What is 5/9 plus 9/13? (Answer: 146/117)

Exact Answer

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Problem: What is 5/9 plus 9/13?
Formula / Expression: 5/9 + 9/13
Final Answer: 1 29/117 (146/117)
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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 5/9 by 13, and multiply the numerator and denominator of 9/13 by 9 so both fractions share the common base 117.
Working: 5 × 13/9 × 13 = 65/117 and 9 × 9/13 × 9 = 81/117

Step 3: Add the Numerators
Now add the numerators (65 + 81 = 146) and keep the common denominator 117 unchanged.
Working: 65 + 81/117 = 146/117

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 146 and 117 is 1, confirming that 146/117 cannot be reduced further—it is already in its simplest irreducible form.
Working: 146/117

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (146) is greater than the denominator (117), divide 146 by 117: it goes in 1 whole time(s) with a remainder of 29, giving the mixed number 1 29/117.
Working: 146/117 = 1 29/117

Step 6: Decimal & Percentage Representation
Dividing the numerator 146 by denominator 117 produces a repeating decimal (approximately 1.247863, or 124.7863%).
Working: 146 ÷ 117 = 1.247863 (124.7863%)

Key Values:
- Simplified Fraction: 146/117
- Mixed Number Form: 1 29/117
- Decimal Value: 1.247863
- Percentage: 124.7863%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-9-plus-9-13/
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5/9 + 9/13 = 146/117

Simplified Fraction

146/117

Mixed Number

1 29/117

Decimal Value

1.247863

Percentage

124.7863%

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

5 × 13/9 × 13 = 65/117 and 9 × 9/13 × 9 = 81/117

Step 3

Add the Numerators

Now add the numerators (65 + 81 = 146) and keep the common denominator 117 unchanged.

65 + 81/117 = 146/117

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 146 and 117 is 1, confirming that 146/117 cannot be reduced further—it is already in its simplest irreducible form.

146/117

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (146) is greater than the denominator (117), divide 146 by 117: it goes in 1 whole time(s) with a remainder of 29, giving the mixed number 1 29/117.

146/117 = 129/117

Step 6

Decimal & Percentage Representation

Dividing the numerator 146 by denominator 117 produces a repeating decimal (approximately 1.247863, or 124.7863%).

146 ÷ 117 = 1.247863 (124.7863%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`146/117`
Mixed Number Form	`1 29/117`
Decimal Form	`1.247863`
Percentage	`124.7863%`

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Frequently Asked Questions

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

5/9 + 9/13 in simplest fraction form is 146/117 (or 1 29/117 as a mixed number).

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

5/9 + 9/13 converted to a decimal is 1.247863.

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

5/9 + 9/13 expressed as a percentage is 124.7863%.

How do you write 5/9 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 146/117 can be written as the mixed number 1 29/117.

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

It results in a repeating decimal (approximately 1.247863...) because the denominator contains prime factors other than 2 and 5.