What is 3/25 plus 9/39? (Answer: 114/325)

Exact Answer

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Problem: What is 3/25 plus 9/39?
Formula / Expression: 3/25 + 9/39
Final Answer: 114/325
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 25 and 39 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 25 × 39 = 975.
Working: LCD(25, 39) = 975

Step 2: Convert to Equivalent Fractions with Common Denominator 975
Multiply the numerator and denominator of 3/25 by 39, and multiply the numerator and denominator of 9/39 by 25 so both fractions share the common base 975.
Working: 3 × 39/25 × 39 = 117/975 and 9 × 25/39 × 25 = 225/975

Step 3: Add the Numerators
Now add the numerators (117 + 225 = 342) and keep the common denominator 975 unchanged.
Working: 117 + 225/975 = 342/975

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 342 and 975, which is 3. Divide both the numerator and denominator by 3.
Working: 342 ÷ 3/975 ÷ 3 = 114/325

Step 5: Decimal & Percentage Representation
Dividing the numerator 114 by denominator 325 produces a repeating decimal (approximately 0.350769, or 35.0769%).
Working: 114 ÷ 325 = 0.350769 (35.0769%)

Key Values:
- Simplified Fraction: 114/325
- Mixed Number Form: 114/325
- Decimal Value: 0.350769
- Percentage: 35.0769%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-25-plus-9-39/
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3/25 + 9/39 = 114/325

Simplified Fraction

114/325

Mixed Number

Proper (114/325)

Decimal Value

0.350769

Percentage

35.0769%

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Step-by-Step Solution: 3/25 + 9/39

Step 1

Find the Least Common Denominator (LCD)

The denominators 25 and 39 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 25 × 39 = 975.

LCD(25, 39) = 975

Step 2

Convert to Equivalent Fractions with Common Denominator 975

Multiply the numerator and denominator of 3/25 by 39, and multiply the numerator and denominator of 9/39 by 25 so both fractions share the common base 975.

3 × 39/25 × 39 = 117/975 and 9 × 25/39 × 25 = 225/975

Step 3

Add the Numerators

Now add the numerators (117 + 225 = 342) and keep the common denominator 975 unchanged.

117 + 225/975 = 342/975

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 342 and 975, which is 3. Divide both the numerator and denominator by 3.

342 ÷ 3/975 ÷ 3 = 114/325

Step 5

Decimal & Percentage Representation

Dividing the numerator 114 by denominator 325 produces a repeating decimal (approximately 0.350769, or 35.0769%).

114 ÷ 325 = 0.350769 (35.0769%)

Visual Representation

The diagram below illustrates 3/25 plus 9/39 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`114/325`
Mixed Number Form	`114/325`
Decimal Form	`0.350769`
Percentage	`35.0769%`

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Frequently Asked Questions

What is 3/25 plus 9/39 as a fraction?

3/25 + 9/39 in simplest fraction form is 114/325.

What is 3/25 plus 9/39 as a decimal?

3/25 + 9/39 converted to a decimal is 0.350769.

What is 3/25 plus 9/39 as a percentage?

3/25 + 9/39 expressed as a percentage is 35.0769%.

Does 3/25 plus 9/39 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.350769...) because the denominator contains prime factors other than 2 and 5.