What is 1/13 plus 2/9? (Answer: 35/117)

Exact Answer

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Problem: What is 1/13 plus 2/9?
Formula / Expression: 1/13 + 2/9
Final Answer: 35/117
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 117
Multiply the numerator and denominator of 1/13 by 9, and multiply the numerator and denominator of 2/9 by 13 so both fractions share the common base 117.
Working: 1 × 9/13 × 9 = 9/117 and 2 × 13/9 × 13 = 26/117

Step 3: Add the Numerators
Now add the numerators (9 + 26 = 35) and keep the common denominator 117 unchanged.
Working: 9 + 26/117 = 35/117

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 35 and 117 is 1, confirming that 35/117 cannot be reduced further—it is already in its simplest irreducible form.
Working: 35/117

Step 5: Decimal & Percentage Representation
Dividing the numerator 35 by denominator 117 produces a repeating decimal (approximately 0.299145, or 29.9145%).
Working: 35 ÷ 117 = 0.299145 (29.9145%)

Key Values:
- Simplified Fraction: 35/117
- Mixed Number Form: 35/117
- Decimal Value: 0.299145
- Percentage: 29.9145%

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Solved with FractionsCalc:
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1/13 + 2/9 = 35/117

Simplified Fraction

35/117

Mixed Number

Proper (35/117)

Decimal Value

0.299145

Percentage

29.9145%

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

Step 1

Find the Least Common Denominator (LCD)

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

LCD(13, 9) = 117

Step 2

Convert to Equivalent Fractions with Common Denominator 117

Multiply the numerator and denominator of 1/13 by 9, and multiply the numerator and denominator of 2/9 by 13 so both fractions share the common base 117.

1 × 9/13 × 9 = 9/117 and 2 × 13/9 × 13 = 26/117

Step 3

Add the Numerators

Now add the numerators (9 + 26 = 35) and keep the common denominator 117 unchanged.

9 + 26/117 = 35/117

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 35 and 117 is 1, confirming that 35/117 cannot be reduced further—it is already in its simplest irreducible form.

35/117

Step 5

Decimal & Percentage Representation

Dividing the numerator 35 by denominator 117 produces a repeating decimal (approximately 0.299145, or 29.9145%).

35 ÷ 117 = 0.299145 (29.9145%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`35/117`
Mixed Number Form	`35/117`
Decimal Form	`0.299145`
Percentage	`29.9145%`

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Frequently Asked Questions

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

1/13 + 2/9 in simplest fraction form is 35/117.

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

1/13 + 2/9 converted to a decimal is 0.299145.

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

1/13 + 2/9 expressed as a percentage is 29.9145%.

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

It results in a repeating decimal (approximately 0.299145...) because the denominator contains prime factors other than 2 and 5.