What is 3/11 plus 5/9?
3/11 plus 5/9 equals 82/99 (or 0.828283 in decimal form). Learn the step-by-step solution to add 3/11 and 5/9 using Least Common Denominator and simplification.
Exact Answer
3/11 + 5/9 = 82/99
Simplified Fraction
82/99
Mixed Number
Proper (82/99)
Decimal Value
0.828283
Percentage
82.8283%
Step-by-Step Solution: 3/11 + 5/9
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 3/11 by 9, and multiply the numerator and denominator of 5/9 by 11 so both fractions share the common base 99.
3 × 9/11 × 9 = 27/99 and 5 × 11/9 × 11 = 55/99
Step 3
Add the Numerators
Now add the numerators (27 + 55 = 82) and keep the common denominator 99 unchanged.
27 + 55/99 = 82/99
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 82 and 99 is 1, confirming that 82/99 cannot be reduced further—it is already in its simplest irreducible form.
82/99
Step 5
Decimal & Percentage Representation
Dividing the numerator 82 by denominator 99 produces a repeating decimal (approximately 0.828283, or 82.8283%).
82 ÷ 99 = 0.828283 (82.8283%)
Visual Representation
The diagram below illustrates 3/11 plus 5/9 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 82/99 |
| Mixed Number Form | 82/99 |
| Decimal Form | 0.828283 |
| Percentage | 82.8283% |
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Frequently Asked Questions
What is 3/11 plus 5/9 as a fraction?
3/11 + 5/9 in simplest fraction form is 82/99.
What is 3/11 plus 5/9 as a decimal?
3/11 + 5/9 converted to a decimal is 0.828283.
What is 3/11 plus 5/9 as a percentage?
3/11 + 5/9 expressed as a percentage is 82.8283%.
Does 3/11 plus 5/9 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 0.828283...) because the denominator contains prime factors other than 2 and 5.