What is 2/9 plus 9/33?
2/9 plus 9/33 equals 49/99 (or 0.494949 in decimal form). Learn the step-by-step solution to add 2/9 and 9/33 using Least Common Denominator and simplification.
Exact Answer
2/9 + 9/33 = 49/99
Simplified Fraction
49/99
Mixed Number
Proper (49/99)
Decimal Value
0.494949
Percentage
49.4949%
Step-by-Step Solution: 2/9 + 9/33
Step 1
Find the Least Common Denominator (LCD)
The denominators 9 and 33 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 99 (which is smaller than their product 9 × 33 = 297, keeping the calculation simpler).
LCD(9, 33) = 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 9/33 by 3 so both fractions share the common base 99.
2 × 11/9 × 11 = 22/99 and 9 × 3/33 × 3 = 27/99
Step 3
Add the Numerators
Now add the numerators (22 + 27 = 49) and keep the common denominator 99 unchanged.
22 + 27/99 = 49/99
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 49 and 99 is 1, confirming that 49/99 cannot be reduced further—it is already in its simplest irreducible form.
49/99
Step 5
Decimal & Percentage Representation
Dividing the numerator 49 by denominator 99 produces a repeating decimal (approximately 0.494949, or 49.4949%).
49 ÷ 99 = 0.494949 (49.4949%)
Visual Representation
The diagram below illustrates 2/9 plus 9/33 visually:
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=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 49/99 |
| Mixed Number Form | 49/99 |
| Decimal Form | 0.494949 |
| Percentage | 49.4949% |
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Frequently Asked Questions
What is 2/9 plus 9/33 as a fraction?
2/9 + 9/33 in simplest fraction form is 49/99.
What is 2/9 plus 9/33 as a decimal?
2/9 + 9/33 converted to a decimal is 0.494949.
What is 2/9 plus 9/33 as a percentage?
2/9 + 9/33 expressed as a percentage is 49.4949%.
Does 2/9 plus 9/33 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 0.494949...) because the denominator contains prime factors other than 2 and 5.