What is 1/2 plus 9/13? (Answer: 31/26)

Exact Answer

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Problem: What is 1/2 plus 9/13?
Formula / Expression: 1/2 + 9/13
Final Answer: 1 5/26 (31/26)
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 26
Multiply the numerator and denominator of 1/2 by 13, and multiply the numerator and denominator of 9/13 by 2 so both fractions share the common base 26.
Working: 1 × 13/2 × 13 = 13/26 and 9 × 2/13 × 2 = 18/26

Step 3: Add the Numerators
Now add the numerators (13 + 18 = 31) and keep the common denominator 26 unchanged.
Working: 13 + 18/26 = 31/26

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 31 and 26 is 1, confirming that 31/26 cannot be reduced further—it is already in its simplest irreducible form.
Working: 31/26

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (31) is greater than the denominator (26), divide 31 by 26: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/26.
Working: 31/26 = 1 5/26

Step 6: Decimal & Percentage Representation
Dividing the numerator 31 by denominator 26 produces a repeating decimal (approximately 1.192308, or 119.2308%).
Working: 31 ÷ 26 = 1.192308 (119.2308%)

Key Values:
- Simplified Fraction: 31/26
- Mixed Number Form: 1 5/26
- Decimal Value: 1.192308
- Percentage: 119.2308%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-2-plus-9-13/
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1/2 + 9/13 = 31/26

Simplified Fraction

31/26

Mixed Number

1 5/26

Decimal Value

1.192308

Percentage

119.2308%

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Step-by-Step Solution: 1/2 + 9/13

Step 1

Find the Least Common Denominator (LCD)

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

LCD(2, 13) = 26

Step 2

Convert to Equivalent Fractions with Common Denominator 26

Multiply the numerator and denominator of 1/2 by 13, and multiply the numerator and denominator of 9/13 by 2 so both fractions share the common base 26.

1 × 13/2 × 13 = 13/26 and 9 × 2/13 × 2 = 18/26

Step 3

Add the Numerators

Now add the numerators (13 + 18 = 31) and keep the common denominator 26 unchanged.

13 + 18/26 = 31/26

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 31 and 26 is 1, confirming that 31/26 cannot be reduced further—it is already in its simplest irreducible form.

31/26

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (31) is greater than the denominator (26), divide 31 by 26: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/26.

31/26 = 15/26

Step 6

Decimal & Percentage Representation

Dividing the numerator 31 by denominator 26 produces a repeating decimal (approximately 1.192308, or 119.2308%).

31 ÷ 26 = 1.192308 (119.2308%)

Visual Representation

The diagram below illustrates 1/2 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`31/26`
Mixed Number Form	`1 5/26`
Decimal Form	`1.192308`
Percentage	`119.2308%`

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Frequently Asked Questions

What is 1/2 plus 9/13 as a fraction?

1/2 + 9/13 in simplest fraction form is 31/26 (or 1 5/26 as a mixed number).

What is 1/2 plus 9/13 as a decimal?

1/2 + 9/13 converted to a decimal is 1.192308.

What is 1/2 plus 9/13 as a percentage?

1/2 + 9/13 expressed as a percentage is 119.2308%.

How do you write 1/2 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 31/26 can be written as the mixed number 1 5/26.

Does 1/2 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.192308...) because the denominator contains prime factors other than 2 and 5.