What is 2/41 plus 3/8? (Answer: 139/328)

Exact Answer

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Problem: What is 2/41 plus 3/8?
Formula / Expression: 2/41 + 3/8
Final Answer: 139/328
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 41 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 41 × 8 = 328.
Working: LCD(41, 8) = 328

Step 2: Convert to Equivalent Fractions with Common Denominator 328
Multiply the numerator and denominator of 2/41 by 8, and multiply the numerator and denominator of 3/8 by 41 so both fractions share the common base 328.
Working: 2 × 8/41 × 8 = 16/328 and 3 × 41/8 × 41 = 123/328

Step 3: Add the Numerators
Now add the numerators (16 + 123 = 139) and keep the common denominator 328 unchanged.
Working: 16 + 123/328 = 139/328

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 139 and 328 is 1, confirming that 139/328 cannot be reduced further—it is already in its simplest irreducible form.
Working: 139/328

Step 5: Decimal & Percentage Representation
Dividing the numerator 139 by denominator 328 produces a repeating decimal (approximately 0.42378, or 42.378%).
Working: 139 ÷ 328 = 0.42378 (42.378%)

Key Values:
- Simplified Fraction: 139/328
- Mixed Number Form: 139/328
- Decimal Value: 0.42378
- Percentage: 42.378%

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2/41 + 3/8 = 139/328

Simplified Fraction

139/328

Mixed Number

Proper (139/328)

Decimal Value

0.42378

Percentage

42.378%

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Step-by-Step Solution: 2/41 + 3/8

Step 1

Find the Least Common Denominator (LCD)

The denominators 41 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 41 × 8 = 328.

LCD(41, 8) = 328

Step 2

Convert to Equivalent Fractions with Common Denominator 328

Multiply the numerator and denominator of 2/41 by 8, and multiply the numerator and denominator of 3/8 by 41 so both fractions share the common base 328.

2 × 8/41 × 8 = 16/328 and 3 × 41/8 × 41 = 123/328

Step 3

Add the Numerators

Now add the numerators (16 + 123 = 139) and keep the common denominator 328 unchanged.

16 + 123/328 = 139/328

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 139 and 328 is 1, confirming that 139/328 cannot be reduced further—it is already in its simplest irreducible form.

139/328

Step 5

Decimal & Percentage Representation

Dividing the numerator 139 by denominator 328 produces a repeating decimal (approximately 0.42378, or 42.378%).

139 ÷ 328 = 0.42378 (42.378%)

Visual Representation

The diagram below illustrates 2/41 plus 3/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`139/328`
Mixed Number Form	`139/328`
Decimal Form	`0.42378`
Percentage	`42.378%`

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Frequently Asked Questions

What is 2/41 plus 3/8 as a fraction?

2/41 + 3/8 in simplest fraction form is 139/328.

What is 2/41 plus 3/8 as a decimal?

2/41 + 3/8 converted to a decimal is 0.42378.

What is 2/41 plus 3/8 as a percentage?

2/41 + 3/8 expressed as a percentage is 42.378%.

Does 2/41 plus 3/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.42378...) because the denominator contains prime factors other than 2 and 5.