What is 2/17 plus 1/3? (Answer: 23/51)

Exact Answer

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Problem: What is 2/17 plus 1/3?
Formula / Expression: 2/17 + 1/3
Final Answer: 23/51
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 17 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 17 × 3 = 51.
Working: LCD(17, 3) = 51

Step 2: Convert to Equivalent Fractions with Common Denominator 51
Multiply the numerator and denominator of 2/17 by 3, and multiply the numerator and denominator of 1/3 by 17 so both fractions share the common base 51.
Working: 2 × 3/17 × 3 = 6/51 and 1 × 17/3 × 17 = 17/51

Step 3: Add the Numerators
Now add the numerators (6 + 17 = 23) and keep the common denominator 51 unchanged.
Working: 6 + 17/51 = 23/51

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 23 and 51 is 1, confirming that 23/51 cannot be reduced further—it is already in its simplest irreducible form.
Working: 23/51

Step 5: Decimal & Percentage Representation
Dividing the numerator 23 by denominator 51 produces a repeating decimal (approximately 0.45098, or 45.098%).
Working: 23 ÷ 51 = 0.45098 (45.098%)

Key Values:
- Simplified Fraction: 23/51
- Mixed Number Form: 23/51
- Decimal Value: 0.45098
- Percentage: 45.098%

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Solved with FractionsCalc:
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2/17 + 1/3 = 23/51

Simplified Fraction

23/51

Mixed Number

Proper (23/51)

Decimal Value

0.45098

Percentage

45.098%

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Step-by-Step Solution: 2/17 + 1/3

Step 1

Find the Least Common Denominator (LCD)

The denominators 17 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 17 × 3 = 51.

LCD(17, 3) = 51

Step 2

Convert to Equivalent Fractions with Common Denominator 51

Multiply the numerator and denominator of 2/17 by 3, and multiply the numerator and denominator of 1/3 by 17 so both fractions share the common base 51.

2 × 3/17 × 3 = 6/51 and 1 × 17/3 × 17 = 17/51

Step 3

Add the Numerators

Now add the numerators (6 + 17 = 23) and keep the common denominator 51 unchanged.

6 + 17/51 = 23/51

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 23 and 51 is 1, confirming that 23/51 cannot be reduced further—it is already in its simplest irreducible form.

23/51

Step 5

Decimal & Percentage Representation

Dividing the numerator 23 by denominator 51 produces a repeating decimal (approximately 0.45098, or 45.098%).

23 ÷ 51 = 0.45098 (45.098%)

Visual Representation

The diagram below illustrates 2/17 plus 1/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`23/51`
Mixed Number Form	`23/51`
Decimal Form	`0.45098`
Percentage	`45.098%`

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Frequently Asked Questions

What is 2/17 plus 1/3 as a fraction?

2/17 + 1/3 in simplest fraction form is 23/51.

What is 2/17 plus 1/3 as a decimal?

2/17 + 1/3 converted to a decimal is 0.45098.

What is 2/17 plus 1/3 as a percentage?

2/17 + 1/3 expressed as a percentage is 45.098%.

Does 2/17 plus 1/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.45098...) because the denominator contains prime factors other than 2 and 5.