What is 2/9 plus 6/11?
2/9 plus 6/11 equals 76/99 (or 0.767677 in decimal form). Learn the step-by-step solution to add 2/9 and 6/11 using Least Common Denominator and simplification.
Exact Answer
2/9 + 6/11 = 76/99
Simplified Fraction
76/99
Mixed Number
Proper (76/99)
Decimal Value
0.767677
Percentage
76.7677%
Step-by-Step Solution: 2/9 + 6/11
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 6/11 by 9 so both fractions share the common base 99.
2 × 11/9 × 11 = 22/99 and 6 × 9/11 × 9 = 54/99
Step 3
Add the Numerators
Now add the numerators (22 + 54 = 76) and keep the common denominator 99 unchanged.
22 + 54/99 = 76/99
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 76 and 99 is 1, confirming that 76/99 cannot be reduced further—it is already in its simplest irreducible form.
76/99
Step 5
Decimal & Percentage Representation
Dividing the numerator 76 by denominator 99 produces a repeating decimal (approximately 0.767677, or 76.7677%).
76 ÷ 99 = 0.767677 (76.7677%)
Visual Representation
The diagram below illustrates 2/9 plus 6/11 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 76/99 |
| Mixed Number Form | 76/99 |
| Decimal Form | 0.767677 |
| Percentage | 76.7677% |
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Frequently Asked Questions
What is 2/9 plus 6/11 as a fraction?
2/9 + 6/11 in simplest fraction form is 76/99.
What is 2/9 plus 6/11 as a decimal?
2/9 + 6/11 converted to a decimal is 0.767677.
What is 2/9 plus 6/11 as a percentage?
2/9 + 6/11 expressed as a percentage is 76.7677%.
Does 2/9 plus 6/11 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 0.767677...) because the denominator contains prime factors other than 2 and 5.