What is 2/20 plus 2/19? (Answer: 39/190)

Exact Answer

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Problem: What is 2/20 plus 2/19?
Formula / Expression: 2/20 + 2/19
Final Answer: 39/190
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 20 and 19 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 20 × 19 = 380.
Working: LCD(20, 19) = 380

Step 2: Convert to Equivalent Fractions with Common Denominator 380
Multiply the numerator and denominator of 2/20 by 19, and multiply the numerator and denominator of 2/19 by 20 so both fractions share the common base 380.
Working: 2 × 19/20 × 19 = 38/380 and 2 × 20/19 × 20 = 40/380

Step 3: Add the Numerators
Now add the numerators (38 + 40 = 78) and keep the common denominator 380 unchanged.
Working: 38 + 40/380 = 78/380

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 78 and 380, which is 2. Divide both the numerator and denominator by 2.
Working: 78 ÷ 2/380 ÷ 2 = 39/190

Step 5: Decimal & Percentage Representation
Dividing the numerator 39 by denominator 190 produces a repeating decimal (approximately 0.205263, or 20.5263%).
Working: 39 ÷ 190 = 0.205263 (20.5263%)

Key Values:
- Simplified Fraction: 39/190
- Mixed Number Form: 39/190
- Decimal Value: 0.205263
- Percentage: 20.5263%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-20-plus-2-19/
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2/20 + 2/19 = 39/190

Simplified Fraction

39/190

Mixed Number

Proper (39/190)

Decimal Value

0.205263

Percentage

20.5263%

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Step-by-Step Solution: 2/20 + 2/19

Step 1

Find the Least Common Denominator (LCD)

The denominators 20 and 19 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 20 × 19 = 380.

LCD(20, 19) = 380

Step 2

Convert to Equivalent Fractions with Common Denominator 380

Multiply the numerator and denominator of 2/20 by 19, and multiply the numerator and denominator of 2/19 by 20 so both fractions share the common base 380.

2 × 19/20 × 19 = 38/380 and 2 × 20/19 × 20 = 40/380

Step 3

Add the Numerators

Now add the numerators (38 + 40 = 78) and keep the common denominator 380 unchanged.

38 + 40/380 = 78/380

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 78 and 380, which is 2. Divide both the numerator and denominator by 2.

78 ÷ 2/380 ÷ 2 = 39/190

Step 5

Decimal & Percentage Representation

Dividing the numerator 39 by denominator 190 produces a repeating decimal (approximately 0.205263, or 20.5263%).

39 ÷ 190 = 0.205263 (20.5263%)

Visual Representation

The diagram below illustrates 2/20 plus 2/19 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`39/190`
Mixed Number Form	`39/190`
Decimal Form	`0.205263`
Percentage	`20.5263%`

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Frequently Asked Questions

What is 2/20 plus 2/19 as a fraction?

2/20 + 2/19 in simplest fraction form is 39/190.

What is 2/20 plus 2/19 as a decimal?

2/20 + 2/19 converted to a decimal is 0.205263.

What is 2/20 plus 2/19 as a percentage?

2/20 + 2/19 expressed as a percentage is 20.5263%.

Does 2/20 plus 2/19 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.205263...) because the denominator contains prime factors other than 2 and 5.