What is 3/9 plus 9/23? (Answer: 50/69)

Exact Answer

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Problem: What is 3/9 plus 9/23?
Formula / Expression: 3/9 + 9/23
Final Answer: 50/69
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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 3/9 by 23, and multiply the numerator and denominator of 9/23 by 9 so both fractions share the common base 207.
Working: 3 × 23/9 × 23 = 69/207 and 9 × 9/23 × 9 = 81/207

Step 3: Add the Numerators
Now add the numerators (69 + 81 = 150) and keep the common denominator 207 unchanged.
Working: 69 + 81/207 = 150/207

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 150 and 207, which is 3. Divide both the numerator and denominator by 3.
Working: 150 ÷ 3/207 ÷ 3 = 50/69

Step 5: Decimal & Percentage Representation
Dividing the numerator 50 by denominator 69 produces a repeating decimal (approximately 0.724638, or 72.4638%).
Working: 50 ÷ 69 = 0.724638 (72.4638%)

Key Values:
- Simplified Fraction: 50/69
- Mixed Number Form: 50/69
- Decimal Value: 0.724638
- Percentage: 72.4638%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-9-plus-9-23/
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3/9 + 9/23 = 50/69

Simplified Fraction

50/69

Mixed Number

Proper (50/69)

Decimal Value

0.724638

Percentage

72.4638%

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Step-by-Step Solution: 3/9 + 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 3/9 by 23, and multiply the numerator and denominator of 9/23 by 9 so both fractions share the common base 207.

3 × 23/9 × 23 = 69/207 and 9 × 9/23 × 9 = 81/207

Step 3

Add the Numerators

Now add the numerators (69 + 81 = 150) and keep the common denominator 207 unchanged.

69 + 81/207 = 150/207

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 150 and 207, which is 3. Divide both the numerator and denominator by 3.

150 ÷ 3/207 ÷ 3 = 50/69

Step 5

Decimal & Percentage Representation

Dividing the numerator 50 by denominator 69 produces a repeating decimal (approximately 0.724638, or 72.4638%).

50 ÷ 69 = 0.724638 (72.4638%)

Visual Representation

The diagram below illustrates 3/9 plus 9/23 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`50/69`
Mixed Number Form	`50/69`
Decimal Form	`0.724638`
Percentage	`72.4638%`

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Frequently Asked Questions

What is 3/9 plus 9/23 as a fraction?

3/9 + 9/23 in simplest fraction form is 50/69.

What is 3/9 plus 9/23 as a decimal?

3/9 + 9/23 converted to a decimal is 0.724638.

What is 3/9 plus 9/23 as a percentage?

3/9 + 9/23 expressed as a percentage is 72.4638%.

Does 3/9 plus 9/23 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.724638...) because the denominator contains prime factors other than 2 and 5.