What is 9/25 plus 4/9? (Answer: 181/225)

Exact Answer

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Problem: What is 9/25 plus 4/9?
Formula / Expression: 9/25 + 4/9
Final Answer: 181/225
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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 4/9 by 25 so both fractions share the common base 225.
Working: 9 × 9/25 × 9 = 81/225 and 4 × 25/9 × 25 = 100/225

Step 3: Add the Numerators
Now add the numerators (81 + 100 = 181) and keep the common denominator 225 unchanged.
Working: 81 + 100/225 = 181/225

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 181 and 225 is 1, confirming that 181/225 cannot be reduced further—it is already in its simplest irreducible form.
Working: 181/225

Step 5: Decimal & Percentage Representation
Dividing the numerator 181 by denominator 225 produces a repeating decimal (approximately 0.804444, or 80.4444%).
Working: 181 ÷ 225 = 0.804444 (80.4444%)

Key Values:
- Simplified Fraction: 181/225
- Mixed Number Form: 181/225
- Decimal Value: 0.804444
- Percentage: 80.4444%

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Solved with FractionsCalc:
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9/25 + 4/9 = 181/225

Simplified Fraction

181/225

Mixed Number

Proper (181/225)

Decimal Value

0.804444

Percentage

80.4444%

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Step-by-Step Solution: 9/25 + 4/9

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 4/9 by 25 so both fractions share the common base 225.

9 × 9/25 × 9 = 81/225 and 4 × 25/9 × 25 = 100/225

Step 3

Add the Numerators

Now add the numerators (81 + 100 = 181) and keep the common denominator 225 unchanged.

81 + 100/225 = 181/225

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 181 and 225 is 1, confirming that 181/225 cannot be reduced further—it is already in its simplest irreducible form.

181/225

Step 5

Decimal & Percentage Representation

Dividing the numerator 181 by denominator 225 produces a repeating decimal (approximately 0.804444, or 80.4444%).

181 ÷ 225 = 0.804444 (80.4444%)

Visual Representation

The diagram below illustrates 9/25 plus 4/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`181/225`
Mixed Number Form	`181/225`
Decimal Form	`0.804444`
Percentage	`80.4444%`

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Frequently Asked Questions

What is 9/25 plus 4/9 as a fraction?

9/25 + 4/9 in simplest fraction form is 181/225.

What is 9/25 plus 4/9 as a decimal?

9/25 + 4/9 converted to a decimal is 0.804444.

What is 9/25 plus 4/9 as a percentage?

9/25 + 4/9 expressed as a percentage is 80.4444%.

Does 9/25 plus 4/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.804444...) because the denominator contains prime factors other than 2 and 5.