What is 2/33 plus 2/9?
2/33 plus 2/9 equals 28/99 (or 0.282828 in decimal form). Learn the step-by-step solution to add 2/33 and 2/9 using Least Common Denominator and simplification.
Exact Answer
2/33 + 2/9 = 28/99
Simplified Fraction
28/99
Mixed Number
Proper (28/99)
Decimal Value
0.282828
Percentage
28.2828%
Step-by-Step Solution: 2/33 + 2/9
Step 1
Find the Least Common Denominator (LCD)
The denominators 33 and 9 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 99 (which is smaller than their product 33 × 9 = 297, keeping the calculation simpler).
LCD(33, 9) = 99
Step 2
Convert to Equivalent Fractions with Common Denominator 99
Multiply the numerator and denominator of 2/33 by 3, and multiply the numerator and denominator of 2/9 by 11 so both fractions share the common base 99.
2 × 3/33 × 3 = 6/99 and 2 × 11/9 × 11 = 22/99
Step 3
Add the Numerators
Now add the numerators (6 + 22 = 28) and keep the common denominator 99 unchanged.
6 + 22/99 = 28/99
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 28 and 99 is 1, confirming that 28/99 cannot be reduced further—it is already in its simplest irreducible form.
28/99
Step 5
Decimal & Percentage Representation
Dividing the numerator 28 by denominator 99 produces a repeating decimal (approximately 0.282828, or 28.2828%).
28 ÷ 99 = 0.282828 (28.2828%)
Visual Representation
The diagram below illustrates 2/33 plus 2/9 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 28/99 |
| Mixed Number Form | 28/99 |
| Decimal Form | 0.282828 |
| Percentage | 28.2828% |
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Frequently Asked Questions
What is 2/33 plus 2/9 as a fraction?
2/33 + 2/9 in simplest fraction form is 28/99.
What is 2/33 plus 2/9 as a decimal?
2/33 + 2/9 converted to a decimal is 0.282828.
What is 2/33 plus 2/9 as a percentage?
2/33 + 2/9 expressed as a percentage is 28.2828%.
Does 2/33 plus 2/9 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 0.282828...) because the denominator contains prime factors other than 2 and 5.