What is 3/8 plus 9/23? (Answer: 141/184)

Exact Answer

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Problem: What is 3/8 plus 9/23?
Formula / Expression: 3/8 + 9/23
Final Answer: 141/184
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 8 and 23 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 8 × 23 = 184.
Working: LCD(8, 23) = 184

Step 2: Convert to Equivalent Fractions with Common Denominator 184
Multiply the numerator and denominator of 3/8 by 23, and multiply the numerator and denominator of 9/23 by 8 so both fractions share the common base 184.
Working: 3 × 23/8 × 23 = 69/184 and 9 × 8/23 × 8 = 72/184

Step 3: Add the Numerators
Now add the numerators (69 + 72 = 141) and keep the common denominator 184 unchanged.
Working: 69 + 72/184 = 141/184

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 141 and 184 is 1, confirming that 141/184 cannot be reduced further—it is already in its simplest irreducible form.
Working: 141/184

Step 5: Decimal & Percentage Representation
Dividing the numerator 141 by denominator 184 produces a repeating decimal (approximately 0.766304, or 76.6304%).
Working: 141 ÷ 184 = 0.766304 (76.6304%)

Key Values:
- Simplified Fraction: 141/184
- Mixed Number Form: 141/184
- Decimal Value: 0.766304
- Percentage: 76.6304%

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Solved with FractionsCalc:
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3/8 + 9/23 = 141/184

Simplified Fraction

141/184

Mixed Number

Proper (141/184)

Decimal Value

0.766304

Percentage

76.6304%

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

Step 1

Find the Least Common Denominator (LCD)

The denominators 8 and 23 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 8 × 23 = 184.

LCD(8, 23) = 184

Step 2

Convert to Equivalent Fractions with Common Denominator 184

Multiply the numerator and denominator of 3/8 by 23, and multiply the numerator and denominator of 9/23 by 8 so both fractions share the common base 184.

3 × 23/8 × 23 = 69/184 and 9 × 8/23 × 8 = 72/184

Step 3

Add the Numerators

Now add the numerators (69 + 72 = 141) and keep the common denominator 184 unchanged.

69 + 72/184 = 141/184

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 141 and 184 is 1, confirming that 141/184 cannot be reduced further—it is already in its simplest irreducible form.

141/184

Step 5

Decimal & Percentage Representation

Dividing the numerator 141 by denominator 184 produces a repeating decimal (approximately 0.766304, or 76.6304%).

141 ÷ 184 = 0.766304 (76.6304%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`141/184`
Mixed Number Form	`141/184`
Decimal Form	`0.766304`
Percentage	`76.6304%`

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Frequently Asked Questions

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

3/8 + 9/23 in simplest fraction form is 141/184.

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

3/8 + 9/23 converted to a decimal is 0.766304.

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

3/8 + 9/23 expressed as a percentage is 76.6304%.

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

It results in a repeating decimal (approximately 0.766304...) because the denominator contains prime factors other than 2 and 5.