What is 14/36 plus 8/13? (Answer: 235/234)

Exact Answer

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Problem: What is 14/36 plus 8/13?
Formula / Expression: 14/36 + 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 36 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 36 × 13 = 468.
Working: LCD(36, 13) = 468

Step 2: Convert to Equivalent Fractions with Common Denominator 468
Multiply the numerator and denominator of 14/36 by 13, and multiply the numerator and denominator of 8/13 by 36 so both fractions share the common base 468.
Working: 14 × 13/36 × 13 = 182/468 and 8 × 36/13 × 36 = 288/468

Step 3: Add the Numerators
Now add the numerators (182 + 288 = 470) and keep the common denominator 468 unchanged.
Working: 182 + 288/468 = 470/468

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 470 and 468, which is 2. Divide both the numerator and denominator by 2.
Working: 470 ÷ 2/468 ÷ 2 = 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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14/36 + 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: 14/36 + 8/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 36 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 36 × 13 = 468.

LCD(36, 13) = 468

Step 2

Convert to Equivalent Fractions with Common Denominator 468

Multiply the numerator and denominator of 14/36 by 13, and multiply the numerator and denominator of 8/13 by 36 so both fractions share the common base 468.

14 × 13/36 × 13 = 182/468 and 8 × 36/13 × 36 = 288/468

Step 3

Add the Numerators

Now add the numerators (182 + 288 = 470) and keep the common denominator 468 unchanged.

182 + 288/468 = 470/468

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 470 and 468, which is 2. Divide both the numerator and denominator by 2.

470 ÷ 2/468 ÷ 2 = 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 14/36 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 14/36 plus 8/13 as a fraction?

14/36 + 8/13 in simplest fraction form is 235/234 (or 1 1/234 as a mixed number).

What is 14/36 plus 8/13 as a decimal?

14/36 + 8/13 converted to a decimal is 1.004274.

What is 14/36 plus 8/13 as a percentage?

14/36 + 8/13 expressed as a percentage is 100.4274%.

How do you write 14/36 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 14/36 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.