What is 4/25 plus 2/9? (Answer: 86/225)

Exact Answer

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Problem: What is 4/25 plus 2/9?
Formula / Expression: 4/25 + 2/9
Final Answer: 86/225
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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 4/25 by 9, and multiply the numerator and denominator of 2/9 by 25 so both fractions share the common base 225.
Working: 4 × 9/25 × 9 = 36/225 and 2 × 25/9 × 25 = 50/225

Step 3: Add the Numerators
Now add the numerators (36 + 50 = 86) and keep the common denominator 225 unchanged.
Working: 36 + 50/225 = 86/225

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 86 and 225 is 1, confirming that 86/225 cannot be reduced further—it is already in its simplest irreducible form.
Working: 86/225

Step 5: Decimal & Percentage Representation
Dividing the numerator 86 by denominator 225 produces a repeating decimal (approximately 0.382222, or 38.2222%).
Working: 86 ÷ 225 = 0.382222 (38.2222%)

Key Values:
- Simplified Fraction: 86/225
- Mixed Number Form: 86/225
- Decimal Value: 0.382222
- Percentage: 38.2222%

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Solved with FractionsCalc:
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4/25 + 2/9 = 86/225

Simplified Fraction

86/225

Mixed Number

Proper (86/225)

Decimal Value

0.382222

Percentage

38.2222%

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Step-by-Step Solution: 4/25 + 2/9

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 4/25 by 9, and multiply the numerator and denominator of 2/9 by 25 so both fractions share the common base 225.

4 × 9/25 × 9 = 36/225 and 2 × 25/9 × 25 = 50/225

Step 3

Add the Numerators

Now add the numerators (36 + 50 = 86) and keep the common denominator 225 unchanged.

36 + 50/225 = 86/225

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 86 and 225 is 1, confirming that 86/225 cannot be reduced further—it is already in its simplest irreducible form.

86/225

Step 5

Decimal & Percentage Representation

Dividing the numerator 86 by denominator 225 produces a repeating decimal (approximately 0.382222, or 38.2222%).

86 ÷ 225 = 0.382222 (38.2222%)

Visual Representation

The diagram below illustrates 4/25 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`86/225`
Mixed Number Form	`86/225`
Decimal Form	`0.382222`
Percentage	`38.2222%`

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Frequently Asked Questions

What is 4/25 plus 2/9 as a fraction?

4/25 + 2/9 in simplest fraction form is 86/225.

What is 4/25 plus 2/9 as a decimal?

4/25 + 2/9 converted to a decimal is 0.382222.

What is 4/25 plus 2/9 as a percentage?

4/25 + 2/9 expressed as a percentage is 38.2222%.

Does 4/25 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.382222...) because the denominator contains prime factors other than 2 and 5.