What is 3/9 plus 9/25? (Answer: 52/75)

Exact Answer

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Problem: What is 3/9 plus 9/25?
Formula / Expression: 3/9 + 9/25
Final Answer: 52/75
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 225
Multiply the numerator and denominator of 3/9 by 25, and multiply the numerator and denominator of 9/25 by 9 so both fractions share the common base 225.
Working: 3 × 25/9 × 25 = 75/225 and 9 × 9/25 × 9 = 81/225

Step 3: Add the Numerators
Now add the numerators (75 + 81 = 156) and keep the common denominator 225 unchanged.
Working: 75 + 81/225 = 156/225

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 156 and 225, which is 3. Divide both the numerator and denominator by 3.
Working: 156 ÷ 3/225 ÷ 3 = 52/75

Step 5: Decimal & Percentage Representation
Dividing the numerator 52 by denominator 75 produces a repeating decimal (approximately 0.693333, or 69.3333%).
Working: 52 ÷ 75 = 0.693333 (69.3333%)

Key Values:
- Simplified Fraction: 52/75
- Mixed Number Form: 52/75
- Decimal Value: 0.693333
- Percentage: 69.3333%

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Solved with FractionsCalc:
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3/9 + 9/25 = 52/75

Simplified Fraction

52/75

Mixed Number

Proper (52/75)

Decimal Value

0.693333

Percentage

69.3333%

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

Step 1

Find the Least Common Denominator (LCD)

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

LCD(9, 25) = 225

Step 2

Convert to Equivalent Fractions with Common Denominator 225

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

3 × 25/9 × 25 = 75/225 and 9 × 9/25 × 9 = 81/225

Step 3

Add the Numerators

Now add the numerators (75 + 81 = 156) and keep the common denominator 225 unchanged.

75 + 81/225 = 156/225

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 156 and 225, which is 3. Divide both the numerator and denominator by 3.

156 ÷ 3/225 ÷ 3 = 52/75

Step 5

Decimal & Percentage Representation

Dividing the numerator 52 by denominator 75 produces a repeating decimal (approximately 0.693333, or 69.3333%).

52 ÷ 75 = 0.693333 (69.3333%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`52/75`
Mixed Number Form	`52/75`
Decimal Form	`0.693333`
Percentage	`69.3333%`

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Frequently Asked Questions

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

3/9 + 9/25 in simplest fraction form is 52/75.

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

3/9 + 9/25 converted to a decimal is 0.693333.

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

3/9 + 9/25 expressed as a percentage is 69.3333%.

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

It results in a repeating decimal (approximately 0.693333...) because the denominator contains prime factors other than 2 and 5.