What is 9/23 plus 5/9? (Answer: 196/207)

Exact Answer

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Problem: What is 9/23 plus 5/9?
Formula / Expression: 9/23 + 5/9
Final Answer: 196/207
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 23 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 9 = 207.
Working: LCD(23, 9) = 207

Step 2: Convert to Equivalent Fractions with Common Denominator 207
Multiply the numerator and denominator of 9/23 by 9, and multiply the numerator and denominator of 5/9 by 23 so both fractions share the common base 207.
Working: 9 × 9/23 × 9 = 81/207 and 5 × 23/9 × 23 = 115/207

Step 3: Add the Numerators
Now add the numerators (81 + 115 = 196) and keep the common denominator 207 unchanged.
Working: 81 + 115/207 = 196/207

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 196 and 207 is 1, confirming that 196/207 cannot be reduced further—it is already in its simplest irreducible form.
Working: 196/207

Step 5: Decimal & Percentage Representation
Dividing the numerator 196 by denominator 207 produces a repeating decimal (approximately 0.94686, or 94.686%).
Working: 196 ÷ 207 = 0.94686 (94.686%)

Key Values:
- Simplified Fraction: 196/207
- Mixed Number Form: 196/207
- Decimal Value: 0.94686
- Percentage: 94.686%

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Solved with FractionsCalc:
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9/23 + 5/9 = 196/207

Simplified Fraction

196/207

Mixed Number

Proper (196/207)

Decimal Value

0.94686

Percentage

94.686%

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Step-by-Step Solution: 9/23 + 5/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 23 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 9 = 207.

LCD(23, 9) = 207

Step 2

Convert to Equivalent Fractions with Common Denominator 207

Multiply the numerator and denominator of 9/23 by 9, and multiply the numerator and denominator of 5/9 by 23 so both fractions share the common base 207.

9 × 9/23 × 9 = 81/207 and 5 × 23/9 × 23 = 115/207

Step 3

Add the Numerators

Now add the numerators (81 + 115 = 196) and keep the common denominator 207 unchanged.

81 + 115/207 = 196/207

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 196 and 207 is 1, confirming that 196/207 cannot be reduced further—it is already in its simplest irreducible form.

196/207

Step 5

Decimal & Percentage Representation

Dividing the numerator 196 by denominator 207 produces a repeating decimal (approximately 0.94686, or 94.686%).

196 ÷ 207 = 0.94686 (94.686%)

Visual Representation

The diagram below illustrates 9/23 plus 5/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`196/207`
Mixed Number Form	`196/207`
Decimal Form	`0.94686`
Percentage	`94.686%`

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Frequently Asked Questions

What is 9/23 plus 5/9 as a fraction?

9/23 + 5/9 in simplest fraction form is 196/207.

What is 9/23 plus 5/9 as a decimal?

9/23 + 5/9 converted to a decimal is 0.94686.

What is 9/23 plus 5/9 as a percentage?

9/23 + 5/9 expressed as a percentage is 94.686%.

Does 9/23 plus 5/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.94686...) because the denominator contains prime factors other than 2 and 5.