What is 5/8 plus 10/13? (Answer: 145/104)

Exact Answer

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Problem: What is 5/8 plus 10/13?
Formula / Expression: 5/8 + 10/13
Final Answer: 1 41/104 (145/104)
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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 5/8 by 13, and multiply the numerator and denominator of 10/13 by 8 so both fractions share the common base 104.
Working: 5 × 13/8 × 13 = 65/104 and 10 × 8/13 × 8 = 80/104

Step 3: Add the Numerators
Now add the numerators (65 + 80 = 145) and keep the common denominator 104 unchanged.
Working: 65 + 80/104 = 145/104

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 145 and 104 is 1, confirming that 145/104 cannot be reduced further—it is already in its simplest irreducible form.
Working: 145/104

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (145) is greater than the denominator (104), divide 145 by 104: it goes in 1 whole time(s) with a remainder of 41, giving the mixed number 1 41/104.
Working: 145/104 = 1 41/104

Step 6: Decimal & Percentage Representation
Dividing the numerator 145 by denominator 104 produces a repeating decimal (approximately 1.394231, or 139.4231%).
Working: 145 ÷ 104 = 1.394231 (139.4231%)

Key Values:
- Simplified Fraction: 145/104
- Mixed Number Form: 1 41/104
- Decimal Value: 1.394231
- Percentage: 139.4231%

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Solved with FractionsCalc:
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5/8 + 10/13 = 145/104

Simplified Fraction

145/104

Mixed Number

1 41/104

Decimal Value

1.394231

Percentage

139.4231%

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Step-by-Step Solution: 5/8 + 10/13

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 5/8 by 13, and multiply the numerator and denominator of 10/13 by 8 so both fractions share the common base 104.

5 × 13/8 × 13 = 65/104 and 10 × 8/13 × 8 = 80/104

Step 3

Add the Numerators

Now add the numerators (65 + 80 = 145) and keep the common denominator 104 unchanged.

65 + 80/104 = 145/104

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 145 and 104 is 1, confirming that 145/104 cannot be reduced further—it is already in its simplest irreducible form.

145/104

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (145) is greater than the denominator (104), divide 145 by 104: it goes in 1 whole time(s) with a remainder of 41, giving the mixed number 1 41/104.

145/104 = 141/104

Step 6

Decimal & Percentage Representation

Dividing the numerator 145 by denominator 104 produces a repeating decimal (approximately 1.394231, or 139.4231%).

145 ÷ 104 = 1.394231 (139.4231%)

Visual Representation

The diagram below illustrates 5/8 plus 10/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`145/104`
Mixed Number Form	`1 41/104`
Decimal Form	`1.394231`
Percentage	`139.4231%`

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Frequently Asked Questions

What is 5/8 plus 10/13 as a fraction?

5/8 + 10/13 in simplest fraction form is 145/104 (or 1 41/104 as a mixed number).

What is 5/8 plus 10/13 as a decimal?

5/8 + 10/13 converted to a decimal is 1.394231.

What is 5/8 plus 10/13 as a percentage?

5/8 + 10/13 expressed as a percentage is 139.4231%.

How do you write 5/8 plus 10/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 145/104 can be written as the mixed number 1 41/104.

Does 5/8 plus 10/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.394231...) because the denominator contains prime factors other than 2 and 5.