What is 2/13 plus 5/9? (Answer: 83/117)

Exact Answer

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Problem: What is 2/13 plus 5/9?
Formula / Expression: 2/13 + 5/9
Final Answer: 83/117
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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 5/9 by 13 so both fractions share the common base 117.
Working: 2 × 9/13 × 9 = 18/117 and 5 × 13/9 × 13 = 65/117

Step 3: Add the Numerators
Now add the numerators (18 + 65 = 83) and keep the common denominator 117 unchanged.
Working: 18 + 65/117 = 83/117

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 83 and 117 is 1, confirming that 83/117 cannot be reduced further—it is already in its simplest irreducible form.
Working: 83/117

Step 5: Decimal & Percentage Representation
Dividing the numerator 83 by denominator 117 produces a repeating decimal (approximately 0.709402, or 70.9402%).
Working: 83 ÷ 117 = 0.709402 (70.9402%)

Key Values:
- Simplified Fraction: 83/117
- Mixed Number Form: 83/117
- Decimal Value: 0.709402
- Percentage: 70.9402%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-13-plus-5-9/
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2/13 + 5/9 = 83/117

Simplified Fraction

83/117

Mixed Number

Proper (83/117)

Decimal Value

0.709402

Percentage

70.9402%

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Step-by-Step Solution: 2/13 + 5/9

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 5/9 by 13 so both fractions share the common base 117.

2 × 9/13 × 9 = 18/117 and 5 × 13/9 × 13 = 65/117

Step 3

Add the Numerators

Now add the numerators (18 + 65 = 83) and keep the common denominator 117 unchanged.

18 + 65/117 = 83/117

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 83 and 117 is 1, confirming that 83/117 cannot be reduced further—it is already in its simplest irreducible form.

83/117

Step 5

Decimal & Percentage Representation

Dividing the numerator 83 by denominator 117 produces a repeating decimal (approximately 0.709402, or 70.9402%).

83 ÷ 117 = 0.709402 (70.9402%)

Visual Representation

The diagram below illustrates 2/13 plus 5/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`83/117`
Mixed Number Form	`83/117`
Decimal Form	`0.709402`
Percentage	`70.9402%`

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Frequently Asked Questions

What is 2/13 plus 5/9 as a fraction?

2/13 + 5/9 in simplest fraction form is 83/117.

What is 2/13 plus 5/9 as a decimal?

2/13 + 5/9 converted to a decimal is 0.709402.

What is 2/13 plus 5/9 as a percentage?

2/13 + 5/9 expressed as a percentage is 70.9402%.

Does 2/13 plus 5/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.709402...) because the denominator contains prime factors other than 2 and 5.