What is 2/19 plus 2/17? (Answer: 72/323)

Exact Answer

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Problem: What is 2/19 plus 2/17?
Formula / Expression: 2/19 + 2/17
Final Answer: 72/323
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 19 and 17 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 19 × 17 = 323.
Working: LCD(19, 17) = 323

Step 2: Convert to Equivalent Fractions with Common Denominator 323
Multiply the numerator and denominator of 2/19 by 17, and multiply the numerator and denominator of 2/17 by 19 so both fractions share the common base 323.
Working: 2 × 17/19 × 17 = 34/323 and 2 × 19/17 × 19 = 38/323

Step 3: Add the Numerators
Now add the numerators (34 + 38 = 72) and keep the common denominator 323 unchanged.
Working: 34 + 38/323 = 72/323

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 72 and 323 is 1, confirming that 72/323 cannot be reduced further—it is already in its simplest irreducible form.
Working: 72/323

Step 5: Decimal & Percentage Representation
Dividing the numerator 72 by denominator 323 produces a repeating decimal (approximately 0.22291, or 22.291%).
Working: 72 ÷ 323 = 0.22291 (22.291%)

Key Values:
- Simplified Fraction: 72/323
- Mixed Number Form: 72/323
- Decimal Value: 0.22291
- Percentage: 22.291%

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Solved with FractionsCalc:
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2/19 + 2/17 = 72/323

Simplified Fraction

72/323

Mixed Number

Proper (72/323)

Decimal Value

0.22291

Percentage

22.291%

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Step-by-Step Solution: 2/19 + 2/17

Step 1

Find the Least Common Denominator (LCD)

The denominators 19 and 17 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 19 × 17 = 323.

LCD(19, 17) = 323

Step 2

Convert to Equivalent Fractions with Common Denominator 323

Multiply the numerator and denominator of 2/19 by 17, and multiply the numerator and denominator of 2/17 by 19 so both fractions share the common base 323.

2 × 17/19 × 17 = 34/323 and 2 × 19/17 × 19 = 38/323

Step 3

Add the Numerators

Now add the numerators (34 + 38 = 72) and keep the common denominator 323 unchanged.

34 + 38/323 = 72/323

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 72 and 323 is 1, confirming that 72/323 cannot be reduced further—it is already in its simplest irreducible form.

72/323

Step 5

Decimal & Percentage Representation

Dividing the numerator 72 by denominator 323 produces a repeating decimal (approximately 0.22291, or 22.291%).

72 ÷ 323 = 0.22291 (22.291%)

Visual Representation

The diagram below illustrates 2/19 plus 2/17 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`72/323`
Mixed Number Form	`72/323`
Decimal Form	`0.22291`
Percentage	`22.291%`

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Frequently Asked Questions

What is 2/19 plus 2/17 as a fraction?

2/19 + 2/17 in simplest fraction form is 72/323.

What is 2/19 plus 2/17 as a decimal?

2/19 + 2/17 converted to a decimal is 0.22291.

What is 2/19 plus 2/17 as a percentage?

2/19 + 2/17 expressed as a percentage is 22.291%.

Does 2/19 plus 2/17 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.22291...) because the denominator contains prime factors other than 2 and 5.