What is 2/23 plus 2/17? (Answer: 80/391)

Exact Answer

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Problem: What is 2/23 plus 2/17?
Formula / Expression: 2/23 + 2/17
Final Answer: 80/391
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 23 and 17 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 17 = 391.
Working: LCD(23, 17) = 391

Step 2: Convert to Equivalent Fractions with Common Denominator 391
Multiply the numerator and denominator of 2/23 by 17, and multiply the numerator and denominator of 2/17 by 23 so both fractions share the common base 391.
Working: 2 × 17/23 × 17 = 34/391 and 2 × 23/17 × 23 = 46/391

Step 3: Add the Numerators
Now add the numerators (34 + 46 = 80) and keep the common denominator 391 unchanged.
Working: 34 + 46/391 = 80/391

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 80 and 391 is 1, confirming that 80/391 cannot be reduced further—it is already in its simplest irreducible form.
Working: 80/391

Step 5: Decimal & Percentage Representation
Dividing the numerator 80 by denominator 391 produces a repeating decimal (approximately 0.204604, or 20.4604%).
Working: 80 ÷ 391 = 0.204604 (20.4604%)

Key Values:
- Simplified Fraction: 80/391
- Mixed Number Form: 80/391
- Decimal Value: 0.204604
- Percentage: 20.4604%

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Solved with FractionsCalc:
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2/23 + 2/17 = 80/391

Simplified Fraction

80/391

Mixed Number

Proper (80/391)

Decimal Value

0.204604

Percentage

20.4604%

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Step-by-Step Solution: 2/23 + 2/17

Step 1

Find the Least Common Denominator (LCD)

The denominators 23 and 17 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 17 = 391.

LCD(23, 17) = 391

Step 2

Convert to Equivalent Fractions with Common Denominator 391

Multiply the numerator and denominator of 2/23 by 17, and multiply the numerator and denominator of 2/17 by 23 so both fractions share the common base 391.

2 × 17/23 × 17 = 34/391 and 2 × 23/17 × 23 = 46/391

Step 3

Add the Numerators

Now add the numerators (34 + 46 = 80) and keep the common denominator 391 unchanged.

34 + 46/391 = 80/391

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 80 and 391 is 1, confirming that 80/391 cannot be reduced further—it is already in its simplest irreducible form.

80/391

Step 5

Decimal & Percentage Representation

Dividing the numerator 80 by denominator 391 produces a repeating decimal (approximately 0.204604, or 20.4604%).

80 ÷ 391 = 0.204604 (20.4604%)

Visual Representation

The diagram below illustrates 2/23 plus 2/17 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`80/391`
Mixed Number Form	`80/391`
Decimal Form	`0.204604`
Percentage	`20.4604%`

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Frequently Asked Questions

What is 2/23 plus 2/17 as a fraction?

2/23 + 2/17 in simplest fraction form is 80/391.

What is 2/23 plus 2/17 as a decimal?

2/23 + 2/17 converted to a decimal is 0.204604.

What is 2/23 plus 2/17 as a percentage?

2/23 + 2/17 expressed as a percentage is 20.4604%.

Does 2/23 plus 2/17 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.204604...) because the denominator contains prime factors other than 2 and 5.