What is 2/9 plus 8/33? (Answer: 46/99)

Exact Answer

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Problem: What is 2/9 plus 8/33?
Formula / Expression: 2/9 + 8/33
Final Answer: 46/99
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Step-by-Step Solution:

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).
Working: 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 8/33 by 3 so both fractions share the common base 99.
Working: 2 × 11/9 × 11 = 22/99 and 8 × 3/33 × 3 = 24/99

Step 3: Add the Numerators
Now add the numerators (22 + 24 = 46) and keep the common denominator 99 unchanged.
Working: 22 + 24/99 = 46/99

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 46 and 99 is 1, confirming that 46/99 cannot be reduced further—it is already in its simplest irreducible form.
Working: 46/99

Step 5: Decimal & Percentage Representation
Dividing the numerator 46 by denominator 99 produces a repeating decimal (approximately 0.464646, or 46.4646%).
Working: 46 ÷ 99 = 0.464646 (46.4646%)

Key Values:
- Simplified Fraction: 46/99
- Mixed Number Form: 46/99
- Decimal Value: 0.464646
- Percentage: 46.4646%

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Solved with FractionsCalc:
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2/9 + 8/33 = 46/99

Simplified Fraction

46/99

Mixed Number

Proper (46/99)

Decimal Value

0.464646

Percentage

46.4646%

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Step-by-Step Solution: 2/9 + 8/33

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 8/33 by 3 so both fractions share the common base 99.

2 × 11/9 × 11 = 22/99 and 8 × 3/33 × 3 = 24/99

Step 3

Add the Numerators

Now add the numerators (22 + 24 = 46) and keep the common denominator 99 unchanged.

22 + 24/99 = 46/99

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 46 and 99 is 1, confirming that 46/99 cannot be reduced further—it is already in its simplest irreducible form.

46/99

Step 5

Decimal & Percentage Representation

Dividing the numerator 46 by denominator 99 produces a repeating decimal (approximately 0.464646, or 46.4646%).

46 ÷ 99 = 0.464646 (46.4646%)

Visual Representation

The diagram below illustrates 2/9 plus 8/33 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`46/99`
Mixed Number Form	`46/99`
Decimal Form	`0.464646`
Percentage	`46.4646%`

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Frequently Asked Questions

What is 2/9 plus 8/33 as a fraction?

2/9 + 8/33 in simplest fraction form is 46/99.

What is 2/9 plus 8/33 as a decimal?

2/9 + 8/33 converted to a decimal is 0.464646.

What is 2/9 plus 8/33 as a percentage?

2/9 + 8/33 expressed as a percentage is 46.4646%.

Does 2/9 plus 8/33 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.464646...) because the denominator contains prime factors other than 2 and 5.