What is 2/13 plus 2/9? (Answer: 44/117)

Exact Answer

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Problem: What is 2/13 plus 2/9?
Formula / Expression: 2/13 + 2/9
Final Answer: 44/117
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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 2/13 by 9, and multiply the numerator and denominator of 2/9 by 13 so both fractions share the common base 117.
Working: 2 × 9/13 × 9 = 18/117 and 2 × 13/9 × 13 = 26/117

Step 3: Add the Numerators
Now add the numerators (18 + 26 = 44) and keep the common denominator 117 unchanged.
Working: 18 + 26/117 = 44/117

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 44 and 117 is 1, confirming that 44/117 cannot be reduced further—it is already in its simplest irreducible form.
Working: 44/117

Step 5: Decimal & Percentage Representation
Dividing the numerator 44 by denominator 117 produces a repeating decimal (approximately 0.376068, or 37.6068%).
Working: 44 ÷ 117 = 0.376068 (37.6068%)

Key Values:
- Simplified Fraction: 44/117
- Mixed Number Form: 44/117
- Decimal Value: 0.376068
- Percentage: 37.6068%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-13-plus-2-9/
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2/13 + 2/9 = 44/117

Simplified Fraction

44/117

Mixed Number

Proper (44/117)

Decimal Value

0.376068

Percentage

37.6068%

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Step-by-Step Solution: 2/13 + 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 2/13 by 9, and multiply the numerator and denominator of 2/9 by 13 so both fractions share the common base 117.

2 × 9/13 × 9 = 18/117 and 2 × 13/9 × 13 = 26/117

Step 3

Add the Numerators

Now add the numerators (18 + 26 = 44) and keep the common denominator 117 unchanged.

18 + 26/117 = 44/117

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 44 and 117 is 1, confirming that 44/117 cannot be reduced further—it is already in its simplest irreducible form.

44/117

Step 5

Decimal & Percentage Representation

Dividing the numerator 44 by denominator 117 produces a repeating decimal (approximately 0.376068, or 37.6068%).

44 ÷ 117 = 0.376068 (37.6068%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`44/117`
Mixed Number Form	`44/117`
Decimal Form	`0.376068`
Percentage	`37.6068%`

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Frequently Asked Questions

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

2/13 + 2/9 in simplest fraction form is 44/117.

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

2/13 + 2/9 converted to a decimal is 0.376068.

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

2/13 + 2/9 expressed as a percentage is 37.6068%.

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

It results in a repeating decimal (approximately 0.376068...) because the denominator contains prime factors other than 2 and 5.