What is 9/17 plus 2/3? (Answer: 61/51)

Exact Answer

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Problem: What is 9/17 plus 2/3?
Formula / Expression: 9/17 + 2/3
Final Answer: 1 10/51 (61/51)
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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 9/17 by 3, and multiply the numerator and denominator of 2/3 by 17 so both fractions share the common base 51.
Working: 9 × 3/17 × 3 = 27/51 and 2 × 17/3 × 17 = 34/51

Step 3: Add the Numerators
Now add the numerators (27 + 34 = 61) and keep the common denominator 51 unchanged.
Working: 27 + 34/51 = 61/51

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 61 and 51 is 1, confirming that 61/51 cannot be reduced further—it is already in its simplest irreducible form.
Working: 61/51

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (61) is greater than the denominator (51), divide 61 by 51: it goes in 1 whole time(s) with a remainder of 10, giving the mixed number 1 10/51.
Working: 61/51 = 1 10/51

Step 6: Decimal & Percentage Representation
Dividing the numerator 61 by denominator 51 produces a repeating decimal (approximately 1.196078, or 119.6078%).
Working: 61 ÷ 51 = 1.196078 (119.6078%)

Key Values:
- Simplified Fraction: 61/51
- Mixed Number Form: 1 10/51
- Decimal Value: 1.196078
- Percentage: 119.6078%

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Solved with FractionsCalc:
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9/17 + 2/3 = 61/51

Simplified Fraction

61/51

Mixed Number

1 10/51

Decimal Value

1.196078

Percentage

119.6078%

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Step-by-Step Solution: 9/17 + 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 9/17 by 3, and multiply the numerator and denominator of 2/3 by 17 so both fractions share the common base 51.

9 × 3/17 × 3 = 27/51 and 2 × 17/3 × 17 = 34/51

Step 3

Add the Numerators

Now add the numerators (27 + 34 = 61) and keep the common denominator 51 unchanged.

27 + 34/51 = 61/51

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 61 and 51 is 1, confirming that 61/51 cannot be reduced further—it is already in its simplest irreducible form.

61/51

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (61) is greater than the denominator (51), divide 61 by 51: it goes in 1 whole time(s) with a remainder of 10, giving the mixed number 1 10/51.

61/51 = 110/51

Step 6

Decimal & Percentage Representation

Dividing the numerator 61 by denominator 51 produces a repeating decimal (approximately 1.196078, or 119.6078%).

61 ÷ 51 = 1.196078 (119.6078%)

Visual Representation

The diagram below illustrates 9/17 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`61/51`
Mixed Number Form	`1 10/51`
Decimal Form	`1.196078`
Percentage	`119.6078%`

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Frequently Asked Questions

What is 9/17 plus 2/3 as a fraction?

9/17 + 2/3 in simplest fraction form is 61/51 (or 1 10/51 as a mixed number).

What is 9/17 plus 2/3 as a decimal?

9/17 + 2/3 converted to a decimal is 1.196078.

What is 9/17 plus 2/3 as a percentage?

9/17 + 2/3 expressed as a percentage is 119.6078%.

How do you write 9/17 plus 2/3 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 61/51 can be written as the mixed number 1 10/51.

Does 9/17 plus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.196078...) because the denominator contains prime factors other than 2 and 5.