What is 2/3 plus 8/11?
2/3 plus 8/11 equals 46/33 (or 1 13/33 as a mixed number) (or 1.393939 in decimal form). Learn the step-by-step solution to add 2/3 and 8/11 using Least Common Denominator and simplification.
Exact Answer
2/3 + 8/11 = 46/33
Simplified Fraction
46/33
Mixed Number
1 13/33
Decimal Value
1.393939
Percentage
139.3939%
Step-by-Step Solution: 2/3 + 8/11
Step 1
Find the Least Common Denominator (LCD)
The denominators 3 and 11 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 3 × 11 = 33.
LCD(3, 11) = 33
Step 2
Convert to Equivalent Fractions with Common Denominator 33
Multiply the numerator and denominator of 2/3 by 11, and multiply the numerator and denominator of 8/11 by 3 so both fractions share the common base 33.
2 × 11/3 × 11 = 22/33 and 8 × 3/11 × 3 = 24/33
Step 3
Add the Numerators
Now add the numerators (22 + 24 = 46) and keep the common denominator 33 unchanged.
22 + 24/33 = 46/33
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 46 and 33 is 1, confirming that 46/33 cannot be reduced further—it is already in its simplest irreducible form.
46/33
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (46) is greater than the denominator (33), divide 46 by 33: it goes in 1 whole time(s) with a remainder of 13, giving the mixed number 1 13/33.
46/33 = 113/33
Step 6
Decimal & Percentage Representation
Dividing the numerator 46 by denominator 33 produces a repeating decimal (approximately 1.393939, or 139.3939%).
46 ÷ 33 = 1.393939 (139.3939%)
Visual Representation
The diagram below illustrates 2/3 plus 8/11 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 46/33 |
| Mixed Number Form | 1 13/33 |
| Decimal Form | 1.393939 |
| Percentage | 139.3939% |
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Frequently Asked Questions
What is 2/3 plus 8/11 as a fraction?
2/3 + 8/11 in simplest fraction form is 46/33 (or 1 13/33 as a mixed number).
What is 2/3 plus 8/11 as a decimal?
2/3 + 8/11 converted to a decimal is 1.393939.
What is 2/3 plus 8/11 as a percentage?
2/3 + 8/11 expressed as a percentage is 139.3939%.
How do you write 2/3 plus 8/11 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 46/33 can be written as the mixed number 1 13/33.
Does 2/3 plus 8/11 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.393939...) because the denominator contains prime factors other than 2 and 5.