What is 2/36 plus 2/22? (Answer: 29/198)

Exact Answer

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Problem: What is 2/36 plus 2/22?
Formula / Expression: 2/36 + 2/22
Final Answer: 29/198
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 36 and 22 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 396 (which is smaller than their product 36 × 22 = 792, keeping the calculation simpler).
Working: LCD(36, 22) = 396

Step 2: Convert to Equivalent Fractions with Common Denominator 396
Multiply the numerator and denominator of 2/36 by 11, and multiply the numerator and denominator of 2/22 by 18 so both fractions share the common base 396.
Working: 2 × 11/36 × 11 = 22/396 and 2 × 18/22 × 18 = 36/396

Step 3: Add the Numerators
Now add the numerators (22 + 36 = 58) and keep the common denominator 396 unchanged.
Working: 22 + 36/396 = 58/396

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 58 and 396, which is 2. Divide both the numerator and denominator by 2.
Working: 58 ÷ 2/396 ÷ 2 = 29/198

Step 5: Decimal & Percentage Representation
Dividing the numerator 29 by denominator 198 produces a repeating decimal (approximately 0.146465, or 14.6465%).
Working: 29 ÷ 198 = 0.146465 (14.6465%)

Key Values:
- Simplified Fraction: 29/198
- Mixed Number Form: 29/198
- Decimal Value: 0.146465
- Percentage: 14.6465%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-36-plus-2-22/
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2/36 + 2/22 = 29/198

Simplified Fraction

29/198

Mixed Number

Proper (29/198)

Decimal Value

0.146465

Percentage

14.6465%

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Step-by-Step Solution: 2/36 + 2/22

Step 1

Find the Least Common Denominator (LCD)

The denominators 36 and 22 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 396 (which is smaller than their product 36 × 22 = 792, keeping the calculation simpler).

LCD(36, 22) = 396

Step 2

Convert to Equivalent Fractions with Common Denominator 396

Multiply the numerator and denominator of 2/36 by 11, and multiply the numerator and denominator of 2/22 by 18 so both fractions share the common base 396.

2 × 11/36 × 11 = 22/396 and 2 × 18/22 × 18 = 36/396

Step 3

Add the Numerators

Now add the numerators (22 + 36 = 58) and keep the common denominator 396 unchanged.

22 + 36/396 = 58/396

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 58 and 396, which is 2. Divide both the numerator and denominator by 2.

58 ÷ 2/396 ÷ 2 = 29/198

Step 5

Decimal & Percentage Representation

Dividing the numerator 29 by denominator 198 produces a repeating decimal (approximately 0.146465, or 14.6465%).

29 ÷ 198 = 0.146465 (14.6465%)

Visual Representation

The diagram below illustrates 2/36 plus 2/22 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`29/198`
Mixed Number Form	`29/198`
Decimal Form	`0.146465`
Percentage	`14.6465%`

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Frequently Asked Questions

What is 2/36 plus 2/22 as a fraction?

2/36 + 2/22 in simplest fraction form is 29/198.

What is 2/36 plus 2/22 as a decimal?

2/36 + 2/22 converted to a decimal is 0.146465.

What is 2/36 plus 2/22 as a percentage?

2/36 + 2/22 expressed as a percentage is 14.6465%.

Does 2/36 plus 2/22 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.146465...) because the denominator contains prime factors other than 2 and 5.