What is 4/13 plus 3/8? (Answer: 71/104)

Exact Answer

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Problem: What is 4/13 plus 3/8?
Formula / Expression: 4/13 + 3/8
Final Answer: 71/104
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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 4/13 by 8, and multiply the numerator and denominator of 3/8 by 13 so both fractions share the common base 104.
Working: 4 × 8/13 × 8 = 32/104 and 3 × 13/8 × 13 = 39/104

Step 3: Add the Numerators
Now add the numerators (32 + 39 = 71) and keep the common denominator 104 unchanged.
Working: 32 + 39/104 = 71/104

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 71 and 104 is 1, confirming that 71/104 cannot be reduced further—it is already in its simplest irreducible form.
Working: 71/104

Step 5: Decimal & Percentage Representation
Dividing the numerator 71 by denominator 104 produces a repeating decimal (approximately 0.682692, or 68.2692%).
Working: 71 ÷ 104 = 0.682692 (68.2692%)

Key Values:
- Simplified Fraction: 71/104
- Mixed Number Form: 71/104
- Decimal Value: 0.682692
- Percentage: 68.2692%

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4/13 + 3/8 = 71/104

Simplified Fraction

71/104

Mixed Number

Proper (71/104)

Decimal Value

0.682692

Percentage

68.2692%

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Step-by-Step Solution: 4/13 + 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 4/13 by 8, and multiply the numerator and denominator of 3/8 by 13 so both fractions share the common base 104.

4 × 8/13 × 8 = 32/104 and 3 × 13/8 × 13 = 39/104

Step 3

Add the Numerators

Now add the numerators (32 + 39 = 71) and keep the common denominator 104 unchanged.

32 + 39/104 = 71/104

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 71 and 104 is 1, confirming that 71/104 cannot be reduced further—it is already in its simplest irreducible form.

71/104

Step 5

Decimal & Percentage Representation

Dividing the numerator 71 by denominator 104 produces a repeating decimal (approximately 0.682692, or 68.2692%).

71 ÷ 104 = 0.682692 (68.2692%)

Visual Representation

The diagram below illustrates 4/13 plus 3/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`71/104`
Mixed Number Form	`71/104`
Decimal Form	`0.682692`
Percentage	`68.2692%`

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Frequently Asked Questions

What is 4/13 plus 3/8 as a fraction?

4/13 + 3/8 in simplest fraction form is 71/104.

What is 4/13 plus 3/8 as a decimal?

4/13 + 3/8 converted to a decimal is 0.682692.

What is 4/13 plus 3/8 as a percentage?

4/13 + 3/8 expressed as a percentage is 68.2692%.

Does 4/13 plus 3/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.682692...) because the denominator contains prime factors other than 2 and 5.