222 (54.2222%)

Visual Representation

The diagram below illustrates 2/9 plus 8/25 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`122/225`
Mixed Number Form	`122/225`
Decimal Form	`0.542222`
Percentage	`54.2222%`

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Frequently Asked Questions

What is 2/9 plus 8/25 as a fraction?

2/9 + 8/25 in simplest fraction form is 122/225.

What is 2/9 plus 8/25 as a decimal?

2/9 + 8/25 converted to a decimal is 0.542222.

What is 2/9 plus 8/25 as a percentage?

2/9 + 8/25 expressed as a percentage is 54.2222%.

Does 2/9 plus 8/25 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.542222...) because the denominator contains prime factors other than 2 and 5.