What is 3/25 plus 2/9? (Answer: 77/225)

Exact Answer

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Problem: What is 3/25 plus 2/9?
Formula / Expression: 3/25 + 2/9
Final Answer: 77/225
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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 3/25 by 9, and multiply the numerator and denominator of 2/9 by 25 so both fractions share the common base 225.
Working: 3 × 9/25 × 9 = 27/225 and 2 × 25/9 × 25 = 50/225

Step 3: Add the Numerators
Now add the numerators (27 + 50 = 77) and keep the common denominator 225 unchanged.
Working: 27 + 50/225 = 77/225

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 77 and 225 is 1, confirming that 77/225 cannot be reduced further—it is already in its simplest irreducible form.
Working: 77/225

Step 5: Decimal & Percentage Representation
Dividing the numerator 77 by denominator 225 produces a repeating decimal (approximately 0.342222, or 34.2222%).
Working: 77 ÷ 225 = 0.342222 (34.2222%)

Key Values:
- Simplified Fraction: 77/225
- Mixed Number Form: 77/225
- Decimal Value: 0.342222
- Percentage: 34.2222%

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Solved with FractionsCalc:
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3/25 + 2/9 = 77/225

Simplified Fraction

77/225

Mixed Number

Proper (77/225)

Decimal Value

0.342222

Percentage

34.2222%

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Step-by-Step Solution: 3/25 + 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 3/25 by 9, and multiply the numerator and denominator of 2/9 by 25 so both fractions share the common base 225.

3 × 9/25 × 9 = 27/225 and 2 × 25/9 × 25 = 50/225

Step 3

Add the Numerators

Now add the numerators (27 + 50 = 77) and keep the common denominator 225 unchanged.

27 + 50/225 = 77/225

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 77 and 225 is 1, confirming that 77/225 cannot be reduced further—it is already in its simplest irreducible form.

77/225

Step 5

Decimal & Percentage Representation

Dividing the numerator 77 by denominator 225 produces a repeating decimal (approximately 0.342222, or 34.2222%).

77 ÷ 225 = 0.342222 (34.2222%)

Visual Representation

The diagram below illustrates 3/25 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`77/225`
Mixed Number Form	`77/225`
Decimal Form	`0.342222`
Percentage	`34.2222%`

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Frequently Asked Questions

What is 3/25 plus 2/9 as a fraction?

3/25 + 2/9 in simplest fraction form is 77/225.

What is 3/25 plus 2/9 as a decimal?

3/25 + 2/9 converted to a decimal is 0.342222.

What is 3/25 plus 2/9 as a percentage?

3/25 + 2/9 expressed as a percentage is 34.2222%.

Does 3/25 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.342222...) because the denominator contains prime factors other than 2 and 5.