What is 2/9 plus 8/17? (Answer: 106/153)

Exact Answer

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Problem: What is 2/9 plus 8/17?
Formula / Expression: 2/9 + 8/17
Final Answer: 106/153
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 153
Multiply the numerator and denominator of 2/9 by 17, and multiply the numerator and denominator of 8/17 by 9 so both fractions share the common base 153.
Working: 2 × 17/9 × 17 = 34/153 and 8 × 9/17 × 9 = 72/153

Step 3: Add the Numerators
Now add the numerators (34 + 72 = 106) and keep the common denominator 153 unchanged.
Working: 34 + 72/153 = 106/153

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 106 and 153 is 1, confirming that 106/153 cannot be reduced further—it is already in its simplest irreducible form.
Working: 106/153

Step 5: Decimal & Percentage Representation
Dividing the numerator 106 by denominator 153 produces a repeating decimal (approximately 0.69281, or 69.281%).
Working: 106 ÷ 153 = 0.69281 (69.281%)

Key Values:
- Simplified Fraction: 106/153
- Mixed Number Form: 106/153
- Decimal Value: 0.69281
- Percentage: 69.281%

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Solved with FractionsCalc:
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2/9 + 8/17 = 106/153

Simplified Fraction

106/153

Mixed Number

Proper (106/153)

Decimal Value

0.69281

Percentage

69.281%

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Step-by-Step Solution: 2/9 + 8/17

Step 1

Find the Least Common Denominator (LCD)

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

LCD(9, 17) = 153

Step 2

Convert to Equivalent Fractions with Common Denominator 153

Multiply the numerator and denominator of 2/9 by 17, and multiply the numerator and denominator of 8/17 by 9 so both fractions share the common base 153.

2 × 17/9 × 17 = 34/153 and 8 × 9/17 × 9 = 72/153

Step 3

Add the Numerators

Now add the numerators (34 + 72 = 106) and keep the common denominator 153 unchanged.

34 + 72/153 = 106/153

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 106 and 153 is 1, confirming that 106/153 cannot be reduced further—it is already in its simplest irreducible form.

106/153

Step 5

Decimal & Percentage Representation

Dividing the numerator 106 by denominator 153 produces a repeating decimal (approximately 0.69281, or 69.281%).

106 ÷ 153 = 0.69281 (69.281%)

Visual Representation

The diagram below illustrates 2/9 plus 8/17 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`106/153`
Mixed Number Form	`106/153`
Decimal Form	`0.69281`
Percentage	`69.281%`

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Frequently Asked Questions

What is 2/9 plus 8/17 as a fraction?

2/9 + 8/17 in simplest fraction form is 106/153.

What is 2/9 plus 8/17 as a decimal?

2/9 + 8/17 converted to a decimal is 0.69281.

What is 2/9 plus 8/17 as a percentage?

2/9 + 8/17 expressed as a percentage is 69.281%.

Does 2/9 plus 8/17 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.69281...) because the denominator contains prime factors other than 2 and 5.