What is 5/8 plus 9/13? (Answer: 137/104)

Exact Answer

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Problem: What is 5/8 plus 9/13?
Formula / Expression: 5/8 + 9/13
Final Answer: 1 33/104 (137/104)
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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 9/13 by 8 so both fractions share the common base 104.
Working: 5 × 13/8 × 13 = 65/104 and 9 × 8/13 × 8 = 72/104

Step 3: Add the Numerators
Now add the numerators (65 + 72 = 137) and keep the common denominator 104 unchanged.
Working: 65 + 72/104 = 137/104

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 137 and 104 is 1, confirming that 137/104 cannot be reduced further—it is already in its simplest irreducible form.
Working: 137/104

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (137) is greater than the denominator (104), divide 137 by 104: it goes in 1 whole time(s) with a remainder of 33, giving the mixed number 1 33/104.
Working: 137/104 = 1 33/104

Step 6: Decimal & Percentage Representation
Dividing the numerator 137 by denominator 104 produces a repeating decimal (approximately 1.317308, or 131.7308%).
Working: 137 ÷ 104 = 1.317308 (131.7308%)

Key Values:
- Simplified Fraction: 137/104
- Mixed Number Form: 1 33/104
- Decimal Value: 1.317308
- Percentage: 131.7308%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-8-plus-9-13/
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5/8 + 9/13 = 137/104

Simplified Fraction

137/104

Mixed Number

1 33/104

Decimal Value

1.317308

Percentage

131.7308%

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Step-by-Step Solution: 5/8 + 9/13

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 9/13 by 8 so both fractions share the common base 104.

5 × 13/8 × 13 = 65/104 and 9 × 8/13 × 8 = 72/104

Step 3

Add the Numerators

Now add the numerators (65 + 72 = 137) and keep the common denominator 104 unchanged.

65 + 72/104 = 137/104

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 137 and 104 is 1, confirming that 137/104 cannot be reduced further—it is already in its simplest irreducible form.

137/104

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (137) is greater than the denominator (104), divide 137 by 104: it goes in 1 whole time(s) with a remainder of 33, giving the mixed number 1 33/104.

137/104 = 133/104

Step 6

Decimal & Percentage Representation

Dividing the numerator 137 by denominator 104 produces a repeating decimal (approximately 1.317308, or 131.7308%).

137 ÷ 104 = 1.317308 (131.7308%)

Visual Representation

The diagram below illustrates 5/8 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`137/104`
Mixed Number Form	`1 33/104`
Decimal Form	`1.317308`
Percentage	`131.7308%`

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Frequently Asked Questions

What is 5/8 plus 9/13 as a fraction?

5/8 + 9/13 in simplest fraction form is 137/104 (or 1 33/104 as a mixed number).

What is 5/8 plus 9/13 as a decimal?

5/8 + 9/13 converted to a decimal is 1.317308.

What is 5/8 plus 9/13 as a percentage?

5/8 + 9/13 expressed as a percentage is 131.7308%.

How do you write 5/8 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 137/104 can be written as the mixed number 1 33/104.

Does 5/8 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.317308...) because the denominator contains prime factors other than 2 and 5.