What is 9/17 plus 5/9? (Answer: 166/153)

Exact Answer

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Problem: What is 9/17 plus 5/9?
Formula / Expression: 9/17 + 5/9
Final Answer: 1 13/153 (166/153)
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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 9/17 by 9, and multiply the numerator and denominator of 5/9 by 17 so both fractions share the common base 153.
Working: 9 × 9/17 × 9 = 81/153 and 5 × 17/9 × 17 = 85/153

Step 3: Add the Numerators
Now add the numerators (81 + 85 = 166) and keep the common denominator 153 unchanged.
Working: 81 + 85/153 = 166/153

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 166 and 153 is 1, confirming that 166/153 cannot be reduced further—it is already in its simplest irreducible form.
Working: 166/153

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (166) is greater than the denominator (153), divide 166 by 153: it goes in 1 whole time(s) with a remainder of 13, giving the mixed number 1 13/153.
Working: 166/153 = 1 13/153

Step 6: Decimal & Percentage Representation
Dividing the numerator 166 by denominator 153 produces a repeating decimal (approximately 1.084967, or 108.4967%).
Working: 166 ÷ 153 = 1.084967 (108.4967%)

Key Values:
- Simplified Fraction: 166/153
- Mixed Number Form: 1 13/153
- Decimal Value: 1.084967
- Percentage: 108.4967%

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Solved with FractionsCalc:
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9/17 + 5/9 = 166/153

Simplified Fraction

166/153

Mixed Number

1 13/153

Decimal Value

1.084967

Percentage

108.4967%

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Step-by-Step Solution: 9/17 + 5/9

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 9/17 by 9, and multiply the numerator and denominator of 5/9 by 17 so both fractions share the common base 153.

9 × 9/17 × 9 = 81/153 and 5 × 17/9 × 17 = 85/153

Step 3

Add the Numerators

Now add the numerators (81 + 85 = 166) and keep the common denominator 153 unchanged.

81 + 85/153 = 166/153

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 166 and 153 is 1, confirming that 166/153 cannot be reduced further—it is already in its simplest irreducible form.

166/153

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (166) is greater than the denominator (153), divide 166 by 153: it goes in 1 whole time(s) with a remainder of 13, giving the mixed number 1 13/153.

166/153 = 113/153

Step 6

Decimal & Percentage Representation

Dividing the numerator 166 by denominator 153 produces a repeating decimal (approximately 1.084967, or 108.4967%).

166 ÷ 153 = 1.084967 (108.4967%)

Visual Representation

The diagram below illustrates 9/17 plus 5/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`166/153`
Mixed Number Form	`1 13/153`
Decimal Form	`1.084967`
Percentage	`108.4967%`

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Frequently Asked Questions

What is 9/17 plus 5/9 as a fraction?

9/17 + 5/9 in simplest fraction form is 166/153 (or 1 13/153 as a mixed number).

What is 9/17 plus 5/9 as a decimal?

9/17 + 5/9 converted to a decimal is 1.084967.

What is 9/17 plus 5/9 as a percentage?

9/17 + 5/9 expressed as a percentage is 108.4967%.

How do you write 9/17 plus 5/9 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 166/153 can be written as the mixed number 1 13/153.

Does 9/17 plus 5/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.084967...) because the denominator contains prime factors other than 2 and 5.