What is 2/38 plus 2/22? (Answer: 30/209)

Exact Answer

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Problem: What is 2/38 plus 2/22?
Formula / Expression: 2/38 + 2/22
Final Answer: 30/209
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 38 and 22 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 418 (which is smaller than their product 38 × 22 = 836, keeping the calculation simpler).
Working: LCD(38, 22) = 418

Step 2: Convert to Equivalent Fractions with Common Denominator 418
Multiply the numerator and denominator of 2/38 by 11, and multiply the numerator and denominator of 2/22 by 19 so both fractions share the common base 418.
Working: 2 × 11/38 × 11 = 22/418 and 2 × 19/22 × 19 = 38/418

Step 3: Add the Numerators
Now add the numerators (22 + 38 = 60) and keep the common denominator 418 unchanged.
Working: 22 + 38/418 = 60/418

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 60 and 418, which is 2. Divide both the numerator and denominator by 2.
Working: 60 ÷ 2/418 ÷ 2 = 30/209

Step 5: Decimal & Percentage Representation
Dividing the numerator 30 by denominator 209 produces a repeating decimal (approximately 0.143541, or 14.3541%).
Working: 30 ÷ 209 = 0.143541 (14.3541%)

Key Values:
- Simplified Fraction: 30/209
- Mixed Number Form: 30/209
- Decimal Value: 0.143541
- Percentage: 14.3541%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-38-plus-2-22/
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2/38 + 2/22 = 30/209

Simplified Fraction

30/209

Mixed Number

Proper (30/209)

Decimal Value

0.143541

Percentage

14.3541%

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Step-by-Step Solution: 2/38 + 2/22

Step 1

Find the Least Common Denominator (LCD)

The denominators 38 and 22 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 418 (which is smaller than their product 38 × 22 = 836, keeping the calculation simpler).

LCD(38, 22) = 418

Step 2

Convert to Equivalent Fractions with Common Denominator 418

Multiply the numerator and denominator of 2/38 by 11, and multiply the numerator and denominator of 2/22 by 19 so both fractions share the common base 418.

2 × 11/38 × 11 = 22/418 and 2 × 19/22 × 19 = 38/418

Step 3

Add the Numerators

Now add the numerators (22 + 38 = 60) and keep the common denominator 418 unchanged.

22 + 38/418 = 60/418

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 60 and 418, which is 2. Divide both the numerator and denominator by 2.

60 ÷ 2/418 ÷ 2 = 30/209

Step 5

Decimal & Percentage Representation

Dividing the numerator 30 by denominator 209 produces a repeating decimal (approximately 0.143541, or 14.3541%).

30 ÷ 209 = 0.143541 (14.3541%)

Visual Representation

The diagram below illustrates 2/38 plus 2/22 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`30/209`
Mixed Number Form	`30/209`
Decimal Form	`0.143541`
Percentage	`14.3541%`

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Frequently Asked Questions

What is 2/38 plus 2/22 as a fraction?

2/38 + 2/22 in simplest fraction form is 30/209.

What is 2/38 plus 2/22 as a decimal?

2/38 + 2/22 converted to a decimal is 0.143541.

What is 2/38 plus 2/22 as a percentage?

2/38 + 2/22 expressed as a percentage is 14.3541%.

Does 2/38 plus 2/22 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.143541...) because the denominator contains prime factors other than 2 and 5.