What is 2/22 plus 2/20? (Answer: 21/110)

Exact Answer

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Problem: What is 2/22 plus 2/20?
Formula / Expression: 2/22 + 2/20
Final Answer: 21/110
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 22 and 20 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 220 (which is smaller than their product 22 × 20 = 440, keeping the calculation simpler).
Working: LCD(22, 20) = 220

Step 2: Convert to Equivalent Fractions with Common Denominator 220
Multiply the numerator and denominator of 2/22 by 10, and multiply the numerator and denominator of 2/20 by 11 so both fractions share the common base 220.
Working: 2 × 10/22 × 10 = 20/220 and 2 × 11/20 × 11 = 22/220

Step 3: Add the Numerators
Now add the numerators (20 + 22 = 42) and keep the common denominator 220 unchanged.
Working: 20 + 22/220 = 42/220

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 42 and 220, which is 2. Divide both the numerator and denominator by 2.
Working: 42 ÷ 2/220 ÷ 2 = 21/110

Step 5: Decimal & Percentage Representation
Dividing the numerator 21 by denominator 110 produces a repeating decimal (approximately 0.190909, or 19.0909%).
Working: 21 ÷ 110 = 0.190909 (19.0909%)

Key Values:
- Simplified Fraction: 21/110
- Mixed Number Form: 21/110
- Decimal Value: 0.190909
- Percentage: 19.0909%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-22-plus-2-20/
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2/22 + 2/20 = 21/110

Simplified Fraction

21/110

Mixed Number

Proper (21/110)

Decimal Value

0.190909

Percentage

19.0909%

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Step-by-Step Solution: 2/22 + 2/20

Step 1

Find the Least Common Denominator (LCD)

The denominators 22 and 20 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 220 (which is smaller than their product 22 × 20 = 440, keeping the calculation simpler).

LCD(22, 20) = 220

Step 2

Convert to Equivalent Fractions with Common Denominator 220

Multiply the numerator and denominator of 2/22 by 10, and multiply the numerator and denominator of 2/20 by 11 so both fractions share the common base 220.

2 × 10/22 × 10 = 20/220 and 2 × 11/20 × 11 = 22/220

Step 3

Add the Numerators

Now add the numerators (20 + 22 = 42) and keep the common denominator 220 unchanged.

20 + 22/220 = 42/220

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 42 and 220, which is 2. Divide both the numerator and denominator by 2.

42 ÷ 2/220 ÷ 2 = 21/110

Step 5

Decimal & Percentage Representation

Dividing the numerator 21 by denominator 110 produces a repeating decimal (approximately 0.190909, or 19.0909%).

21 ÷ 110 = 0.190909 (19.0909%)

Visual Representation

The diagram below illustrates 2/22 plus 2/20 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`21/110`
Mixed Number Form	`21/110`
Decimal Form	`0.190909`
Percentage	`19.0909%`

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Frequently Asked Questions

What is 2/22 plus 2/20 as a fraction?

2/22 + 2/20 in simplest fraction form is 21/110.

What is 2/22 plus 2/20 as a decimal?

2/22 + 2/20 converted to a decimal is 0.190909.

What is 2/22 plus 2/20 as a percentage?

2/22 + 2/20 expressed as a percentage is 19.0909%.

Does 2/22 plus 2/20 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.190909...) because the denominator contains prime factors other than 2 and 5.