What is 3/17 plus 2/3? (Answer: 43/51)

Exact Answer

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Problem: What is 3/17 plus 2/3?
Formula / Expression: 3/17 + 2/3
Final Answer: 43/51
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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 3/17 by 3, and multiply the numerator and denominator of 2/3 by 17 so both fractions share the common base 51.
Working: 3 × 3/17 × 3 = 9/51 and 2 × 17/3 × 17 = 34/51

Step 3: Add the Numerators
Now add the numerators (9 + 34 = 43) and keep the common denominator 51 unchanged.
Working: 9 + 34/51 = 43/51

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 43 and 51 is 1, confirming that 43/51 cannot be reduced further—it is already in its simplest irreducible form.
Working: 43/51

Step 5: Decimal & Percentage Representation
Dividing the numerator 43 by denominator 51 produces a repeating decimal (approximately 0.843137, or 84.3137%).
Working: 43 ÷ 51 = 0.843137 (84.3137%)

Key Values:
- Simplified Fraction: 43/51
- Mixed Number Form: 43/51
- Decimal Value: 0.843137
- Percentage: 84.3137%

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Solved with FractionsCalc:
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3/17 + 2/3 = 43/51

Simplified Fraction

43/51

Mixed Number

Proper (43/51)

Decimal Value

0.843137

Percentage

84.3137%

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

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

3 × 3/17 × 3 = 9/51 and 2 × 17/3 × 17 = 34/51

Step 3

Add the Numerators

Now add the numerators (9 + 34 = 43) and keep the common denominator 51 unchanged.

9 + 34/51 = 43/51

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 43 and 51 is 1, confirming that 43/51 cannot be reduced further—it is already in its simplest irreducible form.

43/51

Step 5

Decimal & Percentage Representation

Dividing the numerator 43 by denominator 51 produces a repeating decimal (approximately 0.843137, or 84.3137%).

43 ÷ 51 = 0.843137 (84.3137%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`43/51`
Mixed Number Form	`43/51`
Decimal Form	`0.843137`
Percentage	`84.3137%`

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Frequently Asked Questions

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

3/17 + 2/3 in simplest fraction form is 43/51.

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

3/17 + 2/3 converted to a decimal is 0.843137.

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

3/17 + 2/3 expressed as a percentage is 84.3137%.

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

It results in a repeating decimal (approximately 0.843137...) because the denominator contains prime factors other than 2 and 5.