What is 2/15 plus 7/39? (Answer: 61/195)

Exact Answer

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Problem: What is 2/15 plus 7/39?
Formula / Expression: 2/15 + 7/39
Final Answer: 61/195
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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 2/15 by 13, and multiply the numerator and denominator of 7/39 by 5 so both fractions share the common base 195.
Working: 2 × 13/15 × 13 = 26/195 and 7 × 5/39 × 5 = 35/195

Step 3: Add the Numerators
Now add the numerators (26 + 35 = 61) and keep the common denominator 195 unchanged.
Working: 26 + 35/195 = 61/195

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 61 and 195 is 1, confirming that 61/195 cannot be reduced further—it is already in its simplest irreducible form.
Working: 61/195

Step 5: Decimal & Percentage Representation
Dividing the numerator 61 by denominator 195 produces a repeating decimal (approximately 0.312821, or 31.2821%).
Working: 61 ÷ 195 = 0.312821 (31.2821%)

Key Values:
- Simplified Fraction: 61/195
- Mixed Number Form: 61/195
- Decimal Value: 0.312821
- Percentage: 31.2821%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-15-plus-7-39/
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2/15 + 7/39 = 61/195

Simplified Fraction

61/195

Mixed Number

Proper (61/195)

Decimal Value

0.312821

Percentage

31.2821%

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Step-by-Step Solution: 2/15 + 7/39

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 2/15 by 13, and multiply the numerator and denominator of 7/39 by 5 so both fractions share the common base 195.

2 × 13/15 × 13 = 26/195 and 7 × 5/39 × 5 = 35/195

Step 3

Add the Numerators

Now add the numerators (26 + 35 = 61) and keep the common denominator 195 unchanged.

26 + 35/195 = 61/195

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 61 and 195 is 1, confirming that 61/195 cannot be reduced further—it is already in its simplest irreducible form.

61/195

Step 5

Decimal & Percentage Representation

Dividing the numerator 61 by denominator 195 produces a repeating decimal (approximately 0.312821, or 31.2821%).

61 ÷ 195 = 0.312821 (31.2821%)

Visual Representation

The diagram below illustrates 2/15 plus 7/39 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`61/195`
Mixed Number Form	`61/195`
Decimal Form	`0.312821`
Percentage	`31.2821%`

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Frequently Asked Questions

What is 2/15 plus 7/39 as a fraction?

2/15 + 7/39 in simplest fraction form is 61/195.

What is 2/15 plus 7/39 as a decimal?

2/15 + 7/39 converted to a decimal is 0.312821.

What is 2/15 plus 7/39 as a percentage?

2/15 + 7/39 expressed as a percentage is 31.2821%.

Does 2/15 plus 7/39 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.312821...) because the denominator contains prime factors other than 2 and 5.