What is 4/23 plus 1/2? (Answer: 31/46)

Exact Answer

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Problem: What is 4/23 plus 1/2?
Formula / Expression: 4/23 + 1/2
Final Answer: 31/46
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 23 and 2 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 2 = 46.
Working: LCD(23, 2) = 46

Step 2: Convert to Equivalent Fractions with Common Denominator 46
Multiply the numerator and denominator of 4/23 by 2, and multiply the numerator and denominator of 1/2 by 23 so both fractions share the common base 46.
Working: 4 × 2/23 × 2 = 8/46 and 1 × 23/2 × 23 = 23/46

Step 3: Add the Numerators
Now add the numerators (8 + 23 = 31) and keep the common denominator 46 unchanged.
Working: 8 + 23/46 = 31/46

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 31 and 46 is 1, confirming that 31/46 cannot be reduced further—it is already in its simplest irreducible form.
Working: 31/46

Step 5: Decimal & Percentage Representation
Dividing the numerator 31 by denominator 46 produces a repeating decimal (approximately 0.673913, or 67.3913%).
Working: 31 ÷ 46 = 0.673913 (67.3913%)

Key Values:
- Simplified Fraction: 31/46
- Mixed Number Form: 31/46
- Decimal Value: 0.673913
- Percentage: 67.3913%

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Solved with FractionsCalc:
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4/23 + 1/2 = 31/46

Simplified Fraction

31/46

Mixed Number

Proper (31/46)

Decimal Value

0.673913

Percentage

67.3913%

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Step-by-Step Solution: 4/23 + 1/2

Step 1

Find the Least Common Denominator (LCD)

The denominators 23 and 2 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 2 = 46.

LCD(23, 2) = 46

Step 2

Convert to Equivalent Fractions with Common Denominator 46

Multiply the numerator and denominator of 4/23 by 2, and multiply the numerator and denominator of 1/2 by 23 so both fractions share the common base 46.

4 × 2/23 × 2 = 8/46 and 1 × 23/2 × 23 = 23/46

Step 3

Add the Numerators

Now add the numerators (8 + 23 = 31) and keep the common denominator 46 unchanged.

8 + 23/46 = 31/46

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 31 and 46 is 1, confirming that 31/46 cannot be reduced further—it is already in its simplest irreducible form.

31/46

Step 5

Decimal & Percentage Representation

Dividing the numerator 31 by denominator 46 produces a repeating decimal (approximately 0.673913, or 67.3913%).

31 ÷ 46 = 0.673913 (67.3913%)

Visual Representation

The diagram below illustrates 4/23 plus 1/2 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`31/46`
Mixed Number Form	`31/46`
Decimal Form	`0.673913`
Percentage	`67.3913%`

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Frequently Asked Questions

What is 4/23 plus 1/2 as a fraction?

4/23 + 1/2 in simplest fraction form is 31/46.

What is 4/23 plus 1/2 as a decimal?

4/23 + 1/2 converted to a decimal is 0.673913.

What is 4/23 plus 1/2 as a percentage?

4/23 + 1/2 expressed as a percentage is 67.3913%.

Does 4/23 plus 1/2 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.673913...) because the denominator contains prime factors other than 2 and 5.