What is 1/9 plus 6/13? (Answer: 67/117)

Exact Answer

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Problem: What is 1/9 plus 6/13?
Formula / Expression: 1/9 + 6/13
Final Answer: 67/117
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 13 = 117.
Working: LCD(9, 13) = 117

Step 2: Convert to Equivalent Fractions with Common Denominator 117
Multiply the numerator and denominator of 1/9 by 13, and multiply the numerator and denominator of 6/13 by 9 so both fractions share the common base 117.
Working: 1 × 13/9 × 13 = 13/117 and 6 × 9/13 × 9 = 54/117

Step 3: Add the Numerators
Now add the numerators (13 + 54 = 67) and keep the common denominator 117 unchanged.
Working: 13 + 54/117 = 67/117

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 67 and 117 is 1, confirming that 67/117 cannot be reduced further—it is already in its simplest irreducible form.
Working: 67/117

Step 5: Decimal & Percentage Representation
Dividing the numerator 67 by denominator 117 produces a repeating decimal (approximately 0.57265, or 57.265%).
Working: 67 ÷ 117 = 0.57265 (57.265%)

Key Values:
- Simplified Fraction: 67/117
- Mixed Number Form: 67/117
- Decimal Value: 0.57265
- Percentage: 57.265%

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Solved with FractionsCalc:
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1/9 + 6/13 = 67/117

Simplified Fraction

67/117

Mixed Number

Proper (67/117)

Decimal Value

0.57265

Percentage

57.265%

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Step-by-Step Solution: 1/9 + 6/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 13 = 117.

LCD(9, 13) = 117

Step 2

Convert to Equivalent Fractions with Common Denominator 117

Multiply the numerator and denominator of 1/9 by 13, and multiply the numerator and denominator of 6/13 by 9 so both fractions share the common base 117.

1 × 13/9 × 13 = 13/117 and 6 × 9/13 × 9 = 54/117

Step 3

Add the Numerators

Now add the numerators (13 + 54 = 67) and keep the common denominator 117 unchanged.

13 + 54/117 = 67/117

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 67 and 117 is 1, confirming that 67/117 cannot be reduced further—it is already in its simplest irreducible form.

67/117

Step 5

Decimal & Percentage Representation

Dividing the numerator 67 by denominator 117 produces a repeating decimal (approximately 0.57265, or 57.265%).

67 ÷ 117 = 0.57265 (57.265%)

Visual Representation

The diagram below illustrates 1/9 plus 6/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`67/117`
Mixed Number Form	`67/117`
Decimal Form	`0.57265`
Percentage	`57.265%`

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Frequently Asked Questions

What is 1/9 plus 6/13 as a fraction?

1/9 + 6/13 in simplest fraction form is 67/117.

What is 1/9 plus 6/13 as a decimal?

1/9 + 6/13 converted to a decimal is 0.57265.

What is 1/9 plus 6/13 as a percentage?

1/9 + 6/13 expressed as a percentage is 57.265%.

Does 1/9 plus 6/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.57265...) because the denominator contains prime factors other than 2 and 5.