What is 2/11 plus 2/9?
2/11 plus 2/9 equals 40/99 (or 0.40404 in decimal form). Learn the step-by-step solution to add 2/11 and 2/9 using Least Common Denominator and simplification.
Exact Answer
2/11 + 2/9 = 40/99
Simplified Fraction
40/99
Mixed Number
Proper (40/99)
Decimal Value
0.40404
Percentage
40.404%
Step-by-Step Solution: 2/11 + 2/9
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 2/9 by 11 so both fractions share the common base 99.
2 × 9/11 × 9 = 18/99 and 2 × 11/9 × 11 = 22/99
Step 3
Add the Numerators
Now add the numerators (18 + 22 = 40) and keep the common denominator 99 unchanged.
18 + 22/99 = 40/99
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 40 and 99 is 1, confirming that 40/99 cannot be reduced further—it is already in its simplest irreducible form.
40/99
Step 5
Decimal & Percentage Representation
Dividing the numerator 40 by denominator 99 produces a repeating decimal (approximately 0.40404, or 40.404%).
40 ÷ 99 = 0.40404 (40.404%)
Visual Representation
The diagram below illustrates 2/11 plus 2/9 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 40/99 |
| Mixed Number Form | 40/99 |
| Decimal Form | 0.40404 |
| Percentage | 40.404% |
Was this solution helpful?
Help us improve our free step-by-step tools
Frequently Asked Questions
What is 2/11 plus 2/9 as a fraction?
2/11 + 2/9 in simplest fraction form is 40/99.
What is 2/11 plus 2/9 as a decimal?
2/11 + 2/9 converted to a decimal is 0.40404.
What is 2/11 plus 2/9 as a percentage?
2/11 + 2/9 expressed as a percentage is 40.404%.
Does 2/11 plus 2/9 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 0.40404...) because the denominator contains prime factors other than 2 and 5.