What is 2/13 plus 7/8?
2/13 plus 7/8 equals 107/104 (or 1 3/104 as a mixed number) (or 1.028846 in decimal form). Learn the step-by-step solution to add 2/13 and 7/8 using Least Common Denominator and simplification.
Exact Answer
2/13 + 7/8 = 107/104
Simplified Fraction
107/104
Mixed Number
1 3/104
Decimal Value
1.028846
Percentage
102.8846%
Step-by-Step Solution: 2/13 + 7/8
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 2/13 by 8, and multiply the numerator and denominator of 7/8 by 13 so both fractions share the common base 104.
2 × 8/13 × 8 = 16/104 and 7 × 13/8 × 13 = 91/104
Step 3
Add the Numerators
Now add the numerators (16 + 91 = 107) and keep the common denominator 104 unchanged.
16 + 91/104 = 107/104
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 107 and 104 is 1, confirming that 107/104 cannot be reduced further—it is already in its simplest irreducible form.
107/104
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (107) is greater than the denominator (104), divide 107 by 104: it goes in 1 whole time(s) with a remainder of 3, giving the mixed number 1 3/104.
107/104 = 13/104
Step 6
Decimal & Percentage Representation
Dividing the numerator 107 by denominator 104 produces a repeating decimal (approximately 1.028846, or 102.8846%).
107 ÷ 104 = 1.028846 (102.8846%)
Visual Representation
The diagram below illustrates 2/13 plus 7/8 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 107/104 |
| Mixed Number Form | 1 3/104 |
| Decimal Form | 1.028846 |
| Percentage | 102.8846% |
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Frequently Asked Questions
What is 2/13 plus 7/8 as a fraction?
2/13 + 7/8 in simplest fraction form is 107/104 (or 1 3/104 as a mixed number).
What is 2/13 plus 7/8 as a decimal?
2/13 + 7/8 converted to a decimal is 1.028846.
What is 2/13 plus 7/8 as a percentage?
2/13 + 7/8 expressed as a percentage is 102.8846%.
How do you write 2/13 plus 7/8 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 107/104 can be written as the mixed number 1 3/104.
Does 2/13 plus 7/8 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.028846...) because the denominator contains prime factors other than 2 and 5.