What is 2/11 plus 8/9?
2/11 plus 8/9 equals 106/99 (or 1 7/99 as a mixed number) (or 1.070707 in decimal form). Learn the step-by-step solution to add 2/11 and 8/9 using Least Common Denominator and simplification.
Exact Answer
2/11 + 8/9 = 106/99
Simplified Fraction
106/99
Mixed Number
1 7/99
Decimal Value
1.070707
Percentage
107.0707%
Step-by-Step Solution: 2/11 + 8/9
Step 1
Find the Least Common Denominator (LCD)
The denominators 11 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 11 × 9 = 99.
LCD(11, 9) = 99
Step 2
Convert to Equivalent Fractions with Common Denominator 99
Multiply the numerator and denominator of 2/11 by 9, and multiply the numerator and denominator of 8/9 by 11 so both fractions share the common base 99.
2 × 9/11 × 9 = 18/99 and 8 × 11/9 × 11 = 88/99
Step 3
Add the Numerators
Now add the numerators (18 + 88 = 106) and keep the common denominator 99 unchanged.
18 + 88/99 = 106/99
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 106 and 99 is 1, confirming that 106/99 cannot be reduced further—it is already in its simplest irreducible form.
106/99
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (106) is greater than the denominator (99), divide 106 by 99: it goes in 1 whole time(s) with a remainder of 7, giving the mixed number 1 7/99.
106/99 = 17/99
Step 6
Decimal & Percentage Representation
Dividing the numerator 106 by denominator 99 produces a repeating decimal (approximately 1.070707, or 107.0707%).
106 ÷ 99 = 1.070707 (107.0707%)
Visual Representation
The diagram below illustrates 2/11 plus 8/9 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 106/99 |
| Mixed Number Form | 1 7/99 |
| Decimal Form | 1.070707 |
| Percentage | 107.0707% |
Was this solution helpful?
Help us improve our free step-by-step tools
Frequently Asked Questions
What is 2/11 plus 8/9 as a fraction?
2/11 + 8/9 in simplest fraction form is 106/99 (or 1 7/99 as a mixed number).
What is 2/11 plus 8/9 as a decimal?
2/11 + 8/9 converted to a decimal is 1.070707.
What is 2/11 plus 8/9 as a percentage?
2/11 + 8/9 expressed as a percentage is 107.0707%.
How do you write 2/11 plus 8/9 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 106/99 can be written as the mixed number 1 7/99.
Does 2/11 plus 8/9 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.070707...) because the denominator contains prime factors other than 2 and 5.