What is 1/18 plus 11/13? (Answer: 211/234)

Exact Answer

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Problem: What is 1/18 plus 11/13?
Formula / Expression: 1/18 + 11/13
Final Answer: 211/234
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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 1/18 by 13, and multiply the numerator and denominator of 11/13 by 18 so both fractions share the common base 234.
Working: 1 × 13/18 × 13 = 13/234 and 11 × 18/13 × 18 = 198/234

Step 3: Add the Numerators
Now add the numerators (13 + 198 = 211) and keep the common denominator 234 unchanged.
Working: 13 + 198/234 = 211/234

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 211 and 234 is 1, confirming that 211/234 cannot be reduced further—it is already in its simplest irreducible form.
Working: 211/234

Step 5: Decimal & Percentage Representation
Dividing the numerator 211 by denominator 234 produces a repeating decimal (approximately 0.901709, or 90.1709%).
Working: 211 ÷ 234 = 0.901709 (90.1709%)

Key Values:
- Simplified Fraction: 211/234
- Mixed Number Form: 211/234
- Decimal Value: 0.901709
- Percentage: 90.1709%

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Solved with FractionsCalc:
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1/18 + 11/13 = 211/234

Simplified Fraction

211/234

Mixed Number

Proper (211/234)

Decimal Value

0.901709

Percentage

90.1709%

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Step-by-Step Solution: 1/18 + 11/13

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 1/18 by 13, and multiply the numerator and denominator of 11/13 by 18 so both fractions share the common base 234.

1 × 13/18 × 13 = 13/234 and 11 × 18/13 × 18 = 198/234

Step 3

Add the Numerators

Now add the numerators (13 + 198 = 211) and keep the common denominator 234 unchanged.

13 + 198/234 = 211/234

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 211 and 234 is 1, confirming that 211/234 cannot be reduced further—it is already in its simplest irreducible form.

211/234

Step 5

Decimal & Percentage Representation

Dividing the numerator 211 by denominator 234 produces a repeating decimal (approximately 0.901709, or 90.1709%).

211 ÷ 234 = 0.901709 (90.1709%)

Visual Representation

The diagram below illustrates 1/18 plus 11/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`211/234`
Mixed Number Form	`211/234`
Decimal Form	`0.901709`
Percentage	`90.1709%`

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Frequently Asked Questions

What is 1/18 plus 11/13 as a fraction?

1/18 + 11/13 in simplest fraction form is 211/234.

What is 1/18 plus 11/13 as a decimal?

1/18 + 11/13 converted to a decimal is 0.901709.

What is 1/18 plus 11/13 as a percentage?

1/18 + 11/13 expressed as a percentage is 90.1709%.

Does 1/18 plus 11/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.901709...) because the denominator contains prime factors other than 2 and 5.