What is 2/20 plus 2/18? (Answer: 19/90)

Exact Answer

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Problem: What is 2/20 plus 2/18?
Formula / Expression: 2/20 + 2/18
Final Answer: 19/90
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 20 and 18 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 180 (which is smaller than their product 20 × 18 = 360, keeping the calculation simpler).
Working: LCD(20, 18) = 180

Step 2: Convert to Equivalent Fractions with Common Denominator 180
Multiply the numerator and denominator of 2/20 by 9, and multiply the numerator and denominator of 2/18 by 10 so both fractions share the common base 180.
Working: 2 × 9/20 × 9 = 18/180 and 2 × 10/18 × 10 = 20/180

Step 3: Add the Numerators
Now add the numerators (18 + 20 = 38) and keep the common denominator 180 unchanged.
Working: 18 + 20/180 = 38/180

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 38 and 180, which is 2. Divide both the numerator and denominator by 2.
Working: 38 ÷ 2/180 ÷ 2 = 19/90

Step 5: Decimal & Percentage Representation
Dividing the numerator 19 by denominator 90 produces a repeating decimal (approximately 0.211111, or 21.1111%).
Working: 19 ÷ 90 = 0.211111 (21.1111%)

Key Values:
- Simplified Fraction: 19/90
- Mixed Number Form: 19/90
- Decimal Value: 0.211111
- Percentage: 21.1111%

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Solved with FractionsCalc:
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2/20 + 2/18 = 19/90

Simplified Fraction

19/90

Mixed Number

Proper (19/90)

Decimal Value

0.211111

Percentage

21.1111%

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Step-by-Step Solution: 2/20 + 2/18

Step 1

Find the Least Common Denominator (LCD)

The denominators 20 and 18 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 180 (which is smaller than their product 20 × 18 = 360, keeping the calculation simpler).

LCD(20, 18) = 180

Step 2

Convert to Equivalent Fractions with Common Denominator 180

Multiply the numerator and denominator of 2/20 by 9, and multiply the numerator and denominator of 2/18 by 10 so both fractions share the common base 180.

2 × 9/20 × 9 = 18/180 and 2 × 10/18 × 10 = 20/180

Step 3

Add the Numerators

Now add the numerators (18 + 20 = 38) and keep the common denominator 180 unchanged.

18 + 20/180 = 38/180

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 38 and 180, which is 2. Divide both the numerator and denominator by 2.

38 ÷ 2/180 ÷ 2 = 19/90

Step 5

Decimal & Percentage Representation

Dividing the numerator 19 by denominator 90 produces a repeating decimal (approximately 0.211111, or 21.1111%).

19 ÷ 90 = 0.211111 (21.1111%)

Visual Representation

The diagram below illustrates 2/20 plus 2/18 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`19/90`
Mixed Number Form	`19/90`
Decimal Form	`0.211111`
Percentage	`21.1111%`

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Frequently Asked Questions

What is 2/20 plus 2/18 as a fraction?

2/20 + 2/18 in simplest fraction form is 19/90.

What is 2/20 plus 2/18 as a decimal?

2/20 + 2/18 converted to a decimal is 0.211111.

What is 2/20 plus 2/18 as a percentage?

2/20 + 2/18 expressed as a percentage is 21.1111%.

Does 2/20 plus 2/18 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.211111...) because the denominator contains prime factors other than 2 and 5.