What is 2/10 plus 9/41? (Answer: 86/205)

Exact Answer

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Problem: What is 2/10 plus 9/41?
Formula / Expression: 2/10 + 9/41
Final Answer: 86/205
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 10 and 41 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 10 × 41 = 410.
Working: LCD(10, 41) = 410

Step 2: Convert to Equivalent Fractions with Common Denominator 410
Multiply the numerator and denominator of 2/10 by 41, and multiply the numerator and denominator of 9/41 by 10 so both fractions share the common base 410.
Working: 2 × 41/10 × 41 = 82/410 and 9 × 10/41 × 10 = 90/410

Step 3: Add the Numerators
Now add the numerators (82 + 90 = 172) and keep the common denominator 410 unchanged.
Working: 82 + 90/410 = 172/410

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 172 and 410, which is 2. Divide both the numerator and denominator by 2.
Working: 172 ÷ 2/410 ÷ 2 = 86/205

Step 5: Decimal & Percentage Representation
Dividing the numerator 86 by denominator 205 produces a repeating decimal (approximately 0.419512, or 41.9512%).
Working: 86 ÷ 205 = 0.419512 (41.9512%)

Key Values:
- Simplified Fraction: 86/205
- Mixed Number Form: 86/205
- Decimal Value: 0.419512
- Percentage: 41.9512%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-10-plus-9-41/
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2/10 + 9/41 = 86/205

Simplified Fraction

86/205

Mixed Number

Proper (86/205)

Decimal Value

0.419512

Percentage

41.9512%

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Step-by-Step Solution: 2/10 + 9/41

Step 1

Find the Least Common Denominator (LCD)

The denominators 10 and 41 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 10 × 41 = 410.

LCD(10, 41) = 410

Step 2

Convert to Equivalent Fractions with Common Denominator 410

Multiply the numerator and denominator of 2/10 by 41, and multiply the numerator and denominator of 9/41 by 10 so both fractions share the common base 410.

2 × 41/10 × 41 = 82/410 and 9 × 10/41 × 10 = 90/410

Step 3

Add the Numerators

Now add the numerators (82 + 90 = 172) and keep the common denominator 410 unchanged.

82 + 90/410 = 172/410

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 172 and 410, which is 2. Divide both the numerator and denominator by 2.

172 ÷ 2/410 ÷ 2 = 86/205

Step 5

Decimal & Percentage Representation

Dividing the numerator 86 by denominator 205 produces a repeating decimal (approximately 0.419512, or 41.9512%).

86 ÷ 205 = 0.419512 (41.9512%)

Visual Representation

The diagram below illustrates 2/10 plus 9/41 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`86/205`
Mixed Number Form	`86/205`
Decimal Form	`0.419512`
Percentage	`41.9512%`

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Frequently Asked Questions

What is 2/10 plus 9/41 as a fraction?

2/10 + 9/41 in simplest fraction form is 86/205.

What is 2/10 plus 9/41 as a decimal?

2/10 + 9/41 converted to a decimal is 0.419512.

What is 2/10 plus 9/41 as a percentage?

2/10 + 9/41 expressed as a percentage is 41.9512%.

Does 2/10 plus 9/41 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.419512...) because the denominator contains prime factors other than 2 and 5.