What is 3/13 plus 3/8? (Answer: 63/104)

Exact Answer

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Problem: What is 3/13 plus 3/8?
Formula / Expression: 3/13 + 3/8
Final Answer: 63/104
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 13 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 8 = 104.
Working: LCD(13, 8) = 104

Step 2: Convert to Equivalent Fractions with Common Denominator 104
Multiply the numerator and denominator of 3/13 by 8, and multiply the numerator and denominator of 3/8 by 13 so both fractions share the common base 104.
Working: 3 × 8/13 × 8 = 24/104 and 3 × 13/8 × 13 = 39/104

Step 3: Add the Numerators
Now add the numerators (24 + 39 = 63) and keep the common denominator 104 unchanged.
Working: 24 + 39/104 = 63/104

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 63 and 104 is 1, confirming that 63/104 cannot be reduced further—it is already in its simplest irreducible form.
Working: 63/104

Step 5: Decimal & Percentage Representation
Dividing the numerator 63 by denominator 104 produces a repeating decimal (approximately 0.605769, or 60.5769%).
Working: 63 ÷ 104 = 0.605769 (60.5769%)

Key Values:
- Simplified Fraction: 63/104
- Mixed Number Form: 63/104
- Decimal Value: 0.605769
- Percentage: 60.5769%

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3/13 + 3/8 = 63/104

Simplified Fraction

63/104

Mixed Number

Proper (63/104)

Decimal Value

0.605769

Percentage

60.5769%

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Step-by-Step Solution: 3/13 + 3/8

Step 1

Find the Least Common Denominator (LCD)

The denominators 13 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 8 = 104.

LCD(13, 8) = 104

Step 2

Convert to Equivalent Fractions with Common Denominator 104

Multiply the numerator and denominator of 3/13 by 8, and multiply the numerator and denominator of 3/8 by 13 so both fractions share the common base 104.

3 × 8/13 × 8 = 24/104 and 3 × 13/8 × 13 = 39/104

Step 3

Add the Numerators

Now add the numerators (24 + 39 = 63) and keep the common denominator 104 unchanged.

24 + 39/104 = 63/104

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 63 and 104 is 1, confirming that 63/104 cannot be reduced further—it is already in its simplest irreducible form.

63/104

Step 5

Decimal & Percentage Representation

Dividing the numerator 63 by denominator 104 produces a repeating decimal (approximately 0.605769, or 60.5769%).

63 ÷ 104 = 0.605769 (60.5769%)

Visual Representation

The diagram below illustrates 3/13 plus 3/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`63/104`
Mixed Number Form	`63/104`
Decimal Form	`0.605769`
Percentage	`60.5769%`

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Frequently Asked Questions

What is 3/13 plus 3/8 as a fraction?

3/13 + 3/8 in simplest fraction form is 63/104.

What is 3/13 plus 3/8 as a decimal?

3/13 + 3/8 converted to a decimal is 0.605769.

What is 3/13 plus 3/8 as a percentage?

3/13 + 3/8 expressed as a percentage is 60.5769%.

Does 3/13 plus 3/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.605769...) because the denominator contains prime factors other than 2 and 5.