What is 2/33 plus 3/8? (Answer: 115/264)

Exact Answer

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Problem: What is 2/33 plus 3/8?
Formula / Expression: 2/33 + 3/8
Final Answer: 115/264
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 33 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 33 × 8 = 264.
Working: LCD(33, 8) = 264

Step 2: Convert to Equivalent Fractions with Common Denominator 264
Multiply the numerator and denominator of 2/33 by 8, and multiply the numerator and denominator of 3/8 by 33 so both fractions share the common base 264.
Working: 2 × 8/33 × 8 = 16/264 and 3 × 33/8 × 33 = 99/264

Step 3: Add the Numerators
Now add the numerators (16 + 99 = 115) and keep the common denominator 264 unchanged.
Working: 16 + 99/264 = 115/264

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 115 and 264 is 1, confirming that 115/264 cannot be reduced further—it is already in its simplest irreducible form.
Working: 115/264

Step 5: Decimal & Percentage Representation
Dividing the numerator 115 by denominator 264 produces a repeating decimal (approximately 0.435606, or 43.5606%).
Working: 115 ÷ 264 = 0.435606 (43.5606%)

Key Values:
- Simplified Fraction: 115/264
- Mixed Number Form: 115/264
- Decimal Value: 0.435606
- Percentage: 43.5606%

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2/33 + 3/8 = 115/264

Simplified Fraction

115/264

Mixed Number

Proper (115/264)

Decimal Value

0.435606

Percentage

43.5606%

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Step-by-Step Solution: 2/33 + 3/8

Step 1

Find the Least Common Denominator (LCD)

The denominators 33 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 33 × 8 = 264.

LCD(33, 8) = 264

Step 2

Convert to Equivalent Fractions with Common Denominator 264

Multiply the numerator and denominator of 2/33 by 8, and multiply the numerator and denominator of 3/8 by 33 so both fractions share the common base 264.

2 × 8/33 × 8 = 16/264 and 3 × 33/8 × 33 = 99/264

Step 3

Add the Numerators

Now add the numerators (16 + 99 = 115) and keep the common denominator 264 unchanged.

16 + 99/264 = 115/264

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 115 and 264 is 1, confirming that 115/264 cannot be reduced further—it is already in its simplest irreducible form.

115/264

Step 5

Decimal & Percentage Representation

Dividing the numerator 115 by denominator 264 produces a repeating decimal (approximately 0.435606, or 43.5606%).

115 ÷ 264 = 0.435606 (43.5606%)

Visual Representation

The diagram below illustrates 2/33 plus 3/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`115/264`
Mixed Number Form	`115/264`
Decimal Form	`0.435606`
Percentage	`43.5606%`

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Frequently Asked Questions

What is 2/33 plus 3/8 as a fraction?

2/33 + 3/8 in simplest fraction form is 115/264.

What is 2/33 plus 3/8 as a decimal?

2/33 + 3/8 converted to a decimal is 0.435606.

What is 2/33 plus 3/8 as a percentage?

2/33 + 3/8 expressed as a percentage is 43.5606%.

Does 2/33 plus 3/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.435606...) because the denominator contains prime factors other than 2 and 5.