What is 2/36 plus 2/5? (Answer: 41/90)

Exact Answer

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Problem: What is 2/36 plus 2/5?
Formula / Expression: 2/36 + 2/5
Final Answer: 41/90
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 36 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 36 × 5 = 180.
Working: LCD(36, 5) = 180

Step 2: Convert to Equivalent Fractions with Common Denominator 180
Multiply the numerator and denominator of 2/36 by 5, and multiply the numerator and denominator of 2/5 by 36 so both fractions share the common base 180.
Working: 2 × 5/36 × 5 = 10/180 and 2 × 36/5 × 36 = 72/180

Step 3: Add the Numerators
Now add the numerators (10 + 72 = 82) and keep the common denominator 180 unchanged.
Working: 10 + 72/180 = 82/180

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 82 and 180, which is 2. Divide both the numerator and denominator by 2.
Working: 82 ÷ 2/180 ÷ 2 = 41/90

Step 5: Decimal & Percentage Representation
Dividing the numerator 41 by denominator 90 produces a repeating decimal (approximately 0.455556, or 45.5556%).
Working: 41 ÷ 90 = 0.455556 (45.5556%)

Key Values:
- Simplified Fraction: 41/90
- Mixed Number Form: 41/90
- Decimal Value: 0.455556
- Percentage: 45.5556%

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Solved with FractionsCalc:
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2/36 + 2/5 = 41/90

Simplified Fraction

41/90

Mixed Number

Proper (41/90)

Decimal Value

0.455556

Percentage

45.5556%

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

Step 1

Find the Least Common Denominator (LCD)

The denominators 36 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 36 × 5 = 180.

LCD(36, 5) = 180

Step 2

Convert to Equivalent Fractions with Common Denominator 180

Multiply the numerator and denominator of 2/36 by 5, and multiply the numerator and denominator of 2/5 by 36 so both fractions share the common base 180.

2 × 5/36 × 5 = 10/180 and 2 × 36/5 × 36 = 72/180

Step 3

Add the Numerators

Now add the numerators (10 + 72 = 82) and keep the common denominator 180 unchanged.

10 + 72/180 = 82/180

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 82 and 180, which is 2. Divide both the numerator and denominator by 2.

82 ÷ 2/180 ÷ 2 = 41/90

Step 5

Decimal & Percentage Representation

Dividing the numerator 41 by denominator 90 produces a repeating decimal (approximately 0.455556, or 45.5556%).

41 ÷ 90 = 0.455556 (45.5556%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`41/90`
Mixed Number Form	`41/90`
Decimal Form	`0.455556`
Percentage	`45.5556%`

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Frequently Asked Questions

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

2/36 + 2/5 in simplest fraction form is 41/90.

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

2/36 + 2/5 converted to a decimal is 0.455556.

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

2/36 + 2/5 expressed as a percentage is 45.5556%.

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

It results in a repeating decimal (approximately 0.455556...) because the denominator contains prime factors other than 2 and 5.