What is 2/38 plus 2/5? (Answer: 43/95)

Exact Answer

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Problem: What is 2/38 plus 2/5?
Formula / Expression: 2/38 + 2/5
Final Answer: 43/95
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 38 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 38 × 5 = 190.
Working: LCD(38, 5) = 190

Step 2: Convert to Equivalent Fractions with Common Denominator 190
Multiply the numerator and denominator of 2/38 by 5, and multiply the numerator and denominator of 2/5 by 38 so both fractions share the common base 190.
Working: 2 × 5/38 × 5 = 10/190 and 2 × 38/5 × 38 = 76/190

Step 3: Add the Numerators
Now add the numerators (10 + 76 = 86) and keep the common denominator 190 unchanged.
Working: 10 + 76/190 = 86/190

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 86 and 190, which is 2. Divide both the numerator and denominator by 2.
Working: 86 ÷ 2/190 ÷ 2 = 43/95

Step 5: Decimal & Percentage Representation
Dividing the numerator 43 by denominator 95 produces a repeating decimal (approximately 0.452632, or 45.2632%).
Working: 43 ÷ 95 = 0.452632 (45.2632%)

Key Values:
- Simplified Fraction: 43/95
- Mixed Number Form: 43/95
- Decimal Value: 0.452632
- Percentage: 45.2632%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-38-plus-2-5/
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2/38 + 2/5 = 43/95

Simplified Fraction

43/95

Mixed Number

Proper (43/95)

Decimal Value

0.452632

Percentage

45.2632%

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Step-by-Step Solution: 2/38 + 2/5

Step 1

Find the Least Common Denominator (LCD)

The denominators 38 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 38 × 5 = 190.

LCD(38, 5) = 190

Step 2

Convert to Equivalent Fractions with Common Denominator 190

Multiply the numerator and denominator of 2/38 by 5, and multiply the numerator and denominator of 2/5 by 38 so both fractions share the common base 190.

2 × 5/38 × 5 = 10/190 and 2 × 38/5 × 38 = 76/190

Step 3

Add the Numerators

Now add the numerators (10 + 76 = 86) and keep the common denominator 190 unchanged.

10 + 76/190 = 86/190

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 86 and 190, which is 2. Divide both the numerator and denominator by 2.

86 ÷ 2/190 ÷ 2 = 43/95

Step 5

Decimal & Percentage Representation

Dividing the numerator 43 by denominator 95 produces a repeating decimal (approximately 0.452632, or 45.2632%).

43 ÷ 95 = 0.452632 (45.2632%)

Visual Representation

The diagram below illustrates 2/38 plus 2/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`43/95`
Mixed Number Form	`43/95`
Decimal Form	`0.452632`
Percentage	`45.2632%`

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Frequently Asked Questions

What is 2/38 plus 2/5 as a fraction?

2/38 + 2/5 in simplest fraction form is 43/95.

What is 2/38 plus 2/5 as a decimal?

2/38 + 2/5 converted to a decimal is 0.452632.

What is 2/38 plus 2/5 as a percentage?

2/38 + 2/5 expressed as a percentage is 45.2632%.

Does 2/38 plus 2/5 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.452632...) because the denominator contains prime factors other than 2 and 5.