What is 7/39 plus 3/15? (Answer: 74/195)

Exact Answer

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Problem: What is 7/39 plus 3/15?
Formula / Expression: 7/39 + 3/15
Final Answer: 74/195
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 195
Multiply the numerator and denominator of 7/39 by 5, and multiply the numerator and denominator of 3/15 by 13 so both fractions share the common base 195.
Working: 7 × 5/39 × 5 = 35/195 and 3 × 13/15 × 13 = 39/195

Step 3: Add the Numerators
Now add the numerators (35 + 39 = 74) and keep the common denominator 195 unchanged.
Working: 35 + 39/195 = 74/195

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 74 and 195 is 1, confirming that 74/195 cannot be reduced further—it is already in its simplest irreducible form.
Working: 74/195

Step 5: Decimal & Percentage Representation
Dividing the numerator 74 by denominator 195 produces a repeating decimal (approximately 0.379487, or 37.9487%).
Working: 74 ÷ 195 = 0.379487 (37.9487%)

Key Values:
- Simplified Fraction: 74/195
- Mixed Number Form: 74/195
- Decimal Value: 0.379487
- Percentage: 37.9487%

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Solved with FractionsCalc:
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7/39 + 3/15 = 74/195

Simplified Fraction

74/195

Mixed Number

Proper (74/195)

Decimal Value

0.379487

Percentage

37.9487%

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Step-by-Step Solution: 7/39 + 3/15

Step 1

Find the Least Common Denominator (LCD)

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

LCD(39, 15) = 195

Step 2

Convert to Equivalent Fractions with Common Denominator 195

Multiply the numerator and denominator of 7/39 by 5, and multiply the numerator and denominator of 3/15 by 13 so both fractions share the common base 195.

7 × 5/39 × 5 = 35/195 and 3 × 13/15 × 13 = 39/195

Step 3

Add the Numerators

Now add the numerators (35 + 39 = 74) and keep the common denominator 195 unchanged.

35 + 39/195 = 74/195

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 74 and 195 is 1, confirming that 74/195 cannot be reduced further—it is already in its simplest irreducible form.

74/195

Step 5

Decimal & Percentage Representation

Dividing the numerator 74 by denominator 195 produces a repeating decimal (approximately 0.379487, or 37.9487%).

74 ÷ 195 = 0.379487 (37.9487%)

Visual Representation

The diagram below illustrates 7/39 plus 3/15 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`74/195`
Mixed Number Form	`74/195`
Decimal Form	`0.379487`
Percentage	`37.9487%`

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Frequently Asked Questions

What is 7/39 plus 3/15 as a fraction?

7/39 + 3/15 in simplest fraction form is 74/195.

What is 7/39 plus 3/15 as a decimal?

7/39 + 3/15 converted to a decimal is 0.379487.

What is 7/39 plus 3/15 as a percentage?

7/39 + 3/15 expressed as a percentage is 37.9487%.

Does 7/39 plus 3/15 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.379487...) because the denominator contains prime factors other than 2 and 5.