What is 4/13 plus 1/2? (Answer: 21/26)

Exact Answer

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Problem: What is 4/13 plus 1/2?
Formula / Expression: 4/13 + 1/2
Final Answer: 21/26
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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 4/13 by 2, and multiply the numerator and denominator of 1/2 by 13 so both fractions share the common base 26.
Working: 4 × 2/13 × 2 = 8/26 and 1 × 13/2 × 13 = 13/26

Step 3: Add the Numerators
Now add the numerators (8 + 13 = 21) and keep the common denominator 26 unchanged.
Working: 8 + 13/26 = 21/26

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 21 and 26 is 1, confirming that 21/26 cannot be reduced further—it is already in its simplest irreducible form.
Working: 21/26

Step 5: Decimal & Percentage Representation
Dividing the numerator 21 by denominator 26 produces a repeating decimal (approximately 0.807692, or 80.7692%).
Working: 21 ÷ 26 = 0.807692 (80.7692%)

Key Values:
- Simplified Fraction: 21/26
- Mixed Number Form: 21/26
- Decimal Value: 0.807692
- Percentage: 80.7692%

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Solved with FractionsCalc:
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4/13 + 1/2 = 21/26

Simplified Fraction

21/26

Mixed Number

Proper (21/26)

Decimal Value

0.807692

Percentage

80.7692%

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Step-by-Step Solution: 4/13 + 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 4/13 by 2, and multiply the numerator and denominator of 1/2 by 13 so both fractions share the common base 26.

4 × 2/13 × 2 = 8/26 and 1 × 13/2 × 13 = 13/26

Step 3

Add the Numerators

Now add the numerators (8 + 13 = 21) and keep the common denominator 26 unchanged.

8 + 13/26 = 21/26

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 21 and 26 is 1, confirming that 21/26 cannot be reduced further—it is already in its simplest irreducible form.

21/26

Step 5

Decimal & Percentage Representation

Dividing the numerator 21 by denominator 26 produces a repeating decimal (approximately 0.807692, or 80.7692%).

21 ÷ 26 = 0.807692 (80.7692%)

Visual Representation

The diagram below illustrates 4/13 plus 1/2 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`21/26`
Mixed Number Form	`21/26`
Decimal Form	`0.807692`
Percentage	`80.7692%`

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Frequently Asked Questions

What is 4/13 plus 1/2 as a fraction?

4/13 + 1/2 in simplest fraction form is 21/26.

What is 4/13 plus 1/2 as a decimal?

4/13 + 1/2 converted to a decimal is 0.807692.

What is 4/13 plus 1/2 as a percentage?

4/13 + 1/2 expressed as a percentage is 80.7692%.

Does 4/13 plus 1/2 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.807692...) because the denominator contains prime factors other than 2 and 5.