What is 3/11 plus 8/9?
3/11 plus 8/9 equals 115/99 (or 1 16/99 as a mixed number) (or 1.161616 in decimal form). Learn the step-by-step solution to add 3/11 and 8/9 using Least Common Denominator and simplification.
Exact Answer
3/11 + 8/9 = 115/99
Simplified Fraction
115/99
Mixed Number
1 16/99
Decimal Value
1.161616
Percentage
116.1616%
Step-by-Step Solution: 3/11 + 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 3/11 by 9, and multiply the numerator and denominator of 8/9 by 11 so both fractions share the common base 99.
3 × 9/11 × 9 = 27/99 and 8 × 11/9 × 11 = 88/99
Step 3
Add the Numerators
Now add the numerators (27 + 88 = 115) and keep the common denominator 99 unchanged.
27 + 88/99 = 115/99
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 115 and 99 is 1, confirming that 115/99 cannot be reduced further—it is already in its simplest irreducible form.
115/99
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (115) is greater than the denominator (99), divide 115 by 99: it goes in 1 whole time(s) with a remainder of 16, giving the mixed number 1 16/99.
115/99 = 116/99
Step 6
Decimal & Percentage Representation
Dividing the numerator 115 by denominator 99 produces a repeating decimal (approximately 1.161616, or 116.1616%).
115 ÷ 99 = 1.161616 (116.1616%)
Visual Representation
The diagram below illustrates 3/11 plus 8/9 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 115/99 |
| Mixed Number Form | 1 16/99 |
| Decimal Form | 1.161616 |
| Percentage | 116.1616% |
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Frequently Asked Questions
What is 3/11 plus 8/9 as a fraction?
3/11 + 8/9 in simplest fraction form is 115/99 (or 1 16/99 as a mixed number).
What is 3/11 plus 8/9 as a decimal?
3/11 + 8/9 converted to a decimal is 1.161616.
What is 3/11 plus 8/9 as a percentage?
3/11 + 8/9 expressed as a percentage is 116.1616%.
How do you write 3/11 plus 8/9 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 115/99 can be written as the mixed number 1 16/99.
Does 3/11 plus 8/9 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.161616...) because the denominator contains prime factors other than 2 and 5.