What is 3/8 plus 5/13? (Answer: 79/104)

Exact Answer

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Problem: What is 3/8 plus 5/13?
Formula / Expression: 3/8 + 5/13
Final Answer: 79/104
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 104
Multiply the numerator and denominator of 3/8 by 13, and multiply the numerator and denominator of 5/13 by 8 so both fractions share the common base 104.
Working: 3 × 13/8 × 13 = 39/104 and 5 × 8/13 × 8 = 40/104

Step 3: Add the Numerators
Now add the numerators (39 + 40 = 79) and keep the common denominator 104 unchanged.
Working: 39 + 40/104 = 79/104

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 79 and 104 is 1, confirming that 79/104 cannot be reduced further—it is already in its simplest irreducible form.
Working: 79/104

Step 5: Decimal & Percentage Representation
Dividing the numerator 79 by denominator 104 produces a repeating decimal (approximately 0.759615, or 75.9615%).
Working: 79 ÷ 104 = 0.759615 (75.9615%)

Key Values:
- Simplified Fraction: 79/104
- Mixed Number Form: 79/104
- Decimal Value: 0.759615
- Percentage: 75.9615%

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Solved with FractionsCalc:
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3/8 + 5/13 = 79/104

Simplified Fraction

79/104

Mixed Number

Proper (79/104)

Decimal Value

0.759615

Percentage

75.9615%

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Step-by-Step Solution: 3/8 + 5/13

Step 1

Find the Least Common Denominator (LCD)

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

LCD(8, 13) = 104

Step 2

Convert to Equivalent Fractions with Common Denominator 104

Multiply the numerator and denominator of 3/8 by 13, and multiply the numerator and denominator of 5/13 by 8 so both fractions share the common base 104.

3 × 13/8 × 13 = 39/104 and 5 × 8/13 × 8 = 40/104

Step 3

Add the Numerators

Now add the numerators (39 + 40 = 79) and keep the common denominator 104 unchanged.

39 + 40/104 = 79/104

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 79 and 104 is 1, confirming that 79/104 cannot be reduced further—it is already in its simplest irreducible form.

79/104

Step 5

Decimal & Percentage Representation

Dividing the numerator 79 by denominator 104 produces a repeating decimal (approximately 0.759615, or 75.9615%).

79 ÷ 104 = 0.759615 (75.9615%)

Visual Representation

The diagram below illustrates 3/8 plus 5/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`79/104`
Mixed Number Form	`79/104`
Decimal Form	`0.759615`
Percentage	`75.9615%`

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Frequently Asked Questions

What is 3/8 plus 5/13 as a fraction?

3/8 + 5/13 in simplest fraction form is 79/104.

What is 3/8 plus 5/13 as a decimal?

3/8 + 5/13 converted to a decimal is 0.759615.

What is 3/8 plus 5/13 as a percentage?

3/8 + 5/13 expressed as a percentage is 75.9615%.

Does 3/8 plus 5/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.759615...) because the denominator contains prime factors other than 2 and 5.