What is 5/13 plus 5/9? (Answer: 110/117)

Exact Answer

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Problem: What is 5/13 plus 5/9?
Formula / Expression: 5/13 + 5/9
Final Answer: 110/117
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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 5/13 by 9, and multiply the numerator and denominator of 5/9 by 13 so both fractions share the common base 117.
Working: 5 × 9/13 × 9 = 45/117 and 5 × 13/9 × 13 = 65/117

Step 3: Add the Numerators
Now add the numerators (45 + 65 = 110) and keep the common denominator 117 unchanged.
Working: 45 + 65/117 = 110/117

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 110 and 117 is 1, confirming that 110/117 cannot be reduced further—it is already in its simplest irreducible form.
Working: 110/117

Step 5: Decimal & Percentage Representation
Dividing the numerator 110 by denominator 117 produces a repeating decimal (approximately 0.940171, or 94.0171%).
Working: 110 ÷ 117 = 0.940171 (94.0171%)

Key Values:
- Simplified Fraction: 110/117
- Mixed Number Form: 110/117
- Decimal Value: 0.940171
- Percentage: 94.0171%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-13-plus-5-9/
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5/13 + 5/9 = 110/117

Simplified Fraction

110/117

Mixed Number

Proper (110/117)

Decimal Value

0.940171

Percentage

94.0171%

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Step-by-Step Solution: 5/13 + 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 5/13 by 9, and multiply the numerator and denominator of 5/9 by 13 so both fractions share the common base 117.

5 × 9/13 × 9 = 45/117 and 5 × 13/9 × 13 = 65/117

Step 3

Add the Numerators

Now add the numerators (45 + 65 = 110) and keep the common denominator 117 unchanged.

45 + 65/117 = 110/117

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 110 and 117 is 1, confirming that 110/117 cannot be reduced further—it is already in its simplest irreducible form.

110/117

Step 5

Decimal & Percentage Representation

Dividing the numerator 110 by denominator 117 produces a repeating decimal (approximately 0.940171, or 94.0171%).

110 ÷ 117 = 0.940171 (94.0171%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`110/117`
Mixed Number Form	`110/117`
Decimal Form	`0.940171`
Percentage	`94.0171%`

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Frequently Asked Questions

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

5/13 + 5/9 in simplest fraction form is 110/117.

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

5/13 + 5/9 converted to a decimal is 0.940171.

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

5/13 + 5/9 expressed as a percentage is 94.0171%.

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

It results in a repeating decimal (approximately 0.940171...) because the denominator contains prime factors other than 2 and 5.