What is 2/13 plus 8/9?
2/13 plus 8/9 equals 122/117 (or 1 5/117 as a mixed number) (or 1.042735 in decimal form). Learn the step-by-step solution to add 2/13 and 8/9 using Least Common Denominator and simplification.
Exact Answer
2/13 + 8/9 = 122/117
Simplified Fraction
122/117
Mixed Number
1 5/117
Decimal Value
1.042735
Percentage
104.2735%
Step-by-Step Solution: 2/13 + 8/9
Step 1
Find the Least Common Denominator (LCD)
The denominators 13 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 9 = 117.
LCD(13, 9) = 117
Step 2
Convert to Equivalent Fractions with Common Denominator 117
Multiply the numerator and denominator of 2/13 by 9, and multiply the numerator and denominator of 8/9 by 13 so both fractions share the common base 117.
2 × 9/13 × 9 = 18/117 and 8 × 13/9 × 13 = 104/117
Step 3
Add the Numerators
Now add the numerators (18 + 104 = 122) and keep the common denominator 117 unchanged.
18 + 104/117 = 122/117
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 122 and 117 is 1, confirming that 122/117 cannot be reduced further—it is already in its simplest irreducible form.
122/117
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (122) is greater than the denominator (117), divide 122 by 117: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/117.
122/117 = 15/117
Step 6
Decimal & Percentage Representation
Dividing the numerator 122 by denominator 117 produces a repeating decimal (approximately 1.042735, or 104.2735%).
122 ÷ 117 = 1.042735 (104.2735%)
Visual Representation
The diagram below illustrates 2/13 plus 8/9 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 122/117 |
| Mixed Number Form | 1 5/117 |
| Decimal Form | 1.042735 |
| Percentage | 104.2735% |
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Frequently Asked Questions
What is 2/13 plus 8/9 as a fraction?
2/13 + 8/9 in simplest fraction form is 122/117 (or 1 5/117 as a mixed number).
What is 2/13 plus 8/9 as a decimal?
2/13 + 8/9 converted to a decimal is 1.042735.
What is 2/13 plus 8/9 as a percentage?
2/13 + 8/9 expressed as a percentage is 104.2735%.
How do you write 2/13 plus 8/9 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 122/117 can be written as the mixed number 1 5/117.
Does 2/13 plus 8/9 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.042735...) because the denominator contains prime factors other than 2 and 5.