What is 1/9 plus 2/13? (Answer: 31/117)

Exact Answer

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Problem: What is 1/9 plus 2/13?
Formula / Expression: 1/9 + 2/13
Final Answer: 31/117
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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 2/13 by 9 so both fractions share the common base 117.
Working: 1 × 13/9 × 13 = 13/117 and 2 × 9/13 × 9 = 18/117

Step 3: Add the Numerators
Now add the numerators (13 + 18 = 31) and keep the common denominator 117 unchanged.
Working: 13 + 18/117 = 31/117

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 31 and 117 is 1, confirming that 31/117 cannot be reduced further—it is already in its simplest irreducible form.
Working: 31/117

Step 5: Decimal & Percentage Representation
Dividing the numerator 31 by denominator 117 produces a repeating decimal (approximately 0.264957, or 26.4957%).
Working: 31 ÷ 117 = 0.264957 (26.4957%)

Key Values:
- Simplified Fraction: 31/117
- Mixed Number Form: 31/117
- Decimal Value: 0.264957
- Percentage: 26.4957%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-9-plus-2-13/
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1/9 + 2/13 = 31/117

Simplified Fraction

31/117

Mixed Number

Proper (31/117)

Decimal Value

0.264957

Percentage

26.4957%

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

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 2/13 by 9 so both fractions share the common base 117.

1 × 13/9 × 13 = 13/117 and 2 × 9/13 × 9 = 18/117

Step 3

Add the Numerators

Now add the numerators (13 + 18 = 31) and keep the common denominator 117 unchanged.

13 + 18/117 = 31/117

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 31 and 117 is 1, confirming that 31/117 cannot be reduced further—it is already in its simplest irreducible form.

31/117

Step 5

Decimal & Percentage Representation

Dividing the numerator 31 by denominator 117 produces a repeating decimal (approximately 0.264957, or 26.4957%).

31 ÷ 117 = 0.264957 (26.4957%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`31/117`
Mixed Number Form	`31/117`
Decimal Form	`0.264957`
Percentage	`26.4957%`

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Frequently Asked Questions

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

1/9 + 2/13 in simplest fraction form is 31/117.

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

1/9 + 2/13 converted to a decimal is 0.264957.

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

1/9 + 2/13 expressed as a percentage is 26.4957%.

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

It results in a repeating decimal (approximately 0.264957...) because the denominator contains prime factors other than 2 and 5.