What is 5/36 plus 2/9? (Answer: 13/36)

Exact Answer

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Problem: What is 5/36 plus 2/9?
Formula / Expression: 5/36 + 2/9
Final Answer: 13/36
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 36 is an exact multiple of 9 (9 × 4 = 36). The Least Common Denominator (LCD) is simply 36, meaning we only need to scale one fraction.
Working: LCD(36, 9) = 36

Step 2: Convert to Equivalent Fractions with Common Denominator 36
Multiply the numerator and denominator of 5/36 by 1, and multiply the numerator and denominator of 2/9 by 4 so both fractions share the common base 36.
Working: 5 × 1/36 × 1 = 5/36 and 2 × 4/9 × 4 = 8/36

Step 3: Add the Numerators
Now add the numerators (5 + 8 = 13) and keep the common denominator 36 unchanged.
Working: 5 + 8/36 = 13/36

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 13 and 36 is 1, confirming that 13/36 cannot be reduced further—it is already in its simplest irreducible form.
Working: 13/36

Step 5: Decimal & Percentage Representation
Dividing the numerator 13 by denominator 36 produces a repeating decimal (approximately 0.361111, or 36.1111%).
Working: 13 ÷ 36 = 0.361111 (36.1111%)

Key Values:
- Simplified Fraction: 13/36
- Mixed Number Form: 13/36
- Decimal Value: 0.361111
- Percentage: 36.1111%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-36-plus-2-9/
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5/36 + 2/9 = 13/36

Simplified Fraction

13/36

Mixed Number

Proper (13/36)

Decimal Value

0.361111

Percentage

36.1111%

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Step-by-Step Solution: 5/36 + 2/9

Step 1

Find the Least Common Denominator (LCD)

Notice that 36 is an exact multiple of 9 (9 × 4 = 36). The Least Common Denominator (LCD) is simply 36, meaning we only need to scale one fraction.

LCD(36, 9) = 36

Step 2

Convert to Equivalent Fractions with Common Denominator 36

Multiply the numerator and denominator of 5/36 by 1, and multiply the numerator and denominator of 2/9 by 4 so both fractions share the common base 36.

5 × 1/36 × 1 = 5/36 and 2 × 4/9 × 4 = 8/36

Step 3

Add the Numerators

Now add the numerators (5 + 8 = 13) and keep the common denominator 36 unchanged.

5 + 8/36 = 13/36

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 13 and 36 is 1, confirming that 13/36 cannot be reduced further—it is already in its simplest irreducible form.

13/36

Step 5

Decimal & Percentage Representation

Dividing the numerator 13 by denominator 36 produces a repeating decimal (approximately 0.361111, or 36.1111%).

13 ÷ 36 = 0.361111 (36.1111%)

Visual Representation

The diagram below illustrates 5/36 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`13/36`
Mixed Number Form	`13/36`
Decimal Form	`0.361111`
Percentage	`36.1111%`

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Frequently Asked Questions

What is 5/36 plus 2/9 as a fraction?

5/36 + 2/9 in simplest fraction form is 13/36.

What is 5/36 plus 2/9 as a decimal?

5/36 + 2/9 converted to a decimal is 0.361111.

What is 5/36 plus 2/9 as a percentage?

5/36 + 2/9 expressed as a percentage is 36.1111%.

Does 5/36 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.361111...) because the denominator contains prime factors other than 2 and 5.