What is 5/9 plus 9/11?
5/9 plus 9/11 equals 136/99 (or 1 37/99 as a mixed number) (or 1.373737 in decimal form). Learn the step-by-step solution to add 5/9 and 9/11 using Least Common Denominator and simplification.
Exact Answer
5/9 + 9/11 = 136/99
Simplified Fraction
136/99
Mixed Number
1 37/99
Decimal Value
1.373737
Percentage
137.3737%
Step-by-Step Solution: 5/9 + 9/11
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 5/9 by 11, and multiply the numerator and denominator of 9/11 by 9 so both fractions share the common base 99.
5 × 11/9 × 11 = 55/99 and 9 × 9/11 × 9 = 81/99
Step 3
Add the Numerators
Now add the numerators (55 + 81 = 136) and keep the common denominator 99 unchanged.
55 + 81/99 = 136/99
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 136 and 99 is 1, confirming that 136/99 cannot be reduced further—it is already in its simplest irreducible form.
136/99
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (136) is greater than the denominator (99), divide 136 by 99: it goes in 1 whole time(s) with a remainder of 37, giving the mixed number 1 37/99.
136/99 = 137/99
Step 6
Decimal & Percentage Representation
Dividing the numerator 136 by denominator 99 produces a repeating decimal (approximately 1.373737, or 137.3737%).
136 ÷ 99 = 1.373737 (137.3737%)
Visual Representation
The diagram below illustrates 5/9 plus 9/11 visually:
+
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 136/99 |
| Mixed Number Form | 1 37/99 |
| Decimal Form | 1.373737 |
| Percentage | 137.3737% |
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Frequently Asked Questions
What is 5/9 plus 9/11 as a fraction?
5/9 + 9/11 in simplest fraction form is 136/99 (or 1 37/99 as a mixed number).
What is 5/9 plus 9/11 as a decimal?
5/9 + 9/11 converted to a decimal is 1.373737.
What is 5/9 plus 9/11 as a percentage?
5/9 + 9/11 expressed as a percentage is 137.3737%.
How do you write 5/9 plus 9/11 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 136/99 can be written as the mixed number 1 37/99.
Does 5/9 plus 9/11 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.373737...) because the denominator contains prime factors other than 2 and 5.