What is 5/13 plus 8/9? (Answer: 149/117)

Exact Answer

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Problem: What is 5/13 plus 8/9?
Formula / Expression: 5/13 + 8/9
Final Answer: 1 32/117 (149/117)
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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 8/9 by 13 so both fractions share the common base 117.
Working: 5 × 9/13 × 9 = 45/117 and 8 × 13/9 × 13 = 104/117

Step 3: Add the Numerators
Now add the numerators (45 + 104 = 149) and keep the common denominator 117 unchanged.
Working: 45 + 104/117 = 149/117

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 149 and 117 is 1, confirming that 149/117 cannot be reduced further—it is already in its simplest irreducible form.
Working: 149/117

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (149) is greater than the denominator (117), divide 149 by 117: it goes in 1 whole time(s) with a remainder of 32, giving the mixed number 1 32/117.
Working: 149/117 = 1 32/117

Step 6: Decimal & Percentage Representation
Dividing the numerator 149 by denominator 117 produces a repeating decimal (approximately 1.273504, or 127.3504%).
Working: 149 ÷ 117 = 1.273504 (127.3504%)

Key Values:
- Simplified Fraction: 149/117
- Mixed Number Form: 1 32/117
- Decimal Value: 1.273504
- Percentage: 127.3504%

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Solved with FractionsCalc:
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5/13 + 8/9 = 149/117

Simplified Fraction

149/117

Mixed Number

1 32/117

Decimal Value

1.273504

Percentage

127.3504%

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Step-by-Step Solution: 5/13 + 8/9

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 8/9 by 13 so both fractions share the common base 117.

5 × 9/13 × 9 = 45/117 and 8 × 13/9 × 13 = 104/117

Step 3

Add the Numerators

Now add the numerators (45 + 104 = 149) and keep the common denominator 117 unchanged.

45 + 104/117 = 149/117

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 149 and 117 is 1, confirming that 149/117 cannot be reduced further—it is already in its simplest irreducible form.

149/117

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (149) is greater than the denominator (117), divide 149 by 117: it goes in 1 whole time(s) with a remainder of 32, giving the mixed number 1 32/117.

149/117 = 132/117

Step 6

Decimal & Percentage Representation

Dividing the numerator 149 by denominator 117 produces a repeating decimal (approximately 1.273504, or 127.3504%).

149 ÷ 117 = 1.273504 (127.3504%)

Visual Representation

The diagram below illustrates 5/13 plus 8/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`149/117`
Mixed Number Form	`1 32/117`
Decimal Form	`1.273504`
Percentage	`127.3504%`

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Frequently Asked Questions

What is 5/13 plus 8/9 as a fraction?

5/13 + 8/9 in simplest fraction form is 149/117 (or 1 32/117 as a mixed number).

What is 5/13 plus 8/9 as a decimal?

5/13 + 8/9 converted to a decimal is 1.273504.

What is 5/13 plus 8/9 as a percentage?

5/13 + 8/9 expressed as a percentage is 127.3504%.

How do you write 5/13 plus 8/9 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 149/117 can be written as the mixed number 1 32/117.

Does 5/13 plus 8/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.273504...) because the denominator contains prime factors other than 2 and 5.