What is 2/19 plus 2/15? (Answer: 68/285)

Exact Answer

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Problem: What is 2/19 plus 2/15?
Formula / Expression: 2/19 + 2/15
Final Answer: 68/285
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 19 and 15 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 19 × 15 = 285.
Working: LCD(19, 15) = 285

Step 2: Convert to Equivalent Fractions with Common Denominator 285
Multiply the numerator and denominator of 2/19 by 15, and multiply the numerator and denominator of 2/15 by 19 so both fractions share the common base 285.
Working: 2 × 15/19 × 15 = 30/285 and 2 × 19/15 × 19 = 38/285

Step 3: Add the Numerators
Now add the numerators (30 + 38 = 68) and keep the common denominator 285 unchanged.
Working: 30 + 38/285 = 68/285

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 68 and 285 is 1, confirming that 68/285 cannot be reduced further—it is already in its simplest irreducible form.
Working: 68/285

Step 5: Decimal & Percentage Representation
Dividing the numerator 68 by denominator 285 produces a repeating decimal (approximately 0.238596, or 23.8596%).
Working: 68 ÷ 285 = 0.238596 (23.8596%)

Key Values:
- Simplified Fraction: 68/285
- Mixed Number Form: 68/285
- Decimal Value: 0.238596
- Percentage: 23.8596%

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Solved with FractionsCalc:
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2/19 + 2/15 = 68/285

Simplified Fraction

68/285

Mixed Number

Proper (68/285)

Decimal Value

0.238596

Percentage

23.8596%

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Step-by-Step Solution: 2/19 + 2/15

Step 1

Find the Least Common Denominator (LCD)

The denominators 19 and 15 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 19 × 15 = 285.

LCD(19, 15) = 285

Step 2

Convert to Equivalent Fractions with Common Denominator 285

Multiply the numerator and denominator of 2/19 by 15, and multiply the numerator and denominator of 2/15 by 19 so both fractions share the common base 285.

2 × 15/19 × 15 = 30/285 and 2 × 19/15 × 19 = 38/285

Step 3

Add the Numerators

Now add the numerators (30 + 38 = 68) and keep the common denominator 285 unchanged.

30 + 38/285 = 68/285

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 68 and 285 is 1, confirming that 68/285 cannot be reduced further—it is already in its simplest irreducible form.

68/285

Step 5

Decimal & Percentage Representation

Dividing the numerator 68 by denominator 285 produces a repeating decimal (approximately 0.238596, or 23.8596%).

68 ÷ 285 = 0.238596 (23.8596%)

Visual Representation

The diagram below illustrates 2/19 plus 2/15 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`68/285`
Mixed Number Form	`68/285`
Decimal Form	`0.238596`
Percentage	`23.8596%`

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Frequently Asked Questions

What is 2/19 plus 2/15 as a fraction?

2/19 + 2/15 in simplest fraction form is 68/285.

What is 2/19 plus 2/15 as a decimal?

2/19 + 2/15 converted to a decimal is 0.238596.

What is 2/19 plus 2/15 as a percentage?

2/19 + 2/15 expressed as a percentage is 23.8596%.

Does 2/19 plus 2/15 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.238596...) because the denominator contains prime factors other than 2 and 5.