What is 9/13 plus 8/9? (Answer: 185/117)

Exact Answer

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Problem: What is 9/13 plus 8/9?
Formula / Expression: 9/13 + 8/9
Final Answer: 1 68/117 (185/117)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 13 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 9 = 117.
Working: LCD(13, 9) = 117

Step 2: Convert to Equivalent Fractions with Common Denominator 117
Multiply the numerator and denominator of 9/13 by 9, and multiply the numerator and denominator of 8/9 by 13 so both fractions share the common base 117.
Working: 9 × 9/13 × 9 = 81/117 and 8 × 13/9 × 13 = 104/117

Step 3: Add the Numerators
Now add the numerators (81 + 104 = 185) and keep the common denominator 117 unchanged.
Working: 81 + 104/117 = 185/117

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 185 and 117 is 1, confirming that 185/117 cannot be reduced further—it is already in its simplest irreducible form.
Working: 185/117

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (185) is greater than the denominator (117), divide 185 by 117: it goes in 1 whole time(s) with a remainder of 68, giving the mixed number 1 68/117.
Working: 185/117 = 1 68/117

Step 6: Decimal & Percentage Representation
Dividing the numerator 185 by denominator 117 produces a repeating decimal (approximately 1.581197, or 158.1197%).
Working: 185 ÷ 117 = 1.581197 (158.1197%)

Key Values:
- Simplified Fraction: 185/117
- Mixed Number Form: 1 68/117
- Decimal Value: 1.581197
- Percentage: 158.1197%

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Solved with FractionsCalc:
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9/13 + 8/9 = 185/117

Simplified Fraction

185/117

Mixed Number

1 68/117

Decimal Value

1.581197

Percentage

158.1197%

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Step-by-Step Solution: 9/13 + 8/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 13 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 9 = 117.

LCD(13, 9) = 117

Step 2

Convert to Equivalent Fractions with Common Denominator 117

Multiply the numerator and denominator of 9/13 by 9, and multiply the numerator and denominator of 8/9 by 13 so both fractions share the common base 117.

9 × 9/13 × 9 = 81/117 and 8 × 13/9 × 13 = 104/117

Step 3

Add the Numerators

Now add the numerators (81 + 104 = 185) and keep the common denominator 117 unchanged.

81 + 104/117 = 185/117

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 185 and 117 is 1, confirming that 185/117 cannot be reduced further—it is already in its simplest irreducible form.

185/117

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (185) is greater than the denominator (117), divide 185 by 117: it goes in 1 whole time(s) with a remainder of 68, giving the mixed number 1 68/117.

185/117 = 168/117

Step 6

Decimal & Percentage Representation

Dividing the numerator 185 by denominator 117 produces a repeating decimal (approximately 1.581197, or 158.1197%).

185 ÷ 117 = 1.581197 (158.1197%)

Visual Representation

The diagram below illustrates 9/13 plus 8/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`185/117`
Mixed Number Form	`1 68/117`
Decimal Form	`1.581197`
Percentage	`158.1197%`

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Frequently Asked Questions

What is 9/13 plus 8/9 as a fraction?

9/13 + 8/9 in simplest fraction form is 185/117 (or 1 68/117 as a mixed number).

What is 9/13 plus 8/9 as a decimal?

9/13 + 8/9 converted to a decimal is 1.581197.

What is 9/13 plus 8/9 as a percentage?

9/13 + 8/9 expressed as a percentage is 158.1197%.

How do you write 9/13 plus 8/9 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 185/117 can be written as the mixed number 1 68/117.

Does 9/13 plus 8/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.581197...) because the denominator contains prime factors other than 2 and 5.