What is 1/9 plus 9/23? (Answer: 104/207)

Exact Answer

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Problem: What is 1/9 plus 9/23?
Formula / Expression: 1/9 + 9/23
Final Answer: 104/207
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 207
Multiply the numerator and denominator of 1/9 by 23, and multiply the numerator and denominator of 9/23 by 9 so both fractions share the common base 207.
Working: 1 × 23/9 × 23 = 23/207 and 9 × 9/23 × 9 = 81/207

Step 3: Add the Numerators
Now add the numerators (23 + 81 = 104) and keep the common denominator 207 unchanged.
Working: 23 + 81/207 = 104/207

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 104 and 207 is 1, confirming that 104/207 cannot be reduced further—it is already in its simplest irreducible form.
Working: 104/207

Step 5: Decimal & Percentage Representation
Dividing the numerator 104 by denominator 207 produces a repeating decimal (approximately 0.502415, or 50.2415%).
Working: 104 ÷ 207 = 0.502415 (50.2415%)

Key Values:
- Simplified Fraction: 104/207
- Mixed Number Form: 104/207
- Decimal Value: 0.502415
- Percentage: 50.2415%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-9-plus-9-23/
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1/9 + 9/23 = 104/207

Simplified Fraction

104/207

Mixed Number

Proper (104/207)

Decimal Value

0.502415

Percentage

50.2415%

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Step-by-Step Solution: 1/9 + 9/23

Step 1

Find the Least Common Denominator (LCD)

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

LCD(9, 23) = 207

Step 2

Convert to Equivalent Fractions with Common Denominator 207

Multiply the numerator and denominator of 1/9 by 23, and multiply the numerator and denominator of 9/23 by 9 so both fractions share the common base 207.

1 × 23/9 × 23 = 23/207 and 9 × 9/23 × 9 = 81/207

Step 3

Add the Numerators

Now add the numerators (23 + 81 = 104) and keep the common denominator 207 unchanged.

23 + 81/207 = 104/207

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 104 and 207 is 1, confirming that 104/207 cannot be reduced further—it is already in its simplest irreducible form.

104/207

Step 5

Decimal & Percentage Representation

Dividing the numerator 104 by denominator 207 produces a repeating decimal (approximately 0.502415, or 50.2415%).

104 ÷ 207 = 0.502415 (50.2415%)

Visual Representation

The diagram below illustrates 1/9 plus 9/23 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`104/207`
Mixed Number Form	`104/207`
Decimal Form	`0.502415`
Percentage	`50.2415%`

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Frequently Asked Questions

What is 1/9 plus 9/23 as a fraction?

1/9 + 9/23 in simplest fraction form is 104/207.

What is 1/9 plus 9/23 as a decimal?

1/9 + 9/23 converted to a decimal is 0.502415.

What is 1/9 plus 9/23 as a percentage?

1/9 + 9/23 expressed as a percentage is 50.2415%.

Does 1/9 plus 9/23 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.502415...) because the denominator contains prime factors other than 2 and 5.