What is 2/33 plus 2/5? (Answer: 76/165)

Exact Answer

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Problem: What is 2/33 plus 2/5?
Formula / Expression: 2/33 + 2/5
Final Answer: 76/165
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 33 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 33 × 5 = 165.
Working: LCD(33, 5) = 165

Step 2: Convert to Equivalent Fractions with Common Denominator 165
Multiply the numerator and denominator of 2/33 by 5, and multiply the numerator and denominator of 2/5 by 33 so both fractions share the common base 165.
Working: 2 × 5/33 × 5 = 10/165 and 2 × 33/5 × 33 = 66/165

Step 3: Add the Numerators
Now add the numerators (10 + 66 = 76) and keep the common denominator 165 unchanged.
Working: 10 + 66/165 = 76/165

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 76 and 165 is 1, confirming that 76/165 cannot be reduced further—it is already in its simplest irreducible form.
Working: 76/165

Step 5: Decimal & Percentage Representation
Dividing the numerator 76 by denominator 165 produces a repeating decimal (approximately 0.460606, or 46.0606%).
Working: 76 ÷ 165 = 0.460606 (46.0606%)

Key Values:
- Simplified Fraction: 76/165
- Mixed Number Form: 76/165
- Decimal Value: 0.460606
- Percentage: 46.0606%

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Solved with FractionsCalc:
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2/33 + 2/5 = 76/165

Simplified Fraction

76/165

Mixed Number

Proper (76/165)

Decimal Value

0.460606

Percentage

46.0606%

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Step-by-Step Solution: 2/33 + 2/5

Step 1

Find the Least Common Denominator (LCD)

The denominators 33 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 33 × 5 = 165.

LCD(33, 5) = 165

Step 2

Convert to Equivalent Fractions with Common Denominator 165

Multiply the numerator and denominator of 2/33 by 5, and multiply the numerator and denominator of 2/5 by 33 so both fractions share the common base 165.

2 × 5/33 × 5 = 10/165 and 2 × 33/5 × 33 = 66/165

Step 3

Add the Numerators

Now add the numerators (10 + 66 = 76) and keep the common denominator 165 unchanged.

10 + 66/165 = 76/165

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 76 and 165 is 1, confirming that 76/165 cannot be reduced further—it is already in its simplest irreducible form.

76/165

Step 5

Decimal & Percentage Representation

Dividing the numerator 76 by denominator 165 produces a repeating decimal (approximately 0.460606, or 46.0606%).

76 ÷ 165 = 0.460606 (46.0606%)

Visual Representation

The diagram below illustrates 2/33 plus 2/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`76/165`
Mixed Number Form	`76/165`
Decimal Form	`0.460606`
Percentage	`46.0606%`

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Frequently Asked Questions

What is 2/33 plus 2/5 as a fraction?

2/33 + 2/5 in simplest fraction form is 76/165.

What is 2/33 plus 2/5 as a decimal?

2/33 + 2/5 converted to a decimal is 0.460606.

What is 2/33 plus 2/5 as a percentage?

2/33 + 2/5 expressed as a percentage is 46.0606%.

Does 2/33 plus 2/5 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.460606...) because the denominator contains prime factors other than 2 and 5.