What is 2/9 plus 9/13? (Answer: 107/117)

Exact Answer

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Problem: What is 2/9 plus 9/13?
Formula / Expression: 2/9 + 9/13
Final Answer: 107/117
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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 2/9 by 13, and multiply the numerator and denominator of 9/13 by 9 so both fractions share the common base 117.
Working: 2 × 13/9 × 13 = 26/117 and 9 × 9/13 × 9 = 81/117

Step 3: Add the Numerators
Now add the numerators (26 + 81 = 107) and keep the common denominator 117 unchanged.
Working: 26 + 81/117 = 107/117

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 107 and 117 is 1, confirming that 107/117 cannot be reduced further—it is already in its simplest irreducible form.
Working: 107/117

Step 5: Decimal & Percentage Representation
Dividing the numerator 107 by denominator 117 produces a repeating decimal (approximately 0.91453, or 91.453%).
Working: 107 ÷ 117 = 0.91453 (91.453%)

Key Values:
- Simplified Fraction: 107/117
- Mixed Number Form: 107/117
- Decimal Value: 0.91453
- Percentage: 91.453%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-9-plus-9-13/
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2/9 + 9/13 = 107/117

Simplified Fraction

107/117

Mixed Number

Proper (107/117)

Decimal Value

0.91453

Percentage

91.453%

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

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

2 × 13/9 × 13 = 26/117 and 9 × 9/13 × 9 = 81/117

Step 3

Add the Numerators

Now add the numerators (26 + 81 = 107) and keep the common denominator 117 unchanged.

26 + 81/117 = 107/117

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 107 and 117 is 1, confirming that 107/117 cannot be reduced further—it is already in its simplest irreducible form.

107/117

Step 5

Decimal & Percentage Representation

Dividing the numerator 107 by denominator 117 produces a repeating decimal (approximately 0.91453, or 91.453%).

107 ÷ 117 = 0.91453 (91.453%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`107/117`
Mixed Number Form	`107/117`
Decimal Form	`0.91453`
Percentage	`91.453%`

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Frequently Asked Questions

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

2/9 + 9/13 in simplest fraction form is 107/117.

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

2/9 + 9/13 converted to a decimal is 0.91453.

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

2/9 + 9/13 expressed as a percentage is 91.453%.

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

It results in a repeating decimal (approximately 0.91453...) because the denominator contains prime factors other than 2 and 5.