What is 3/13 plus 4/15? (Answer: 97/195)

Exact Answer

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Problem: What is 3/13 plus 4/15?
Formula / Expression: 3/13 + 4/15
Final Answer: 97/195
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 13 and 15 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 15 = 195.
Working: LCD(13, 15) = 195

Step 2: Convert to Equivalent Fractions with Common Denominator 195
Multiply the numerator and denominator of 3/13 by 15, and multiply the numerator and denominator of 4/15 by 13 so both fractions share the common base 195.
Working: 3 × 15/13 × 15 = 45/195 and 4 × 13/15 × 13 = 52/195

Step 3: Add the Numerators
Now add the numerators (45 + 52 = 97) and keep the common denominator 195 unchanged.
Working: 45 + 52/195 = 97/195

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 97 and 195 is 1, confirming that 97/195 cannot be reduced further—it is already in its simplest irreducible form.
Working: 97/195

Step 5: Decimal & Percentage Representation
Dividing the numerator 97 by denominator 195 produces a repeating decimal (approximately 0.497436, or 49.7436%).
Working: 97 ÷ 195 = 0.497436 (49.7436%)

Key Values:
- Simplified Fraction: 97/195
- Mixed Number Form: 97/195
- Decimal Value: 0.497436
- Percentage: 49.7436%

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Solved with FractionsCalc:
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3/13 + 4/15 = 97/195

Simplified Fraction

97/195

Mixed Number

Proper (97/195)

Decimal Value

0.497436

Percentage

49.7436%

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Step-by-Step Solution: 3/13 + 4/15

Step 1

Find the Least Common Denominator (LCD)

The denominators 13 and 15 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 15 = 195.

LCD(13, 15) = 195

Step 2

Convert to Equivalent Fractions with Common Denominator 195

Multiply the numerator and denominator of 3/13 by 15, and multiply the numerator and denominator of 4/15 by 13 so both fractions share the common base 195.

3 × 15/13 × 15 = 45/195 and 4 × 13/15 × 13 = 52/195

Step 3

Add the Numerators

Now add the numerators (45 + 52 = 97) and keep the common denominator 195 unchanged.

45 + 52/195 = 97/195

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 97 and 195 is 1, confirming that 97/195 cannot be reduced further—it is already in its simplest irreducible form.

97/195

Step 5

Decimal & Percentage Representation

Dividing the numerator 97 by denominator 195 produces a repeating decimal (approximately 0.497436, or 49.7436%).

97 ÷ 195 = 0.497436 (49.7436%)

Visual Representation

The diagram below illustrates 3/13 plus 4/15 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`97/195`
Mixed Number Form	`97/195`
Decimal Form	`0.497436`
Percentage	`49.7436%`

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Frequently Asked Questions

What is 3/13 plus 4/15 as a fraction?

3/13 + 4/15 in simplest fraction form is 97/195.

What is 3/13 plus 4/15 as a decimal?

3/13 + 4/15 converted to a decimal is 0.497436.

What is 3/13 plus 4/15 as a percentage?

3/13 + 4/15 expressed as a percentage is 49.7436%.

Does 3/13 plus 4/15 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.497436...) because the denominator contains prime factors other than 2 and 5.