What is 5/13 plus 1/2? (Answer: 23/26)

Exact Answer

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Problem: What is 5/13 plus 1/2?
Formula / Expression: 5/13 + 1/2
Final Answer: 23/26
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 13 and 2 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 2 = 26.
Working: LCD(13, 2) = 26

Step 2: Convert to Equivalent Fractions with Common Denominator 26
Multiply the numerator and denominator of 5/13 by 2, and multiply the numerator and denominator of 1/2 by 13 so both fractions share the common base 26.
Working: 5 × 2/13 × 2 = 10/26 and 1 × 13/2 × 13 = 13/26

Step 3: Add the Numerators
Now add the numerators (10 + 13 = 23) and keep the common denominator 26 unchanged.
Working: 10 + 13/26 = 23/26

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 23 and 26 is 1, confirming that 23/26 cannot be reduced further—it is already in its simplest irreducible form.
Working: 23/26

Step 5: Decimal & Percentage Representation
Dividing the numerator 23 by denominator 26 produces a repeating decimal (approximately 0.884615, or 88.4615%).
Working: 23 ÷ 26 = 0.884615 (88.4615%)

Key Values:
- Simplified Fraction: 23/26
- Mixed Number Form: 23/26
- Decimal Value: 0.884615
- Percentage: 88.4615%

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Solved with FractionsCalc:
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5/13 + 1/2 = 23/26

Simplified Fraction

23/26

Mixed Number

Proper (23/26)

Decimal Value

0.884615

Percentage

88.4615%

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Step-by-Step Solution: 5/13 + 1/2

Step 1

Find the Least Common Denominator (LCD)

The denominators 13 and 2 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 2 = 26.

LCD(13, 2) = 26

Step 2

Convert to Equivalent Fractions with Common Denominator 26

Multiply the numerator and denominator of 5/13 by 2, and multiply the numerator and denominator of 1/2 by 13 so both fractions share the common base 26.

5 × 2/13 × 2 = 10/26 and 1 × 13/2 × 13 = 13/26

Step 3

Add the Numerators

Now add the numerators (10 + 13 = 23) and keep the common denominator 26 unchanged.

10 + 13/26 = 23/26

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 23 and 26 is 1, confirming that 23/26 cannot be reduced further—it is already in its simplest irreducible form.

23/26

Step 5

Decimal & Percentage Representation

Dividing the numerator 23 by denominator 26 produces a repeating decimal (approximately 0.884615, or 88.4615%).

23 ÷ 26 = 0.884615 (88.4615%)

Visual Representation

The diagram below illustrates 5/13 plus 1/2 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`23/26`
Mixed Number Form	`23/26`
Decimal Form	`0.884615`
Percentage	`88.4615%`

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Frequently Asked Questions

What is 5/13 plus 1/2 as a fraction?

5/13 + 1/2 in simplest fraction form is 23/26.

What is 5/13 plus 1/2 as a decimal?

5/13 + 1/2 converted to a decimal is 0.884615.

What is 5/13 plus 1/2 as a percentage?

5/13 + 1/2 expressed as a percentage is 88.4615%.

Does 5/13 plus 1/2 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.884615...) because the denominator contains prime factors other than 2 and 5.