What is 8/17 plus 2/3? (Answer: 58/51)

Exact Answer

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Problem: What is 8/17 plus 2/3?
Formula / Expression: 8/17 + 2/3
Final Answer: 1 7/51 (58/51)
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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 8/17 by 3, and multiply the numerator and denominator of 2/3 by 17 so both fractions share the common base 51.
Working: 8 × 3/17 × 3 = 24/51 and 2 × 17/3 × 17 = 34/51

Step 3: Add the Numerators
Now add the numerators (24 + 34 = 58) and keep the common denominator 51 unchanged.
Working: 24 + 34/51 = 58/51

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 58 and 51 is 1, confirming that 58/51 cannot be reduced further—it is already in its simplest irreducible form.
Working: 58/51

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (58) is greater than the denominator (51), divide 58 by 51: it goes in 1 whole time(s) with a remainder of 7, giving the mixed number 1 7/51.
Working: 58/51 = 1 7/51

Step 6: Decimal & Percentage Representation
Dividing the numerator 58 by denominator 51 produces a repeating decimal (approximately 1.137255, or 113.7255%).
Working: 58 ÷ 51 = 1.137255 (113.7255%)

Key Values:
- Simplified Fraction: 58/51
- Mixed Number Form: 1 7/51
- Decimal Value: 1.137255
- Percentage: 113.7255%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-8-17-plus-2-3/
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8/17 + 2/3 = 58/51

Simplified Fraction

58/51

Mixed Number

1 7/51

Decimal Value

1.137255

Percentage

113.7255%

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Step-by-Step Solution: 8/17 + 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 8/17 by 3, and multiply the numerator and denominator of 2/3 by 17 so both fractions share the common base 51.

8 × 3/17 × 3 = 24/51 and 2 × 17/3 × 17 = 34/51

Step 3

Add the Numerators

Now add the numerators (24 + 34 = 58) and keep the common denominator 51 unchanged.

24 + 34/51 = 58/51

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 58 and 51 is 1, confirming that 58/51 cannot be reduced further—it is already in its simplest irreducible form.

58/51

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (58) is greater than the denominator (51), divide 58 by 51: it goes in 1 whole time(s) with a remainder of 7, giving the mixed number 1 7/51.

58/51 = 17/51

Step 6

Decimal & Percentage Representation

Dividing the numerator 58 by denominator 51 produces a repeating decimal (approximately 1.137255, or 113.7255%).

58 ÷ 51 = 1.137255 (113.7255%)

Visual Representation

The diagram below illustrates 8/17 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`58/51`
Mixed Number Form	`1 7/51`
Decimal Form	`1.137255`
Percentage	`113.7255%`

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Frequently Asked Questions

What is 8/17 plus 2/3 as a fraction?

8/17 + 2/3 in simplest fraction form is 58/51 (or 1 7/51 as a mixed number).

What is 8/17 plus 2/3 as a decimal?

8/17 + 2/3 converted to a decimal is 1.137255.

What is 8/17 plus 2/3 as a percentage?

8/17 + 2/3 expressed as a percentage is 113.7255%.

How do you write 8/17 plus 2/3 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 58/51 can be written as the mixed number 1 7/51.

Does 8/17 plus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.137255...) because the denominator contains prime factors other than 2 and 5.