What is 1/5 plus 11/13? (Answer: 68/65)

Exact Answer

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Problem: What is 1/5 plus 11/13?
Formula / Expression: 1/5 + 11/13
Final Answer: 1 3/65 (68/65)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 5 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 13 = 65.
Working: LCD(5, 13) = 65

Step 2: Convert to Equivalent Fractions with Common Denominator 65
Multiply the numerator and denominator of 1/5 by 13, and multiply the numerator and denominator of 11/13 by 5 so both fractions share the common base 65.
Working: 1 × 13/5 × 13 = 13/65 and 11 × 5/13 × 5 = 55/65

Step 3: Add the Numerators
Now add the numerators (13 + 55 = 68) and keep the common denominator 65 unchanged.
Working: 13 + 55/65 = 68/65

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 68 and 65 is 1, confirming that 68/65 cannot be reduced further—it is already in its simplest irreducible form.
Working: 68/65

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (68) is greater than the denominator (65), divide 68 by 65: it goes in 1 whole time(s) with a remainder of 3, giving the mixed number 1 3/65.
Working: 68/65 = 1 3/65

Step 6: Decimal & Percentage Representation
Dividing the numerator 68 by denominator 65 produces a repeating decimal (approximately 1.046154, or 104.6154%).
Working: 68 ÷ 65 = 1.046154 (104.6154%)

Key Values:
- Simplified Fraction: 68/65
- Mixed Number Form: 1 3/65
- Decimal Value: 1.046154
- Percentage: 104.6154%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-5-plus-11-13/
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1/5 + 11/13 = 68/65

Simplified Fraction

68/65

Mixed Number

1 3/65

Decimal Value

1.046154

Percentage

104.6154%

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Step-by-Step Solution: 1/5 + 11/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 5 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 13 = 65.

LCD(5, 13) = 65

Step 2

Convert to Equivalent Fractions with Common Denominator 65

Multiply the numerator and denominator of 1/5 by 13, and multiply the numerator and denominator of 11/13 by 5 so both fractions share the common base 65.

1 × 13/5 × 13 = 13/65 and 11 × 5/13 × 5 = 55/65

Step 3

Add the Numerators

Now add the numerators (13 + 55 = 68) and keep the common denominator 65 unchanged.

13 + 55/65 = 68/65

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 68 and 65 is 1, confirming that 68/65 cannot be reduced further—it is already in its simplest irreducible form.

68/65

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (68) is greater than the denominator (65), divide 68 by 65: it goes in 1 whole time(s) with a remainder of 3, giving the mixed number 1 3/65.

68/65 = 13/65

Step 6

Decimal & Percentage Representation

Dividing the numerator 68 by denominator 65 produces a repeating decimal (approximately 1.046154, or 104.6154%).

68 ÷ 65 = 1.046154 (104.6154%)

Visual Representation

The diagram below illustrates 1/5 plus 11/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`68/65`
Mixed Number Form	`1 3/65`
Decimal Form	`1.046154`
Percentage	`104.6154%`

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Frequently Asked Questions

What is 1/5 plus 11/13 as a fraction?

1/5 + 11/13 in simplest fraction form is 68/65 (or 1 3/65 as a mixed number).

What is 1/5 plus 11/13 as a decimal?

1/5 + 11/13 converted to a decimal is 1.046154.

What is 1/5 plus 11/13 as a percentage?

1/5 + 11/13 expressed as a percentage is 104.6154%.

How do you write 1/5 plus 11/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 68/65 can be written as the mixed number 1 3/65.

Does 1/5 plus 11/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.046154...) because the denominator contains prime factors other than 2 and 5.