What is 4/18 plus 11/13? (Answer: 125/117)

Exact Answer

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Problem: What is 4/18 plus 11/13?
Formula / Expression: 4/18 + 11/13
Final Answer: 1 8/117 (125/117)
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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 4/18 by 13, and multiply the numerator and denominator of 11/13 by 18 so both fractions share the common base 234.
Working: 4 × 13/18 × 13 = 52/234 and 11 × 18/13 × 18 = 198/234

Step 3: Add the Numerators
Now add the numerators (52 + 198 = 250) and keep the common denominator 234 unchanged.
Working: 52 + 198/234 = 250/234

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 250 and 234, which is 2. Divide both the numerator and denominator by 2.
Working: 250 ÷ 2/234 ÷ 2 = 125/117

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (125) is greater than the denominator (117), divide 125 by 117: it goes in 1 whole time(s) with a remainder of 8, giving the mixed number 1 8/117.
Working: 125/117 = 1 8/117

Step 6: Decimal & Percentage Representation
Dividing the numerator 125 by denominator 117 produces a repeating decimal (approximately 1.068376, or 106.8376%).
Working: 125 ÷ 117 = 1.068376 (106.8376%)

Key Values:
- Simplified Fraction: 125/117
- Mixed Number Form: 1 8/117
- Decimal Value: 1.068376
- Percentage: 106.8376%

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Solved with FractionsCalc:
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4/18 + 11/13 = 125/117

Simplified Fraction

125/117

Mixed Number

1 8/117

Decimal Value

1.068376

Percentage

106.8376%

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Step-by-Step Solution: 4/18 + 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 4/18 by 13, and multiply the numerator and denominator of 11/13 by 18 so both fractions share the common base 234.

4 × 13/18 × 13 = 52/234 and 11 × 18/13 × 18 = 198/234

Step 3

Add the Numerators

Now add the numerators (52 + 198 = 250) and keep the common denominator 234 unchanged.

52 + 198/234 = 250/234

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 250 and 234, which is 2. Divide both the numerator and denominator by 2.

250 ÷ 2/234 ÷ 2 = 125/117

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (125) is greater than the denominator (117), divide 125 by 117: it goes in 1 whole time(s) with a remainder of 8, giving the mixed number 1 8/117.

125/117 = 18/117

Step 6

Decimal & Percentage Representation

Dividing the numerator 125 by denominator 117 produces a repeating decimal (approximately 1.068376, or 106.8376%).

125 ÷ 117 = 1.068376 (106.8376%)

Visual Representation

The diagram below illustrates 4/18 plus 11/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`125/117`
Mixed Number Form	`1 8/117`
Decimal Form	`1.068376`
Percentage	`106.8376%`

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Frequently Asked Questions

What is 4/18 plus 11/13 as a fraction?

4/18 + 11/13 in simplest fraction form is 125/117 (or 1 8/117 as a mixed number).

What is 4/18 plus 11/13 as a decimal?

4/18 + 11/13 converted to a decimal is 1.068376.

What is 4/18 plus 11/13 as a percentage?

4/18 + 11/13 expressed as a percentage is 106.8376%.

How do you write 4/18 plus 11/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 125/117 can be written as the mixed number 1 8/117.

Does 4/18 plus 11/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.068376...) because the denominator contains prime factors other than 2 and 5.