What is 2/33 plus 3/4? (Answer: 107/132)

Exact Answer

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Problem: What is 2/33 plus 3/4?
Formula / Expression: 2/33 + 3/4
Final Answer: 107/132
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 33 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 33 × 4 = 132.
Working: LCD(33, 4) = 132

Step 2: Convert to Equivalent Fractions with Common Denominator 132
Multiply the numerator and denominator of 2/33 by 4, and multiply the numerator and denominator of 3/4 by 33 so both fractions share the common base 132.
Working: 2 × 4/33 × 4 = 8/132 and 3 × 33/4 × 33 = 99/132

Step 3: Add the Numerators
Now add the numerators (8 + 99 = 107) and keep the common denominator 132 unchanged.
Working: 8 + 99/132 = 107/132

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 107 and 132 is 1, confirming that 107/132 cannot be reduced further—it is already in its simplest irreducible form.
Working: 107/132

Step 5: Decimal & Percentage Representation
Dividing the numerator 107 by denominator 132 produces a repeating decimal (approximately 0.810606, or 81.0606%).
Working: 107 ÷ 132 = 0.810606 (81.0606%)

Key Values:
- Simplified Fraction: 107/132
- Mixed Number Form: 107/132
- Decimal Value: 0.810606
- Percentage: 81.0606%

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2/33 + 3/4 = 107/132

Simplified Fraction

107/132

Mixed Number

Proper (107/132)

Decimal Value

0.810606

Percentage

81.0606%

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Step-by-Step Solution: 2/33 + 3/4

Step 1

Find the Least Common Denominator (LCD)

The denominators 33 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 33 × 4 = 132.

LCD(33, 4) = 132

Step 2

Convert to Equivalent Fractions with Common Denominator 132

Multiply the numerator and denominator of 2/33 by 4, and multiply the numerator and denominator of 3/4 by 33 so both fractions share the common base 132.

2 × 4/33 × 4 = 8/132 and 3 × 33/4 × 33 = 99/132

Step 3

Add the Numerators

Now add the numerators (8 + 99 = 107) and keep the common denominator 132 unchanged.

8 + 99/132 = 107/132

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 107 and 132 is 1, confirming that 107/132 cannot be reduced further—it is already in its simplest irreducible form.

107/132

Step 5

Decimal & Percentage Representation

Dividing the numerator 107 by denominator 132 produces a repeating decimal (approximately 0.810606, or 81.0606%).

107 ÷ 132 = 0.810606 (81.0606%)

Visual Representation

The diagram below illustrates 2/33 plus 3/4 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`107/132`
Mixed Number Form	`107/132`
Decimal Form	`0.810606`
Percentage	`81.0606%`

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Frequently Asked Questions

What is 2/33 plus 3/4 as a fraction?

2/33 + 3/4 in simplest fraction form is 107/132.

What is 2/33 plus 3/4 as a decimal?

2/33 + 3/4 converted to a decimal is 0.810606.

What is 2/33 plus 3/4 as a percentage?

2/33 + 3/4 expressed as a percentage is 81.0606%.

Does 2/33 plus 3/4 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.810606...) because the denominator contains prime factors other than 2 and 5.