What is 2/22 plus 2/18? (Answer: 20/99)

Exact Answer

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Problem: What is 2/22 plus 2/18?
Formula / Expression: 2/22 + 2/18
Final Answer: 20/99
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 22 and 18 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 198 (which is smaller than their product 22 × 18 = 396, keeping the calculation simpler).
Working: LCD(22, 18) = 198

Step 2: Convert to Equivalent Fractions with Common Denominator 198
Multiply the numerator and denominator of 2/22 by 9, and multiply the numerator and denominator of 2/18 by 11 so both fractions share the common base 198.
Working: 2 × 9/22 × 9 = 18/198 and 2 × 11/18 × 11 = 22/198

Step 3: Add the Numerators
Now add the numerators (18 + 22 = 40) and keep the common denominator 198 unchanged.
Working: 18 + 22/198 = 40/198

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 40 and 198, which is 2. Divide both the numerator and denominator by 2.
Working: 40 ÷ 2/198 ÷ 2 = 20/99

Step 5: Decimal & Percentage Representation
Dividing the numerator 20 by denominator 99 produces a repeating decimal (approximately 0.20202, or 20.202%).
Working: 20 ÷ 99 = 0.20202 (20.202%)

Key Values:
- Simplified Fraction: 20/99
- Mixed Number Form: 20/99
- Decimal Value: 0.20202
- Percentage: 20.202%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-22-plus-2-18/
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2/22 + 2/18 = 20/99

Simplified Fraction

20/99

Mixed Number

Proper (20/99)

Decimal Value

0.20202

Percentage

20.202%

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Step-by-Step Solution: 2/22 + 2/18

Step 1

Find the Least Common Denominator (LCD)

The denominators 22 and 18 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 198 (which is smaller than their product 22 × 18 = 396, keeping the calculation simpler).

LCD(22, 18) = 198

Step 2

Convert to Equivalent Fractions with Common Denominator 198

Multiply the numerator and denominator of 2/22 by 9, and multiply the numerator and denominator of 2/18 by 11 so both fractions share the common base 198.

2 × 9/22 × 9 = 18/198 and 2 × 11/18 × 11 = 22/198

Step 3

Add the Numerators

Now add the numerators (18 + 22 = 40) and keep the common denominator 198 unchanged.

18 + 22/198 = 40/198

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 40 and 198, which is 2. Divide both the numerator and denominator by 2.

40 ÷ 2/198 ÷ 2 = 20/99

Step 5

Decimal & Percentage Representation

Dividing the numerator 20 by denominator 99 produces a repeating decimal (approximately 0.20202, or 20.202%).

20 ÷ 99 = 0.20202 (20.202%)

Visual Representation

The diagram below illustrates 2/22 plus 2/18 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`20/99`
Mixed Number Form	`20/99`
Decimal Form	`0.20202`
Percentage	`20.202%`

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Frequently Asked Questions

What is 2/22 plus 2/18 as a fraction?

2/22 + 2/18 in simplest fraction form is 20/99.

What is 2/22 plus 2/18 as a decimal?

2/22 + 2/18 converted to a decimal is 0.20202.

What is 2/22 plus 2/18 as a percentage?

2/22 + 2/18 expressed as a percentage is 20.202%.

Does 2/22 plus 2/18 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.20202...) because the denominator contains prime factors other than 2 and 5.