What is 4/23 plus 3/8? (Answer: 101/184)

Exact Answer

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Problem: What is 4/23 plus 3/8?
Formula / Expression: 4/23 + 3/8
Final Answer: 101/184
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 184
Multiply the numerator and denominator of 4/23 by 8, and multiply the numerator and denominator of 3/8 by 23 so both fractions share the common base 184.
Working: 4 × 8/23 × 8 = 32/184 and 3 × 23/8 × 23 = 69/184

Step 3: Add the Numerators
Now add the numerators (32 + 69 = 101) and keep the common denominator 184 unchanged.
Working: 32 + 69/184 = 101/184

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 101 and 184 is 1, confirming that 101/184 cannot be reduced further—it is already in its simplest irreducible form.
Working: 101/184

Step 5: Decimal & Percentage Representation
Dividing the numerator 101 by denominator 184 produces a repeating decimal (approximately 0.548913, or 54.8913%).
Working: 101 ÷ 184 = 0.548913 (54.8913%)

Key Values:
- Simplified Fraction: 101/184
- Mixed Number Form: 101/184
- Decimal Value: 0.548913
- Percentage: 54.8913%

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4/23 + 3/8 = 101/184

Simplified Fraction

101/184

Mixed Number

Proper (101/184)

Decimal Value

0.548913

Percentage

54.8913%

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Step-by-Step Solution: 4/23 + 3/8

Step 1

Find the Least Common Denominator (LCD)

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

LCD(23, 8) = 184

Step 2

Convert to Equivalent Fractions with Common Denominator 184

Multiply the numerator and denominator of 4/23 by 8, and multiply the numerator and denominator of 3/8 by 23 so both fractions share the common base 184.

4 × 8/23 × 8 = 32/184 and 3 × 23/8 × 23 = 69/184

Step 3

Add the Numerators

Now add the numerators (32 + 69 = 101) and keep the common denominator 184 unchanged.

32 + 69/184 = 101/184

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 101 and 184 is 1, confirming that 101/184 cannot be reduced further—it is already in its simplest irreducible form.

101/184

Step 5

Decimal & Percentage Representation

Dividing the numerator 101 by denominator 184 produces a repeating decimal (approximately 0.548913, or 54.8913%).

101 ÷ 184 = 0.548913 (54.8913%)

Visual Representation

The diagram below illustrates 4/23 plus 3/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`101/184`
Mixed Number Form	`101/184`
Decimal Form	`0.548913`
Percentage	`54.8913%`

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Frequently Asked Questions

What is 4/23 plus 3/8 as a fraction?

4/23 + 3/8 in simplest fraction form is 101/184.

What is 4/23 plus 3/8 as a decimal?

4/23 + 3/8 converted to a decimal is 0.548913.

What is 4/23 plus 3/8 as a percentage?

4/23 + 3/8 expressed as a percentage is 54.8913%.

Does 4/23 plus 3/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.548913...) because the denominator contains prime factors other than 2 and 5.