What is 1/8 plus 4/13? (Answer: 45/104)

Exact Answer

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Problem: What is 1/8 plus 4/13?
Formula / Expression: 1/8 + 4/13
Final Answer: 45/104
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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 1/8 by 13, and multiply the numerator and denominator of 4/13 by 8 so both fractions share the common base 104.
Working: 1 × 13/8 × 13 = 13/104 and 4 × 8/13 × 8 = 32/104

Step 3: Add the Numerators
Now add the numerators (13 + 32 = 45) and keep the common denominator 104 unchanged.
Working: 13 + 32/104 = 45/104

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 45 and 104 is 1, confirming that 45/104 cannot be reduced further—it is already in its simplest irreducible form.
Working: 45/104

Step 5: Decimal & Percentage Representation
Dividing the numerator 45 by denominator 104 produces a repeating decimal (approximately 0.432692, or 43.2692%).
Working: 45 ÷ 104 = 0.432692 (43.2692%)

Key Values:
- Simplified Fraction: 45/104
- Mixed Number Form: 45/104
- Decimal Value: 0.432692
- Percentage: 43.2692%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-8-plus-4-13/
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1/8 + 4/13 = 45/104

Simplified Fraction

45/104

Mixed Number

Proper (45/104)

Decimal Value

0.432692

Percentage

43.2692%

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Step-by-Step Solution: 1/8 + 4/13

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 1/8 by 13, and multiply the numerator and denominator of 4/13 by 8 so both fractions share the common base 104.

1 × 13/8 × 13 = 13/104 and 4 × 8/13 × 8 = 32/104

Step 3

Add the Numerators

Now add the numerators (13 + 32 = 45) and keep the common denominator 104 unchanged.

13 + 32/104 = 45/104

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 45 and 104 is 1, confirming that 45/104 cannot be reduced further—it is already in its simplest irreducible form.

45/104

Step 5

Decimal & Percentage Representation

Dividing the numerator 45 by denominator 104 produces a repeating decimal (approximately 0.432692, or 43.2692%).

45 ÷ 104 = 0.432692 (43.2692%)

Visual Representation

The diagram below illustrates 1/8 plus 4/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`45/104`
Mixed Number Form	`45/104`
Decimal Form	`0.432692`
Percentage	`43.2692%`

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Frequently Asked Questions

What is 1/8 plus 4/13 as a fraction?

1/8 + 4/13 in simplest fraction form is 45/104.

What is 1/8 plus 4/13 as a decimal?

1/8 + 4/13 converted to a decimal is 0.432692.

What is 1/8 plus 4/13 as a percentage?

1/8 + 4/13 expressed as a percentage is 43.2692%.

Does 1/8 plus 4/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.432692...) because the denominator contains prime factors other than 2 and 5.