What is 3/15 plus 9/39? (Answer: 28/65)

Exact Answer

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Problem: What is 3/15 plus 9/39?
Formula / Expression: 3/15 + 9/39
Final Answer: 28/65
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 15 and 39 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 195 (which is smaller than their product 15 × 39 = 585, keeping the calculation simpler).
Working: LCD(15, 39) = 195

Step 2: Convert to Equivalent Fractions with Common Denominator 195
Multiply the numerator and denominator of 3/15 by 13, and multiply the numerator and denominator of 9/39 by 5 so both fractions share the common base 195.
Working: 3 × 13/15 × 13 = 39/195 and 9 × 5/39 × 5 = 45/195

Step 3: Add the Numerators
Now add the numerators (39 + 45 = 84) and keep the common denominator 195 unchanged.
Working: 39 + 45/195 = 84/195

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 84 and 195, which is 3. Divide both the numerator and denominator by 3.
Working: 84 ÷ 3/195 ÷ 3 = 28/65

Step 5: Decimal & Percentage Representation
Dividing the numerator 28 by denominator 65 produces a repeating decimal (approximately 0.430769, or 43.0769%).
Working: 28 ÷ 65 = 0.430769 (43.0769%)

Key Values:
- Simplified Fraction: 28/65
- Mixed Number Form: 28/65
- Decimal Value: 0.430769
- Percentage: 43.0769%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-15-plus-9-39/
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3/15 + 9/39 = 28/65

Simplified Fraction

28/65

Mixed Number

Proper (28/65)

Decimal Value

0.430769

Percentage

43.0769%

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Step-by-Step Solution: 3/15 + 9/39

Step 1

Find the Least Common Denominator (LCD)

The denominators 15 and 39 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 195 (which is smaller than their product 15 × 39 = 585, keeping the calculation simpler).

LCD(15, 39) = 195

Step 2

Convert to Equivalent Fractions with Common Denominator 195

Multiply the numerator and denominator of 3/15 by 13, and multiply the numerator and denominator of 9/39 by 5 so both fractions share the common base 195.

3 × 13/15 × 13 = 39/195 and 9 × 5/39 × 5 = 45/195

Step 3

Add the Numerators

Now add the numerators (39 + 45 = 84) and keep the common denominator 195 unchanged.

39 + 45/195 = 84/195

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 84 and 195, which is 3. Divide both the numerator and denominator by 3.

84 ÷ 3/195 ÷ 3 = 28/65

Step 5

Decimal & Percentage Representation

Dividing the numerator 28 by denominator 65 produces a repeating decimal (approximately 0.430769, or 43.0769%).

28 ÷ 65 = 0.430769 (43.0769%)

Visual Representation

The diagram below illustrates 3/15 plus 9/39 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`28/65`
Mixed Number Form	`28/65`
Decimal Form	`0.430769`
Percentage	`43.0769%`

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Frequently Asked Questions

What is 3/15 plus 9/39 as a fraction?

3/15 + 9/39 in simplest fraction form is 28/65.

What is 3/15 plus 9/39 as a decimal?

3/15 + 9/39 converted to a decimal is 0.430769.

What is 3/15 plus 9/39 as a percentage?

3/15 + 9/39 expressed as a percentage is 43.0769%.

Does 3/15 plus 9/39 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.430769...) because the denominator contains prime factors other than 2 and 5.