What is 1/33 plus 2/9? (Answer: 25/99)

Exact Answer

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Problem: What is 1/33 plus 2/9?
Formula / Expression: 1/33 + 2/9
Final Answer: 25/99
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Step-by-Step Solution:

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).
Working: LCD(33, 9) = 99

Step 2: Convert to Equivalent Fractions with Common Denominator 99
Multiply the numerator and denominator of 1/33 by 3, and multiply the numerator and denominator of 2/9 by 11 so both fractions share the common base 99.
Working: 1 × 3/33 × 3 = 3/99 and 2 × 11/9 × 11 = 22/99

Step 3: Add the Numerators
Now add the numerators (3 + 22 = 25) and keep the common denominator 99 unchanged.
Working: 3 + 22/99 = 25/99

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 25 and 99 is 1, confirming that 25/99 cannot be reduced further—it is already in its simplest irreducible form.
Working: 25/99

Step 5: Decimal & Percentage Representation
Dividing the numerator 25 by denominator 99 produces a repeating decimal (approximately 0.252525, or 25.2525%).
Working: 25 ÷ 99 = 0.252525 (25.2525%)

Key Values:
- Simplified Fraction: 25/99
- Mixed Number Form: 25/99
- Decimal Value: 0.252525
- Percentage: 25.2525%

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Solved with FractionsCalc:
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1/33 + 2/9 = 25/99

Simplified Fraction

25/99

Mixed Number

Proper (25/99)

Decimal Value

0.252525

Percentage

25.2525%

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Step-by-Step Solution: 1/33 + 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 1/33 by 3, and multiply the numerator and denominator of 2/9 by 11 so both fractions share the common base 99.

1 × 3/33 × 3 = 3/99 and 2 × 11/9 × 11 = 22/99

Step 3

Add the Numerators

Now add the numerators (3 + 22 = 25) and keep the common denominator 99 unchanged.

3 + 22/99 = 25/99

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 25 and 99 is 1, confirming that 25/99 cannot be reduced further—it is already in its simplest irreducible form.

25/99

Step 5

Decimal & Percentage Representation

Dividing the numerator 25 by denominator 99 produces a repeating decimal (approximately 0.252525, or 25.2525%).

25 ÷ 99 = 0.252525 (25.2525%)

Visual Representation

The diagram below illustrates 1/33 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`25/99`
Mixed Number Form	`25/99`
Decimal Form	`0.252525`
Percentage	`25.2525%`

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Frequently Asked Questions

What is 1/33 plus 2/9 as a fraction?

1/33 + 2/9 in simplest fraction form is 25/99.

What is 1/33 plus 2/9 as a decimal?

1/33 + 2/9 converted to a decimal is 0.252525.

What is 1/33 plus 2/9 as a percentage?

1/33 + 2/9 expressed as a percentage is 25.2525%.

Does 1/33 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.252525...) because the denominator contains prime factors other than 2 and 5.