What is 5/23 plus 3/9? (Answer: 38/69)

Exact Answer

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Problem: What is 5/23 plus 3/9?
Formula / Expression: 5/23 + 3/9
Final Answer: 38/69
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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 5/23 by 9, and multiply the numerator and denominator of 3/9 by 23 so both fractions share the common base 207.
Working: 5 × 9/23 × 9 = 45/207 and 3 × 23/9 × 23 = 69/207

Step 3: Add the Numerators
Now add the numerators (45 + 69 = 114) and keep the common denominator 207 unchanged.
Working: 45 + 69/207 = 114/207

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 114 and 207, which is 3. Divide both the numerator and denominator by 3.
Working: 114 ÷ 3/207 ÷ 3 = 38/69

Step 5: Decimal & Percentage Representation
Dividing the numerator 38 by denominator 69 produces a repeating decimal (approximately 0.550725, or 55.0725%).
Working: 38 ÷ 69 = 0.550725 (55.0725%)

Key Values:
- Simplified Fraction: 38/69
- Mixed Number Form: 38/69
- Decimal Value: 0.550725
- Percentage: 55.0725%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-23-plus-3-9/
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5/23 + 3/9 = 38/69

Simplified Fraction

38/69

Mixed Number

Proper (38/69)

Decimal Value

0.550725

Percentage

55.0725%

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Step-by-Step Solution: 5/23 + 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 5/23 by 9, and multiply the numerator and denominator of 3/9 by 23 so both fractions share the common base 207.

5 × 9/23 × 9 = 45/207 and 3 × 23/9 × 23 = 69/207

Step 3

Add the Numerators

Now add the numerators (45 + 69 = 114) and keep the common denominator 207 unchanged.

45 + 69/207 = 114/207

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 114 and 207, which is 3. Divide both the numerator and denominator by 3.

114 ÷ 3/207 ÷ 3 = 38/69

Step 5

Decimal & Percentage Representation

Dividing the numerator 38 by denominator 69 produces a repeating decimal (approximately 0.550725, or 55.0725%).

38 ÷ 69 = 0.550725 (55.0725%)

Visual Representation

The diagram below illustrates 5/23 plus 3/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`38/69`
Mixed Number Form	`38/69`
Decimal Form	`0.550725`
Percentage	`55.0725%`

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Frequently Asked Questions

What is 5/23 plus 3/9 as a fraction?

5/23 + 3/9 in simplest fraction form is 38/69.

What is 5/23 plus 3/9 as a decimal?

5/23 + 3/9 converted to a decimal is 0.550725.

What is 5/23 plus 3/9 as a percentage?

5/23 + 3/9 expressed as a percentage is 55.0725%.

Does 5/23 plus 3/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.550725...) because the denominator contains prime factors other than 2 and 5.