What is 11/18 plus 9/13? (Answer: 305/234)

Exact Answer

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Problem: What is 11/18 plus 9/13?
Formula / Expression: 11/18 + 9/13
Final Answer: 1 71/234 (305/234)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 18 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 18 × 13 = 234.
Working: LCD(18, 13) = 234

Step 2: Convert to Equivalent Fractions with Common Denominator 234
Multiply the numerator and denominator of 11/18 by 13, and multiply the numerator and denominator of 9/13 by 18 so both fractions share the common base 234.
Working: 11 × 13/18 × 13 = 143/234 and 9 × 18/13 × 18 = 162/234

Step 3: Add the Numerators
Now add the numerators (143 + 162 = 305) and keep the common denominator 234 unchanged.
Working: 143 + 162/234 = 305/234

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 305 and 234 is 1, confirming that 305/234 cannot be reduced further—it is already in its simplest irreducible form.
Working: 305/234

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (305) is greater than the denominator (234), divide 305 by 234: it goes in 1 whole time(s) with a remainder of 71, giving the mixed number 1 71/234.
Working: 305/234 = 1 71/234

Step 6: Decimal & Percentage Representation
Dividing the numerator 305 by denominator 234 produces a repeating decimal (approximately 1.303419, or 130.3419%).
Working: 305 ÷ 234 = 1.303419 (130.3419%)

Key Values:
- Simplified Fraction: 305/234
- Mixed Number Form: 1 71/234
- Decimal Value: 1.303419
- Percentage: 130.3419%

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Solved with FractionsCalc:
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11/18 + 9/13 = 305/234

Simplified Fraction

305/234

Mixed Number

1 71/234

Decimal Value

1.303419

Percentage

130.3419%

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Step-by-Step Solution: 11/18 + 9/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 18 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 18 × 13 = 234.

LCD(18, 13) = 234

Step 2

Convert to Equivalent Fractions with Common Denominator 234

Multiply the numerator and denominator of 11/18 by 13, and multiply the numerator and denominator of 9/13 by 18 so both fractions share the common base 234.

11 × 13/18 × 13 = 143/234 and 9 × 18/13 × 18 = 162/234

Step 3

Add the Numerators

Now add the numerators (143 + 162 = 305) and keep the common denominator 234 unchanged.

143 + 162/234 = 305/234

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 305 and 234 is 1, confirming that 305/234 cannot be reduced further—it is already in its simplest irreducible form.

305/234

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (305) is greater than the denominator (234), divide 305 by 234: it goes in 1 whole time(s) with a remainder of 71, giving the mixed number 1 71/234.

305/234 = 171/234

Step 6

Decimal & Percentage Representation

Dividing the numerator 305 by denominator 234 produces a repeating decimal (approximately 1.303419, or 130.3419%).

305 ÷ 234 = 1.303419 (130.3419%)

Visual Representation

The diagram below illustrates 11/18 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`305/234`
Mixed Number Form	`1 71/234`
Decimal Form	`1.303419`
Percentage	`130.3419%`

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Frequently Asked Questions

What is 11/18 plus 9/13 as a fraction?

11/18 + 9/13 in simplest fraction form is 305/234 (or 1 71/234 as a mixed number).

What is 11/18 plus 9/13 as a decimal?

11/18 + 9/13 converted to a decimal is 1.303419.

What is 11/18 plus 9/13 as a percentage?

11/18 + 9/13 expressed as a percentage is 130.3419%.

How do you write 11/18 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 305/234 can be written as the mixed number 1 71/234.

Does 11/18 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.303419...) because the denominator contains prime factors other than 2 and 5.