What is 3/17 plus 3/9? (Answer: 26/51)

Exact Answer

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Problem: What is 3/17 plus 3/9?
Formula / Expression: 3/17 + 3/9
Final Answer: 26/51
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 17 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 17 × 9 = 153.
Working: LCD(17, 9) = 153

Step 2: Convert to Equivalent Fractions with Common Denominator 153
Multiply the numerator and denominator of 3/17 by 9, and multiply the numerator and denominator of 3/9 by 17 so both fractions share the common base 153.
Working: 3 × 9/17 × 9 = 27/153 and 3 × 17/9 × 17 = 51/153

Step 3: Add the Numerators
Now add the numerators (27 + 51 = 78) and keep the common denominator 153 unchanged.
Working: 27 + 51/153 = 78/153

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 78 and 153, which is 3. Divide both the numerator and denominator by 3.
Working: 78 ÷ 3/153 ÷ 3 = 26/51

Step 5: Decimal & Percentage Representation
Dividing the numerator 26 by denominator 51 produces a repeating decimal (approximately 0.509804, or 50.9804%).
Working: 26 ÷ 51 = 0.509804 (50.9804%)

Key Values:
- Simplified Fraction: 26/51
- Mixed Number Form: 26/51
- Decimal Value: 0.509804
- Percentage: 50.9804%

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Solved with FractionsCalc:
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3/17 + 3/9 = 26/51

Simplified Fraction

26/51

Mixed Number

Proper (26/51)

Decimal Value

0.509804

Percentage

50.9804%

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Step-by-Step Solution: 3/17 + 3/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 17 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 17 × 9 = 153.

LCD(17, 9) = 153

Step 2

Convert to Equivalent Fractions with Common Denominator 153

Multiply the numerator and denominator of 3/17 by 9, and multiply the numerator and denominator of 3/9 by 17 so both fractions share the common base 153.

3 × 9/17 × 9 = 27/153 and 3 × 17/9 × 17 = 51/153

Step 3

Add the Numerators

Now add the numerators (27 + 51 = 78) and keep the common denominator 153 unchanged.

27 + 51/153 = 78/153

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 78 and 153, which is 3. Divide both the numerator and denominator by 3.

78 ÷ 3/153 ÷ 3 = 26/51

Step 5

Decimal & Percentage Representation

Dividing the numerator 26 by denominator 51 produces a repeating decimal (approximately 0.509804, or 50.9804%).

26 ÷ 51 = 0.509804 (50.9804%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`26/51`
Mixed Number Form	`26/51`
Decimal Form	`0.509804`
Percentage	`50.9804%`

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Frequently Asked Questions

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

3/17 + 3/9 in simplest fraction form is 26/51.

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

3/17 + 3/9 converted to a decimal is 0.509804.

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

3/17 + 3/9 expressed as a percentage is 50.9804%.

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

It results in a repeating decimal (approximately 0.509804...) because the denominator contains prime factors other than 2 and 5.