What is 3/17 plus 2/9? (Answer: 61/153)

Exact Answer

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Problem: What is 3/17 plus 2/9?
Formula / Expression: 3/17 + 2/9
Final Answer: 61/153
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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 2/9 by 17 so both fractions share the common base 153.
Working: 3 × 9/17 × 9 = 27/153 and 2 × 17/9 × 17 = 34/153

Step 3: Add the Numerators
Now add the numerators (27 + 34 = 61) and keep the common denominator 153 unchanged.
Working: 27 + 34/153 = 61/153

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 61 and 153 is 1, confirming that 61/153 cannot be reduced further—it is already in its simplest irreducible form.
Working: 61/153

Step 5: Decimal & Percentage Representation
Dividing the numerator 61 by denominator 153 produces a repeating decimal (approximately 0.398693, or 39.8693%).
Working: 61 ÷ 153 = 0.398693 (39.8693%)

Key Values:
- Simplified Fraction: 61/153
- Mixed Number Form: 61/153
- Decimal Value: 0.398693
- Percentage: 39.8693%

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Solved with FractionsCalc:
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3/17 + 2/9 = 61/153

Simplified Fraction

61/153

Mixed Number

Proper (61/153)

Decimal Value

0.398693

Percentage

39.8693%

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Step-by-Step Solution: 3/17 + 2/9

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 2/9 by 17 so both fractions share the common base 153.

3 × 9/17 × 9 = 27/153 and 2 × 17/9 × 17 = 34/153

Step 3

Add the Numerators

Now add the numerators (27 + 34 = 61) and keep the common denominator 153 unchanged.

27 + 34/153 = 61/153

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 61 and 153 is 1, confirming that 61/153 cannot be reduced further—it is already in its simplest irreducible form.

61/153

Step 5

Decimal & Percentage Representation

Dividing the numerator 61 by denominator 153 produces a repeating decimal (approximately 0.398693, or 39.8693%).

61 ÷ 153 = 0.398693 (39.8693%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`61/153`
Mixed Number Form	`61/153`
Decimal Form	`0.398693`
Percentage	`39.8693%`

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Frequently Asked Questions

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

3/17 + 2/9 in simplest fraction form is 61/153.

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

3/17 + 2/9 converted to a decimal is 0.398693.

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

3/17 + 2/9 expressed as a percentage is 39.8693%.

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

It results in a repeating decimal (approximately 0.398693...) because the denominator contains prime factors other than 2 and 5.