What is 5/9 plus 2/3?
5/9 plus 2/3 equals 11/9 (or 1 2/9 as a mixed number) (or 1.222222 in decimal form). Learn the step-by-step solution to add 5/9 and 2/3 using Least Common Denominator and simplification.
Exact Answer
5/9 + 2/3 = 11/9
Simplified Fraction
11/9
Mixed Number
1 2/9
Decimal Value
1.222222
Percentage
122.2222%
Step-by-Step Solution: 5/9 + 2/3
Step 1
Find the Least Common Denominator (LCD)
Notice that 9 is an exact multiple of 3 (3 × 3 = 9). The Least Common Denominator (LCD) is simply 9, meaning we only need to scale one fraction.
LCD(9, 3) = 9
Step 2
Convert to Equivalent Fractions with Common Denominator 9
Multiply the numerator and denominator of 5/9 by 1, and multiply the numerator and denominator of 2/3 by 3 so both fractions share the common base 9.
5 × 1/9 × 1 = 5/9 and 2 × 3/3 × 3 = 6/9
Step 3
Add the Numerators
Now add the numerators (5 + 6 = 11) and keep the common denominator 9 unchanged.
5 + 6/9 = 11/9
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 11 and 9 is 1, confirming that 11/9 cannot be reduced further—it is already in its simplest irreducible form.
11/9
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (11) is greater than the denominator (9), divide 11 by 9: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/9.
11/9 = 12/9
Step 6
Decimal & Percentage Representation
Dividing the numerator 11 by denominator 9 produces a repeating decimal (approximately 1.222222, or 122.2222%).
11 ÷ 9 = 1.222222 (122.2222%)
Visual Representation
The diagram below illustrates 5/9 plus 2/3 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 11/9 |
| Mixed Number Form | 1 2/9 |
| Decimal Form | 1.222222 |
| Percentage | 122.2222% |
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Frequently Asked Questions
What is 5/9 plus 2/3 as a fraction?
5/9 + 2/3 in simplest fraction form is 11/9 (or 1 2/9 as a mixed number).
What is 5/9 plus 2/3 as a decimal?
5/9 + 2/3 converted to a decimal is 1.222222.
What is 5/9 plus 2/3 as a percentage?
5/9 + 2/3 expressed as a percentage is 122.2222%.
How do you write 5/9 plus 2/3 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 11/9 can be written as the mixed number 1 2/9.
Does 5/9 plus 2/3 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.222222...) because the denominator contains prime factors other than 2 and 5.