What is 2/9 plus 3/13? (Answer: 53/117)

Exact Answer

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Problem: What is 2/9 plus 3/13?
Formula / Expression: 2/9 + 3/13
Final Answer: 53/117
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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 3/13 by 9 so both fractions share the common base 117.
Working: 2 × 13/9 × 13 = 26/117 and 3 × 9/13 × 9 = 27/117

Step 3: Add the Numerators
Now add the numerators (26 + 27 = 53) and keep the common denominator 117 unchanged.
Working: 26 + 27/117 = 53/117

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 53 and 117 is 1, confirming that 53/117 cannot be reduced further—it is already in its simplest irreducible form.
Working: 53/117

Step 5: Decimal & Percentage Representation
Dividing the numerator 53 by denominator 117 produces a repeating decimal (approximately 0.452991, or 45.2991%).
Working: 53 ÷ 117 = 0.452991 (45.2991%)

Key Values:
- Simplified Fraction: 53/117
- Mixed Number Form: 53/117
- Decimal Value: 0.452991
- Percentage: 45.2991%

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Solved with FractionsCalc:
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2/9 + 3/13 = 53/117

Simplified Fraction

53/117

Mixed Number

Proper (53/117)

Decimal Value

0.452991

Percentage

45.2991%

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Step-by-Step Solution: 2/9 + 3/13

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 3/13 by 9 so both fractions share the common base 117.

2 × 13/9 × 13 = 26/117 and 3 × 9/13 × 9 = 27/117

Step 3

Add the Numerators

Now add the numerators (26 + 27 = 53) and keep the common denominator 117 unchanged.

26 + 27/117 = 53/117

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 53 and 117 is 1, confirming that 53/117 cannot be reduced further—it is already in its simplest irreducible form.

53/117

Step 5

Decimal & Percentage Representation

Dividing the numerator 53 by denominator 117 produces a repeating decimal (approximately 0.452991, or 45.2991%).

53 ÷ 117 = 0.452991 (45.2991%)

Visual Representation

The diagram below illustrates 2/9 plus 3/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`53/117`
Mixed Number Form	`53/117`
Decimal Form	`0.452991`
Percentage	`45.2991%`

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Frequently Asked Questions

What is 2/9 plus 3/13 as a fraction?

2/9 + 3/13 in simplest fraction form is 53/117.

What is 2/9 plus 3/13 as a decimal?

2/9 + 3/13 converted to a decimal is 0.452991.

What is 2/9 plus 3/13 as a percentage?

2/9 + 3/13 expressed as a percentage is 45.2991%.

Does 2/9 plus 3/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.452991...) because the denominator contains prime factors other than 2 and 5.