What is 1/36 plus 5/13? (Answer: 193/468)

Exact Answer

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Problem: What is 1/36 plus 5/13?
Formula / Expression: 1/36 + 5/13
Final Answer: 193/468
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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 1/36 by 13, and multiply the numerator and denominator of 5/13 by 36 so both fractions share the common base 468.
Working: 1 × 13/36 × 13 = 13/468 and 5 × 36/13 × 36 = 180/468

Step 3: Add the Numerators
Now add the numerators (13 + 180 = 193) and keep the common denominator 468 unchanged.
Working: 13 + 180/468 = 193/468

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 193 and 468 is 1, confirming that 193/468 cannot be reduced further—it is already in its simplest irreducible form.
Working: 193/468

Step 5: Decimal & Percentage Representation
Dividing the numerator 193 by denominator 468 produces a repeating decimal (approximately 0.412393, or 41.2393%).
Working: 193 ÷ 468 = 0.412393 (41.2393%)

Key Values:
- Simplified Fraction: 193/468
- Mixed Number Form: 193/468
- Decimal Value: 0.412393
- Percentage: 41.2393%

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Solved with FractionsCalc:
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1/36 + 5/13 = 193/468

Simplified Fraction

193/468

Mixed Number

Proper (193/468)

Decimal Value

0.412393

Percentage

41.2393%

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Step-by-Step Solution: 1/36 + 5/13

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 1/36 by 13, and multiply the numerator and denominator of 5/13 by 36 so both fractions share the common base 468.

1 × 13/36 × 13 = 13/468 and 5 × 36/13 × 36 = 180/468

Step 3

Add the Numerators

Now add the numerators (13 + 180 = 193) and keep the common denominator 468 unchanged.

13 + 180/468 = 193/468

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 193 and 468 is 1, confirming that 193/468 cannot be reduced further—it is already in its simplest irreducible form.

193/468

Step 5

Decimal & Percentage Representation

Dividing the numerator 193 by denominator 468 produces a repeating decimal (approximately 0.412393, or 41.2393%).

193 ÷ 468 = 0.412393 (41.2393%)

Visual Representation

The diagram below illustrates 1/36 plus 5/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`193/468`
Mixed Number Form	`193/468`
Decimal Form	`0.412393`
Percentage	`41.2393%`

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Frequently Asked Questions

What is 1/36 plus 5/13 as a fraction?

1/36 + 5/13 in simplest fraction form is 193/468.

What is 1/36 plus 5/13 as a decimal?

1/36 + 5/13 converted to a decimal is 0.412393.

What is 1/36 plus 5/13 as a percentage?

1/36 + 5/13 expressed as a percentage is 41.2393%.

Does 1/36 plus 5/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.412393...) because the denominator contains prime factors other than 2 and 5.