What is 5/13 plus 10/13? (Answer: 15/13)

Exact Answer

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Problem: What is 5/13 plus 10/13?
Formula / Expression: 5/13 + 10/13
Final Answer: 1 2/13 (15/13)
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Step-by-Step Solution:

Step 1: Check the Denominators (Like Fractions)
Both fractions already share the identical denominator (13). Because these are like fractions, no conversion to a common denominator is required—we directly add their numerators while keeping the denominator 13.
Working: 5/13 + 10/13

Step 2: Add the Numerators
Now add the numerators (5 + 10 = 15) and keep the common denominator 13 unchanged.
Working: 5 + 10/13 = 15/13

Step 3: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 15 and 13 is 1, confirming that 15/13 cannot be reduced further—it is already in its simplest irreducible form.
Working: 15/13

Step 4: Convert Improper Fraction to a Mixed Number
Since the numerator (15) is greater than the denominator (13), divide 15 by 13: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/13.
Working: 15/13 = 1 2/13

Step 5: Decimal & Percentage Representation
Dividing the numerator 15 by denominator 13 produces a repeating decimal (approximately 1.153846, or 115.3846%).
Working: 15 ÷ 13 = 1.153846 (115.3846%)

Key Values:
- Simplified Fraction: 15/13
- Mixed Number Form: 1 2/13
- Decimal Value: 1.153846
- Percentage: 115.3846%

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Solved with FractionsCalc:
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5/13 + 10/13 = 15/13

Simplified Fraction

15/13

Mixed Number

1 2/13

Decimal Value

1.153846

Percentage

115.3846%

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Step-by-Step Solution: 5/13 + 10/13

Step 1

Check the Denominators (Like Fractions)

Both fractions already share the identical denominator (13). Because these are like fractions, no conversion to a common denominator is required—we directly add their numerators while keeping the denominator 13.

5/13 + 10/13

Step 2

Add the Numerators

Now add the numerators (5 + 10 = 15) and keep the common denominator 13 unchanged.

5 + 10/13 = 15/13

Step 3

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 15 and 13 is 1, confirming that 15/13 cannot be reduced further—it is already in its simplest irreducible form.

15/13

Step 4

Convert Improper Fraction to a Mixed Number

Since the numerator (15) is greater than the denominator (13), divide 15 by 13: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/13.

15/13 = 12/13

Step 5

Decimal & Percentage Representation

Dividing the numerator 15 by denominator 13 produces a repeating decimal (approximately 1.153846, or 115.3846%).

15 ÷ 13 = 1.153846 (115.3846%)

Visual Representation

The diagram below illustrates 5/13 plus 10/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`15/13`
Mixed Number Form	`1 2/13`
Decimal Form	`1.153846`
Percentage	`115.3846%`

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Frequently Asked Questions

What is 5/13 plus 10/13 as a fraction?

5/13 + 10/13 in simplest fraction form is 15/13 (or 1 2/13 as a mixed number).

What is 5/13 plus 10/13 as a decimal?

5/13 + 10/13 converted to a decimal is 1.153846.

What is 5/13 plus 10/13 as a percentage?

5/13 + 10/13 expressed as a percentage is 115.3846%.

How do you write 5/13 plus 10/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 15/13 can be written as the mixed number 1 2/13.

Does 5/13 plus 10/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.153846...) because the denominator contains prime factors other than 2 and 5.