What is 2/9 plus 10/11?
2/9 plus 10/11 equals 112/99 (or 1 13/99 as a mixed number) (or 1.131313 in decimal form). Learn the step-by-step solution to add 2/9 and 10/11 using Least Common Denominator and simplification.
Exact Answer
2/9 + 10/11 = 112/99
Simplified Fraction
112/99
Mixed Number
1 13/99
Decimal Value
1.131313
Percentage
113.1313%
Step-by-Step Solution: 2/9 + 10/11
Step 1
Find the Least Common Denominator (LCD)
The denominators 9 and 11 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 11 = 99.
LCD(9, 11) = 99
Step 2
Convert to Equivalent Fractions with Common Denominator 99
Multiply the numerator and denominator of 2/9 by 11, and multiply the numerator and denominator of 10/11 by 9 so both fractions share the common base 99.
2 × 11/9 × 11 = 22/99 and 10 × 9/11 × 9 = 90/99
Step 3
Add the Numerators
Now add the numerators (22 + 90 = 112) and keep the common denominator 99 unchanged.
22 + 90/99 = 112/99
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 112 and 99 is 1, confirming that 112/99 cannot be reduced further—it is already in its simplest irreducible form.
112/99
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (112) is greater than the denominator (99), divide 112 by 99: it goes in 1 whole time(s) with a remainder of 13, giving the mixed number 1 13/99.
112/99 = 113/99
Step 6
Decimal & Percentage Representation
Dividing the numerator 112 by denominator 99 produces a repeating decimal (approximately 1.131313, or 113.1313%).
112 ÷ 99 = 1.131313 (113.1313%)
Visual Representation
The diagram below illustrates 2/9 plus 10/11 visually:
+
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 112/99 |
| Mixed Number Form | 1 13/99 |
| Decimal Form | 1.131313 |
| Percentage | 113.1313% |
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Frequently Asked Questions
What is 2/9 plus 10/11 as a fraction?
2/9 + 10/11 in simplest fraction form is 112/99 (or 1 13/99 as a mixed number).
What is 2/9 plus 10/11 as a decimal?
2/9 + 10/11 converted to a decimal is 1.131313.
What is 2/9 plus 10/11 as a percentage?
2/9 + 10/11 expressed as a percentage is 113.1313%.
How do you write 2/9 plus 10/11 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 112/99 can be written as the mixed number 1 13/99.
Does 2/9 plus 10/11 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.131313...) because the denominator contains prime factors other than 2 and 5.