What is 2/25 plus 3/9? (Answer: 31/75)

Exact Answer

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Problem: What is 2/25 plus 3/9?
Formula / Expression: 2/25 + 3/9
Final Answer: 31/75
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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 2/25 by 9, and multiply the numerator and denominator of 3/9 by 25 so both fractions share the common base 225.
Working: 2 × 9/25 × 9 = 18/225 and 3 × 25/9 × 25 = 75/225

Step 3: Add the Numerators
Now add the numerators (18 + 75 = 93) and keep the common denominator 225 unchanged.
Working: 18 + 75/225 = 93/225

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 93 and 225, which is 3. Divide both the numerator and denominator by 3.
Working: 93 ÷ 3/225 ÷ 3 = 31/75

Step 5: Decimal & Percentage Representation
Dividing the numerator 31 by denominator 75 produces a repeating decimal (approximately 0.413333, or 41.3333%).
Working: 31 ÷ 75 = 0.413333 (41.3333%)

Key Values:
- Simplified Fraction: 31/75
- Mixed Number Form: 31/75
- Decimal Value: 0.413333
- Percentage: 41.3333%

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Solved with FractionsCalc:
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2/25 + 3/9 = 31/75

Simplified Fraction

31/75

Mixed Number

Proper (31/75)

Decimal Value

0.413333

Percentage

41.3333%

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Step-by-Step Solution: 2/25 + 3/9

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

2 × 9/25 × 9 = 18/225 and 3 × 25/9 × 25 = 75/225

Step 3

Add the Numerators

Now add the numerators (18 + 75 = 93) and keep the common denominator 225 unchanged.

18 + 75/225 = 93/225

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 93 and 225, which is 3. Divide both the numerator and denominator by 3.

93 ÷ 3/225 ÷ 3 = 31/75

Step 5

Decimal & Percentage Representation

Dividing the numerator 31 by denominator 75 produces a repeating decimal (approximately 0.413333, or 41.3333%).

31 ÷ 75 = 0.413333 (41.3333%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`31/75`
Mixed Number Form	`31/75`
Decimal Form	`0.413333`
Percentage	`41.3333%`

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Frequently Asked Questions

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

2/25 + 3/9 in simplest fraction form is 31/75.

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

2/25 + 3/9 converted to a decimal is 0.413333.

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

2/25 + 3/9 expressed as a percentage is 41.3333%.

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

It results in a repeating decimal (approximately 0.413333...) because the denominator contains prime factors other than 2 and 5.