What is 7/18 plus 8/13? (Answer: 235/234)

Exact Answer

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Problem: What is 7/18 plus 8/13?
Formula / Expression: 7/18 + 8/13
Final Answer: 1 1/234 (235/234)
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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 7/18 by 13, and multiply the numerator and denominator of 8/13 by 18 so both fractions share the common base 234.
Working: 7 × 13/18 × 13 = 91/234 and 8 × 18/13 × 18 = 144/234

Step 3: Add the Numerators
Now add the numerators (91 + 144 = 235) and keep the common denominator 234 unchanged.
Working: 91 + 144/234 = 235/234

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 235 and 234 is 1, confirming that 235/234 cannot be reduced further—it is already in its simplest irreducible form.
Working: 235/234

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (235) is greater than the denominator (234), divide 235 by 234: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/234.
Working: 235/234 = 1 1/234

Step 6: Decimal & Percentage Representation
Dividing the numerator 235 by denominator 234 produces a repeating decimal (approximately 1.004274, or 100.4274%).
Working: 235 ÷ 234 = 1.004274 (100.4274%)

Key Values:
- Simplified Fraction: 235/234
- Mixed Number Form: 1 1/234
- Decimal Value: 1.004274
- Percentage: 100.4274%

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Solved with FractionsCalc:
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7/18 + 8/13 = 235/234

Simplified Fraction

235/234

Mixed Number

1 1/234

Decimal Value

1.004274

Percentage

100.4274%

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Step-by-Step Solution: 7/18 + 8/13

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 7/18 by 13, and multiply the numerator and denominator of 8/13 by 18 so both fractions share the common base 234.

7 × 13/18 × 13 = 91/234 and 8 × 18/13 × 18 = 144/234

Step 3

Add the Numerators

Now add the numerators (91 + 144 = 235) and keep the common denominator 234 unchanged.

91 + 144/234 = 235/234

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 235 and 234 is 1, confirming that 235/234 cannot be reduced further—it is already in its simplest irreducible form.

235/234

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (235) is greater than the denominator (234), divide 235 by 234: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/234.

235/234 = 11/234

Step 6

Decimal & Percentage Representation

Dividing the numerator 235 by denominator 234 produces a repeating decimal (approximately 1.004274, or 100.4274%).

235 ÷ 234 = 1.004274 (100.4274%)

Visual Representation

The diagram below illustrates 7/18 plus 8/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`235/234`
Mixed Number Form	`1 1/234`
Decimal Form	`1.004274`
Percentage	`100.4274%`

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Frequently Asked Questions

What is 7/18 plus 8/13 as a fraction?

7/18 + 8/13 in simplest fraction form is 235/234 (or 1 1/234 as a mixed number).

What is 7/18 plus 8/13 as a decimal?

7/18 + 8/13 converted to a decimal is 1.004274.

What is 7/18 plus 8/13 as a percentage?

7/18 + 8/13 expressed as a percentage is 100.4274%.

How do you write 7/18 plus 8/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 235/234 can be written as the mixed number 1 1/234.

Does 7/18 plus 8/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.004274...) because the denominator contains prime factors other than 2 and 5.