What is 7/41 plus 2/8? (Answer: 69/164)

Exact Answer

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Problem: What is 7/41 plus 2/8?
Formula / Expression: 7/41 + 2/8
Final Answer: 69/164
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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 7/41 by 8, and multiply the numerator and denominator of 2/8 by 41 so both fractions share the common base 328.
Working: 7 × 8/41 × 8 = 56/328 and 2 × 41/8 × 41 = 82/328

Step 3: Add the Numerators
Now add the numerators (56 + 82 = 138) and keep the common denominator 328 unchanged.
Working: 56 + 82/328 = 138/328

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 138 and 328, which is 2. Divide both the numerator and denominator by 2.
Working: 138 ÷ 2/328 ÷ 2 = 69/164

Step 5: Decimal & Percentage Representation
Dividing the numerator 69 by denominator 164 produces a repeating decimal (approximately 0.420732, or 42.0732%).
Working: 69 ÷ 164 = 0.420732 (42.0732%)

Key Values:
- Simplified Fraction: 69/164
- Mixed Number Form: 69/164
- Decimal Value: 0.420732
- Percentage: 42.0732%

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Solved with FractionsCalc:
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7/41 + 2/8 = 69/164

Simplified Fraction

69/164

Mixed Number

Proper (69/164)

Decimal Value

0.420732

Percentage

42.0732%

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Step-by-Step Solution: 7/41 + 2/8

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 7/41 by 8, and multiply the numerator and denominator of 2/8 by 41 so both fractions share the common base 328.

7 × 8/41 × 8 = 56/328 and 2 × 41/8 × 41 = 82/328

Step 3

Add the Numerators

Now add the numerators (56 + 82 = 138) and keep the common denominator 328 unchanged.

56 + 82/328 = 138/328

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 138 and 328, which is 2. Divide both the numerator and denominator by 2.

138 ÷ 2/328 ÷ 2 = 69/164

Step 5

Decimal & Percentage Representation

Dividing the numerator 69 by denominator 164 produces a repeating decimal (approximately 0.420732, or 42.0732%).

69 ÷ 164 = 0.420732 (42.0732%)

Visual Representation

The diagram below illustrates 7/41 plus 2/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`69/164`
Mixed Number Form	`69/164`
Decimal Form	`0.420732`
Percentage	`42.0732%`

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Frequently Asked Questions

What is 7/41 plus 2/8 as a fraction?

7/41 + 2/8 in simplest fraction form is 69/164.

What is 7/41 plus 2/8 as a decimal?

7/41 + 2/8 converted to a decimal is 0.420732.

What is 7/41 plus 2/8 as a percentage?

7/41 + 2/8 expressed as a percentage is 42.0732%.

Does 7/41 plus 2/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.420732...) because the denominator contains prime factors other than 2 and 5.