What is 5/9 plus 10/13? (Answer: 155/117)

Exact Answer

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Problem: What is 5/9 plus 10/13?
Formula / Expression: 5/9 + 10/13
Final Answer: 1 38/117 (155/117)
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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 10/13 by 9 so both fractions share the common base 117.
Working: 5 × 13/9 × 13 = 65/117 and 10 × 9/13 × 9 = 90/117

Step 3: Add the Numerators
Now add the numerators (65 + 90 = 155) and keep the common denominator 117 unchanged.
Working: 65 + 90/117 = 155/117

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 155 and 117 is 1, confirming that 155/117 cannot be reduced further—it is already in its simplest irreducible form.
Working: 155/117

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (155) is greater than the denominator (117), divide 155 by 117: it goes in 1 whole time(s) with a remainder of 38, giving the mixed number 1 38/117.
Working: 155/117 = 1 38/117

Step 6: Decimal & Percentage Representation
Dividing the numerator 155 by denominator 117 produces a repeating decimal (approximately 1.324786, or 132.4786%).
Working: 155 ÷ 117 = 1.324786 (132.4786%)

Key Values:
- Simplified Fraction: 155/117
- Mixed Number Form: 1 38/117
- Decimal Value: 1.324786
- Percentage: 132.4786%

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Solved with FractionsCalc:
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5/9 + 10/13 = 155/117

Simplified Fraction

155/117

Mixed Number

1 38/117

Decimal Value

1.324786

Percentage

132.4786%

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Step-by-Step Solution: 5/9 + 10/13

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 10/13 by 9 so both fractions share the common base 117.

5 × 13/9 × 13 = 65/117 and 10 × 9/13 × 9 = 90/117

Step 3

Add the Numerators

Now add the numerators (65 + 90 = 155) and keep the common denominator 117 unchanged.

65 + 90/117 = 155/117

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 155 and 117 is 1, confirming that 155/117 cannot be reduced further—it is already in its simplest irreducible form.

155/117

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (155) is greater than the denominator (117), divide 155 by 117: it goes in 1 whole time(s) with a remainder of 38, giving the mixed number 1 38/117.

155/117 = 138/117

Step 6

Decimal & Percentage Representation

Dividing the numerator 155 by denominator 117 produces a repeating decimal (approximately 1.324786, or 132.4786%).

155 ÷ 117 = 1.324786 (132.4786%)

Visual Representation

The diagram below illustrates 5/9 plus 10/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`155/117`
Mixed Number Form	`1 38/117`
Decimal Form	`1.324786`
Percentage	`132.4786%`

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Frequently Asked Questions

What is 5/9 plus 10/13 as a fraction?

5/9 + 10/13 in simplest fraction form is 155/117 (or 1 38/117 as a mixed number).

What is 5/9 plus 10/13 as a decimal?

5/9 + 10/13 converted to a decimal is 1.324786.

What is 5/9 plus 10/13 as a percentage?

5/9 + 10/13 expressed as a percentage is 132.4786%.

How do you write 5/9 plus 10/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 155/117 can be written as the mixed number 1 38/117.

Does 5/9 plus 10/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.324786...) because the denominator contains prime factors other than 2 and 5.