What is 9/25 plus 5/9? (Answer: 206/225)

Exact Answer

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Problem: What is 9/25 plus 5/9?
Formula / Expression: 9/25 + 5/9
Final Answer: 206/225
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 225
Multiply the numerator and denominator of 9/25 by 9, and multiply the numerator and denominator of 5/9 by 25 so both fractions share the common base 225.
Working: 9 × 9/25 × 9 = 81/225 and 5 × 25/9 × 25 = 125/225

Step 3: Add the Numerators
Now add the numerators (81 + 125 = 206) and keep the common denominator 225 unchanged.
Working: 81 + 125/225 = 206/225

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 206 and 225 is 1, confirming that 206/225 cannot be reduced further—it is already in its simplest irreducible form.
Working: 206/225

Step 5: Decimal & Percentage Representation
Dividing the numerator 206 by denominator 225 produces a repeating decimal (approximately 0.915556, or 91.5556%).
Working: 206 ÷ 225 = 0.915556 (91.5556%)

Key Values:
- Simplified Fraction: 206/225
- Mixed Number Form: 206/225
- Decimal Value: 0.915556
- Percentage: 91.5556%

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Solved with FractionsCalc:
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9/25 + 5/9 = 206/225

Simplified Fraction

206/225

Mixed Number

Proper (206/225)

Decimal Value

0.915556

Percentage

91.5556%

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Step-by-Step Solution: 9/25 + 5/9

Step 1

Find the Least Common Denominator (LCD)

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

LCD(25, 9) = 225

Step 2

Convert to Equivalent Fractions with Common Denominator 225

Multiply the numerator and denominator of 9/25 by 9, and multiply the numerator and denominator of 5/9 by 25 so both fractions share the common base 225.

9 × 9/25 × 9 = 81/225 and 5 × 25/9 × 25 = 125/225

Step 3

Add the Numerators

Now add the numerators (81 + 125 = 206) and keep the common denominator 225 unchanged.

81 + 125/225 = 206/225

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 206 and 225 is 1, confirming that 206/225 cannot be reduced further—it is already in its simplest irreducible form.

206/225

Step 5

Decimal & Percentage Representation

Dividing the numerator 206 by denominator 225 produces a repeating decimal (approximately 0.915556, or 91.5556%).

206 ÷ 225 = 0.915556 (91.5556%)

Visual Representation

The diagram below illustrates 9/25 plus 5/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`206/225`
Mixed Number Form	`206/225`
Decimal Form	`0.915556`
Percentage	`91.5556%`

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Frequently Asked Questions

What is 9/25 plus 5/9 as a fraction?

9/25 + 5/9 in simplest fraction form is 206/225.

What is 9/25 plus 5/9 as a decimal?

9/25 + 5/9 converted to a decimal is 0.915556.

What is 9/25 plus 5/9 as a percentage?

9/25 + 5/9 expressed as a percentage is 91.5556%.

Does 9/25 plus 5/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.915556...) because the denominator contains prime factors other than 2 and 5.