What is 2/36 plus 2/10? (Answer: 23/90)

Exact Answer

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Problem: What is 2/36 plus 2/10?
Formula / Expression: 2/36 + 2/10
Final Answer: 23/90
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 36 and 10 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 180 (which is smaller than their product 36 × 10 = 360, keeping the calculation simpler).
Working: LCD(36, 10) = 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 2/10 by 18 so both fractions share the common base 180.
Working: 2 × 5/36 × 5 = 10/180 and 2 × 18/10 × 18 = 36/180

Step 3: Add the Numerators
Now add the numerators (10 + 36 = 46) and keep the common denominator 180 unchanged.
Working: 10 + 36/180 = 46/180

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 46 and 180, which is 2. Divide both the numerator and denominator by 2.
Working: 46 ÷ 2/180 ÷ 2 = 23/90

Step 5: Decimal & Percentage Representation
Dividing the numerator 23 by denominator 90 produces a repeating decimal (approximately 0.255556, or 25.5556%).
Working: 23 ÷ 90 = 0.255556 (25.5556%)

Key Values:
- Simplified Fraction: 23/90
- Mixed Number Form: 23/90
- Decimal Value: 0.255556
- Percentage: 25.5556%

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Solved with FractionsCalc:
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2/36 + 2/10 = 23/90

Simplified Fraction

23/90

Mixed Number

Proper (23/90)

Decimal Value

0.255556

Percentage

25.5556%

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Step-by-Step Solution: 2/36 + 2/10

Step 1

Find the Least Common Denominator (LCD)

The denominators 36 and 10 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 180 (which is smaller than their product 36 × 10 = 360, keeping the calculation simpler).

LCD(36, 10) = 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 2/10 by 18 so both fractions share the common base 180.

2 × 5/36 × 5 = 10/180 and 2 × 18/10 × 18 = 36/180

Step 3

Add the Numerators

Now add the numerators (10 + 36 = 46) and keep the common denominator 180 unchanged.

10 + 36/180 = 46/180

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 46 and 180, which is 2. Divide both the numerator and denominator by 2.

46 ÷ 2/180 ÷ 2 = 23/90

Step 5

Decimal & Percentage Representation

Dividing the numerator 23 by denominator 90 produces a repeating decimal (approximately 0.255556, or 25.5556%).

23 ÷ 90 = 0.255556 (25.5556%)

Visual Representation

The diagram below illustrates 2/36 plus 2/10 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`23/90`
Mixed Number Form	`23/90`
Decimal Form	`0.255556`
Percentage	`25.5556%`

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Frequently Asked Questions

What is 2/36 plus 2/10 as a fraction?

2/36 + 2/10 in simplest fraction form is 23/90.

What is 2/36 plus 2/10 as a decimal?

2/36 + 2/10 converted to a decimal is 0.255556.

What is 2/36 plus 2/10 as a percentage?

2/36 + 2/10 expressed as a percentage is 25.5556%.

Does 2/36 plus 2/10 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.255556...) because the denominator contains prime factors other than 2 and 5.