What is 3/23 plus 3/9? (Answer: 32/69)

Exact Answer

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Problem: What is 3/23 plus 3/9?
Formula / Expression: 3/23 + 3/9
Final Answer: 32/69
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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 3/23 by 9, and multiply the numerator and denominator of 3/9 by 23 so both fractions share the common base 207.
Working: 3 × 9/23 × 9 = 27/207 and 3 × 23/9 × 23 = 69/207

Step 3: Add the Numerators
Now add the numerators (27 + 69 = 96) and keep the common denominator 207 unchanged.
Working: 27 + 69/207 = 96/207

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 96 and 207, which is 3. Divide both the numerator and denominator by 3.
Working: 96 ÷ 3/207 ÷ 3 = 32/69

Step 5: Decimal & Percentage Representation
Dividing the numerator 32 by denominator 69 produces a repeating decimal (approximately 0.463768, or 46.3768%).
Working: 32 ÷ 69 = 0.463768 (46.3768%)

Key Values:
- Simplified Fraction: 32/69
- Mixed Number Form: 32/69
- Decimal Value: 0.463768
- Percentage: 46.3768%

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Solved with FractionsCalc:
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3/23 + 3/9 = 32/69

Simplified Fraction

32/69

Mixed Number

Proper (32/69)

Decimal Value

0.463768

Percentage

46.3768%

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Step-by-Step Solution: 3/23 + 3/9

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

3 × 9/23 × 9 = 27/207 and 3 × 23/9 × 23 = 69/207

Step 3

Add the Numerators

Now add the numerators (27 + 69 = 96) and keep the common denominator 207 unchanged.

27 + 69/207 = 96/207

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 96 and 207, which is 3. Divide both the numerator and denominator by 3.

96 ÷ 3/207 ÷ 3 = 32/69

Step 5

Decimal & Percentage Representation

Dividing the numerator 32 by denominator 69 produces a repeating decimal (approximately 0.463768, or 46.3768%).

32 ÷ 69 = 0.463768 (46.3768%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`32/69`
Mixed Number Form	`32/69`
Decimal Form	`0.463768`
Percentage	`46.3768%`

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Frequently Asked Questions

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

3/23 + 3/9 in simplest fraction form is 32/69.

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

3/23 + 3/9 converted to a decimal is 0.463768.

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

3/23 + 3/9 expressed as a percentage is 46.3768%.

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

It results in a repeating decimal (approximately 0.463768...) because the denominator contains prime factors other than 2 and 5.