What is 2/15 plus 2/11? (Answer: 52/165)

Exact Answer

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Problem: What is 2/15 plus 2/11?
Formula / Expression: 2/15 + 2/11
Final Answer: 52/165
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 15 and 11 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 15 × 11 = 165.
Working: LCD(15, 11) = 165

Step 2: Convert to Equivalent Fractions with Common Denominator 165
Multiply the numerator and denominator of 2/15 by 11, and multiply the numerator and denominator of 2/11 by 15 so both fractions share the common base 165.
Working: 2 × 11/15 × 11 = 22/165 and 2 × 15/11 × 15 = 30/165

Step 3: Add the Numerators
Now add the numerators (22 + 30 = 52) and keep the common denominator 165 unchanged.
Working: 22 + 30/165 = 52/165

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 52 and 165 is 1, confirming that 52/165 cannot be reduced further—it is already in its simplest irreducible form.
Working: 52/165

Step 5: Decimal & Percentage Representation
Dividing the numerator 52 by denominator 165 produces a repeating decimal (approximately 0.315152, or 31.5152%).
Working: 52 ÷ 165 = 0.315152 (31.5152%)

Key Values:
- Simplified Fraction: 52/165
- Mixed Number Form: 52/165
- Decimal Value: 0.315152
- Percentage: 31.5152%

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Solved with FractionsCalc:
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2/15 + 2/11 = 52/165

Simplified Fraction

52/165

Mixed Number

Proper (52/165)

Decimal Value

0.315152

Percentage

31.5152%

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Step-by-Step Solution: 2/15 + 2/11

Step 1

Find the Least Common Denominator (LCD)

The denominators 15 and 11 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 15 × 11 = 165.

LCD(15, 11) = 165

Step 2

Convert to Equivalent Fractions with Common Denominator 165

Multiply the numerator and denominator of 2/15 by 11, and multiply the numerator and denominator of 2/11 by 15 so both fractions share the common base 165.

2 × 11/15 × 11 = 22/165 and 2 × 15/11 × 15 = 30/165

Step 3

Add the Numerators

Now add the numerators (22 + 30 = 52) and keep the common denominator 165 unchanged.

22 + 30/165 = 52/165

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 52 and 165 is 1, confirming that 52/165 cannot be reduced further—it is already in its simplest irreducible form.

52/165

Step 5

Decimal & Percentage Representation

Dividing the numerator 52 by denominator 165 produces a repeating decimal (approximately 0.315152, or 31.5152%).

52 ÷ 165 = 0.315152 (31.5152%)

Visual Representation

The diagram below illustrates 2/15 plus 2/11 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`52/165`
Mixed Number Form	`52/165`
Decimal Form	`0.315152`
Percentage	`31.5152%`

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Frequently Asked Questions

What is 2/15 plus 2/11 as a fraction?

2/15 + 2/11 in simplest fraction form is 52/165.

What is 2/15 plus 2/11 as a decimal?

2/15 + 2/11 converted to a decimal is 0.315152.

What is 2/15 plus 2/11 as a percentage?

2/15 + 2/11 expressed as a percentage is 31.5152%.

Does 2/15 plus 2/11 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.315152...) because the denominator contains prime factors other than 2 and 5.