What is 8/13 plus 5/8? (Answer: 129/104)

Exact Answer

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Problem: What is 8/13 plus 5/8?
Formula / Expression: 8/13 + 5/8
Final Answer: 1 25/104 (129/104)
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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 8/13 by 8, and multiply the numerator and denominator of 5/8 by 13 so both fractions share the common base 104.
Working: 8 × 8/13 × 8 = 64/104 and 5 × 13/8 × 13 = 65/104

Step 3: Add the Numerators
Now add the numerators (64 + 65 = 129) and keep the common denominator 104 unchanged.
Working: 64 + 65/104 = 129/104

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 129 and 104 is 1, confirming that 129/104 cannot be reduced further—it is already in its simplest irreducible form.
Working: 129/104

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (129) is greater than the denominator (104), divide 129 by 104: it goes in 1 whole time(s) with a remainder of 25, giving the mixed number 1 25/104.
Working: 129/104 = 1 25/104

Step 6: Decimal & Percentage Representation
Dividing the numerator 129 by denominator 104 produces a repeating decimal (approximately 1.240385, or 124.0385%).
Working: 129 ÷ 104 = 1.240385 (124.0385%)

Key Values:
- Simplified Fraction: 129/104
- Mixed Number Form: 1 25/104
- Decimal Value: 1.240385
- Percentage: 124.0385%

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Solved with FractionsCalc:
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8/13 + 5/8 = 129/104

Simplified Fraction

129/104

Mixed Number

1 25/104

Decimal Value

1.240385

Percentage

124.0385%

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

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

8 × 8/13 × 8 = 64/104 and 5 × 13/8 × 13 = 65/104

Step 3

Add the Numerators

Now add the numerators (64 + 65 = 129) and keep the common denominator 104 unchanged.

64 + 65/104 = 129/104

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 129 and 104 is 1, confirming that 129/104 cannot be reduced further—it is already in its simplest irreducible form.

129/104

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (129) is greater than the denominator (104), divide 129 by 104: it goes in 1 whole time(s) with a remainder of 25, giving the mixed number 1 25/104.

129/104 = 125/104

Step 6

Decimal & Percentage Representation

Dividing the numerator 129 by denominator 104 produces a repeating decimal (approximately 1.240385, or 124.0385%).

129 ÷ 104 = 1.240385 (124.0385%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`129/104`
Mixed Number Form	`1 25/104`
Decimal Form	`1.240385`
Percentage	`124.0385%`

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Frequently Asked Questions

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

8/13 + 5/8 in simplest fraction form is 129/104 (or 1 25/104 as a mixed number).

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

8/13 + 5/8 converted to a decimal is 1.240385.

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

8/13 + 5/8 expressed as a percentage is 124.0385%.

How do you write 8/13 plus 5/8 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 129/104 can be written as the mixed number 1 25/104.

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

It results in a repeating decimal (approximately 1.240385...) because the denominator contains prime factors other than 2 and 5.