What is 8/18 plus 8/13? (Answer: 124/117)

Exact Answer

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Problem: What is 8/18 plus 8/13?
Formula / Expression: 8/18 + 8/13
Final Answer: 1 7/117 (124/117)
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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 8/18 by 13, and multiply the numerator and denominator of 8/13 by 18 so both fractions share the common base 234.
Working: 8 × 13/18 × 13 = 104/234 and 8 × 18/13 × 18 = 144/234

Step 3: Add the Numerators
Now add the numerators (104 + 144 = 248) and keep the common denominator 234 unchanged.
Working: 104 + 144/234 = 248/234

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 248 and 234, which is 2. Divide both the numerator and denominator by 2.
Working: 248 ÷ 2/234 ÷ 2 = 124/117

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (124) is greater than the denominator (117), divide 124 by 117: it goes in 1 whole time(s) with a remainder of 7, giving the mixed number 1 7/117.
Working: 124/117 = 1 7/117

Step 6: Decimal & Percentage Representation
Dividing the numerator 124 by denominator 117 produces a repeating decimal (approximately 1.059829, or 105.9829%).
Working: 124 ÷ 117 = 1.059829 (105.9829%)

Key Values:
- Simplified Fraction: 124/117
- Mixed Number Form: 1 7/117
- Decimal Value: 1.059829
- Percentage: 105.9829%

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Solved with FractionsCalc:
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8/18 + 8/13 = 124/117

Simplified Fraction

124/117

Mixed Number

1 7/117

Decimal Value

1.059829

Percentage

105.9829%

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Step-by-Step Solution: 8/18 + 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 8/18 by 13, and multiply the numerator and denominator of 8/13 by 18 so both fractions share the common base 234.

8 × 13/18 × 13 = 104/234 and 8 × 18/13 × 18 = 144/234

Step 3

Add the Numerators

Now add the numerators (104 + 144 = 248) and keep the common denominator 234 unchanged.

104 + 144/234 = 248/234

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 248 and 234, which is 2. Divide both the numerator and denominator by 2.

248 ÷ 2/234 ÷ 2 = 124/117

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (124) is greater than the denominator (117), divide 124 by 117: it goes in 1 whole time(s) with a remainder of 7, giving the mixed number 1 7/117.

124/117 = 17/117

Step 6

Decimal & Percentage Representation

Dividing the numerator 124 by denominator 117 produces a repeating decimal (approximately 1.059829, or 105.9829%).

124 ÷ 117 = 1.059829 (105.9829%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`124/117`
Mixed Number Form	`1 7/117`
Decimal Form	`1.059829`
Percentage	`105.9829%`

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Frequently Asked Questions

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

8/18 + 8/13 in simplest fraction form is 124/117 (or 1 7/117 as a mixed number).

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

8/18 + 8/13 converted to a decimal is 1.059829.

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

8/18 + 8/13 expressed as a percentage is 105.9829%.

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

Because the numerator is greater than the denominator, the improper fraction 124/117 can be written as the mixed number 1 7/117.

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

It results in a repeating decimal (approximately 1.059829...) because the denominator contains prime factors other than 2 and 5.