What is 3/9 plus 8/23? (Answer: 47/69)

Exact Answer

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Problem: What is 3/9 plus 8/23?
Formula / Expression: 3/9 + 8/23
Final Answer: 47/69
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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 8/23 by 9 so both fractions share the common base 207.
Working: 3 × 23/9 × 23 = 69/207 and 8 × 9/23 × 9 = 72/207

Step 3: Add the Numerators
Now add the numerators (69 + 72 = 141) and keep the common denominator 207 unchanged.
Working: 69 + 72/207 = 141/207

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 141 and 207, which is 3. Divide both the numerator and denominator by 3.
Working: 141 ÷ 3/207 ÷ 3 = 47/69

Step 5: Decimal & Percentage Representation
Dividing the numerator 47 by denominator 69 produces a repeating decimal (approximately 0.681159, or 68.1159%).
Working: 47 ÷ 69 = 0.681159 (68.1159%)

Key Values:
- Simplified Fraction: 47/69
- Mixed Number Form: 47/69
- Decimal Value: 0.681159
- Percentage: 68.1159%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-9-plus-8-23/
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3/9 + 8/23 = 47/69

Simplified Fraction

47/69

Mixed Number

Proper (47/69)

Decimal Value

0.681159

Percentage

68.1159%

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Step-by-Step Solution: 3/9 + 8/23

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 8/23 by 9 so both fractions share the common base 207.

3 × 23/9 × 23 = 69/207 and 8 × 9/23 × 9 = 72/207

Step 3

Add the Numerators

Now add the numerators (69 + 72 = 141) and keep the common denominator 207 unchanged.

69 + 72/207 = 141/207

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 141 and 207, which is 3. Divide both the numerator and denominator by 3.

141 ÷ 3/207 ÷ 3 = 47/69

Step 5

Decimal & Percentage Representation

Dividing the numerator 47 by denominator 69 produces a repeating decimal (approximately 0.681159, or 68.1159%).

47 ÷ 69 = 0.681159 (68.1159%)

Visual Representation

The diagram below illustrates 3/9 plus 8/23 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`47/69`
Mixed Number Form	`47/69`
Decimal Form	`0.681159`
Percentage	`68.1159%`

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Frequently Asked Questions

What is 3/9 plus 8/23 as a fraction?

3/9 + 8/23 in simplest fraction form is 47/69.

What is 3/9 plus 8/23 as a decimal?

3/9 + 8/23 converted to a decimal is 0.681159.

What is 3/9 plus 8/23 as a percentage?

3/9 + 8/23 expressed as a percentage is 68.1159%.

Does 3/9 plus 8/23 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.681159...) because the denominator contains prime factors other than 2 and 5.