What is 3/9 plus 8/11?
3/9 plus 8/11 equals 35/33 (or 1 2/33 as a mixed number) (or 1.060606 in decimal form). Learn the step-by-step solution to add 3/9 and 8/11 using Least Common Denominator and simplification.
Exact Answer
3/9 + 8/11 = 35/33
Simplified Fraction
35/33
Mixed Number
1 2/33
Decimal Value
1.060606
Percentage
106.0606%
Step-by-Step Solution: 3/9 + 8/11
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 3/9 by 11, and multiply the numerator and denominator of 8/11 by 9 so both fractions share the common base 99.
3 × 11/9 × 11 = 33/99 and 8 × 9/11 × 9 = 72/99
Step 3
Add the Numerators
Now add the numerators (33 + 72 = 105) and keep the common denominator 99 unchanged.
33 + 72/99 = 105/99
Step 4
Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 105 and 99, which is 3. Divide both the numerator and denominator by 3.
105 ÷ 3/99 ÷ 3 = 35/33
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (35) is greater than the denominator (33), divide 35 by 33: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/33.
35/33 = 12/33
Step 6
Decimal & Percentage Representation
Dividing the numerator 35 by denominator 33 produces a repeating decimal (approximately 1.060606, or 106.0606%).
35 ÷ 33 = 1.060606 (106.0606%)
Visual Representation
The diagram below illustrates 3/9 plus 8/11 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 35/33 |
| Mixed Number Form | 1 2/33 |
| Decimal Form | 1.060606 |
| Percentage | 106.0606% |
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Frequently Asked Questions
What is 3/9 plus 8/11 as a fraction?
3/9 + 8/11 in simplest fraction form is 35/33 (or 1 2/33 as a mixed number).
What is 3/9 plus 8/11 as a decimal?
3/9 + 8/11 converted to a decimal is 1.060606.
What is 3/9 plus 8/11 as a percentage?
3/9 + 8/11 expressed as a percentage is 106.0606%.
How do you write 3/9 plus 8/11 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 35/33 can be written as the mixed number 1 2/33.
Does 3/9 plus 8/11 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.060606...) because the denominator contains prime factors other than 2 and 5.