What is 1/8 plus 10/13? (Answer: 93/104)

Exact Answer

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Problem: What is 1/8 plus 10/13?
Formula / Expression: 1/8 + 10/13
Final Answer: 93/104
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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 10/13 by 8 so both fractions share the common base 104.
Working: 1 × 13/8 × 13 = 13/104 and 10 × 8/13 × 8 = 80/104

Step 3: Add the Numerators
Now add the numerators (13 + 80 = 93) and keep the common denominator 104 unchanged.
Working: 13 + 80/104 = 93/104

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 93 and 104 is 1, confirming that 93/104 cannot be reduced further—it is already in its simplest irreducible form.
Working: 93/104

Step 5: Decimal & Percentage Representation
Dividing the numerator 93 by denominator 104 produces a repeating decimal (approximately 0.894231, or 89.4231%).
Working: 93 ÷ 104 = 0.894231 (89.4231%)

Key Values:
- Simplified Fraction: 93/104
- Mixed Number Form: 93/104
- Decimal Value: 0.894231
- Percentage: 89.4231%

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Solved with FractionsCalc:
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1/8 + 10/13 = 93/104

Simplified Fraction

93/104

Mixed Number

Proper (93/104)

Decimal Value

0.894231

Percentage

89.4231%

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Step-by-Step Solution: 1/8 + 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 1/8 by 13, and multiply the numerator and denominator of 10/13 by 8 so both fractions share the common base 104.

1 × 13/8 × 13 = 13/104 and 10 × 8/13 × 8 = 80/104

Step 3

Add the Numerators

Now add the numerators (13 + 80 = 93) and keep the common denominator 104 unchanged.

13 + 80/104 = 93/104

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 93 and 104 is 1, confirming that 93/104 cannot be reduced further—it is already in its simplest irreducible form.

93/104

Step 5

Decimal & Percentage Representation

Dividing the numerator 93 by denominator 104 produces a repeating decimal (approximately 0.894231, or 89.4231%).

93 ÷ 104 = 0.894231 (89.4231%)

Visual Representation

The diagram below illustrates 1/8 plus 10/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`93/104`
Mixed Number Form	`93/104`
Decimal Form	`0.894231`
Percentage	`89.4231%`

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Frequently Asked Questions

What is 1/8 plus 10/13 as a fraction?

1/8 + 10/13 in simplest fraction form is 93/104.

What is 1/8 plus 10/13 as a decimal?

1/8 + 10/13 converted to a decimal is 0.894231.

What is 1/8 plus 10/13 as a percentage?

1/8 + 10/13 expressed as a percentage is 89.4231%.

Does 1/8 plus 10/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.894231...) because the denominator contains prime factors other than 2 and 5.