What is 11/18 plus 10/13? (Answer: 323/234)

Exact Answer

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Problem: What is 11/18 plus 10/13?
Formula / Expression: 11/18 + 10/13
Final Answer: 1 89/234 (323/234)
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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 10/13 by 18 so both fractions share the common base 234.
Working: 11 × 13/18 × 13 = 143/234 and 10 × 18/13 × 18 = 180/234

Step 3: Add the Numerators
Now add the numerators (143 + 180 = 323) and keep the common denominator 234 unchanged.
Working: 143 + 180/234 = 323/234

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 323 and 234 is 1, confirming that 323/234 cannot be reduced further—it is already in its simplest irreducible form.
Working: 323/234

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (323) is greater than the denominator (234), divide 323 by 234: it goes in 1 whole time(s) with a remainder of 89, giving the mixed number 1 89/234.
Working: 323/234 = 1 89/234

Step 6: Decimal & Percentage Representation
Dividing the numerator 323 by denominator 234 produces a repeating decimal (approximately 1.380342, or 138.0342%).
Working: 323 ÷ 234 = 1.380342 (138.0342%)

Key Values:
- Simplified Fraction: 323/234
- Mixed Number Form: 1 89/234
- Decimal Value: 1.380342
- Percentage: 138.0342%

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11/18 + 10/13 = 323/234

Simplified Fraction

323/234

Mixed Number

1 89/234

Decimal Value

1.380342

Percentage

138.0342%

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Step-by-Step Solution: 11/18 + 10/13

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 10/13 by 18 so both fractions share the common base 234.

11 × 13/18 × 13 = 143/234 and 10 × 18/13 × 18 = 180/234

Step 3

Add the Numerators

Now add the numerators (143 + 180 = 323) and keep the common denominator 234 unchanged.

143 + 180/234 = 323/234

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 323 and 234 is 1, confirming that 323/234 cannot be reduced further—it is already in its simplest irreducible form.

323/234

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (323) is greater than the denominator (234), divide 323 by 234: it goes in 1 whole time(s) with a remainder of 89, giving the mixed number 1 89/234.

323/234 = 189/234

Step 6

Decimal & Percentage Representation

Dividing the numerator 323 by denominator 234 produces a repeating decimal (approximately 1.380342, or 138.0342%).

323 ÷ 234 = 1.380342 (138.0342%)

Visual Representation

The diagram below illustrates 11/18 plus 10/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`323/234`
Mixed Number Form	`1 89/234`
Decimal Form	`1.380342`
Percentage	`138.0342%`

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Frequently Asked Questions

What is 11/18 plus 10/13 as a fraction?

11/18 + 10/13 in simplest fraction form is 323/234 (or 1 89/234 as a mixed number).

What is 11/18 plus 10/13 as a decimal?

11/18 + 10/13 converted to a decimal is 1.380342.

What is 11/18 plus 10/13 as a percentage?

11/18 + 10/13 expressed as a percentage is 138.0342%.

How do you write 11/18 plus 10/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 323/234 can be written as the mixed number 1 89/234.

Does 11/18 plus 10/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.380342...) because the denominator contains prime factors other than 2 and 5.