What is 5/21 plus 10/41? (Answer: 415/861)

Exact Answer

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Problem: What is 5/21 plus 10/41?
Formula / Expression: 5/21 + 10/41
Final Answer: 415/861
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 41 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 41 = 861.
Working: LCD(21, 41) = 861

Step 2: Convert to Equivalent Fractions with Common Denominator 861
Multiply the numerator and denominator of 5/21 by 41, and multiply the numerator and denominator of 10/41 by 21 so both fractions share the common base 861.
Working: 5 × 41/21 × 41 = 205/861 and 10 × 21/41 × 21 = 210/861

Step 3: Add the Numerators
Now add the numerators (205 + 210 = 415) and keep the common denominator 861 unchanged.
Working: 205 + 210/861 = 415/861

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 415 and 861 is 1, confirming that 415/861 cannot be reduced further—it is already in its simplest irreducible form.
Working: 415/861

Step 5: Decimal & Percentage Representation
Dividing the numerator 415 by denominator 861 produces a repeating decimal (approximately 0.481998, or 48.1998%).
Working: 415 ÷ 861 = 0.481998 (48.1998%)

Key Values:
- Simplified Fraction: 415/861
- Mixed Number Form: 415/861
- Decimal Value: 0.481998
- Percentage: 48.1998%

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Solved with FractionsCalc:
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5/21 + 10/41 = 415/861

Simplified Fraction

415/861

Mixed Number

Proper (415/861)

Decimal Value

0.481998

Percentage

48.1998%

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Step-by-Step Solution: 5/21 + 10/41

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 41 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 41 = 861.

LCD(21, 41) = 861

Step 2

Convert to Equivalent Fractions with Common Denominator 861

Multiply the numerator and denominator of 5/21 by 41, and multiply the numerator and denominator of 10/41 by 21 so both fractions share the common base 861.

5 × 41/21 × 41 = 205/861 and 10 × 21/41 × 21 = 210/861

Step 3

Add the Numerators

Now add the numerators (205 + 210 = 415) and keep the common denominator 861 unchanged.

205 + 210/861 = 415/861

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 415 and 861 is 1, confirming that 415/861 cannot be reduced further—it is already in its simplest irreducible form.

415/861

Step 5

Decimal & Percentage Representation

Dividing the numerator 415 by denominator 861 produces a repeating decimal (approximately 0.481998, or 48.1998%).

415 ÷ 861 = 0.481998 (48.1998%)

Visual Representation

The diagram below illustrates 5/21 plus 10/41 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`415/861`
Mixed Number Form	`415/861`
Decimal Form	`0.481998`
Percentage	`48.1998%`

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Frequently Asked Questions

What is 5/21 plus 10/41 as a fraction?

5/21 + 10/41 in simplest fraction form is 415/861.

What is 5/21 plus 10/41 as a decimal?

5/21 + 10/41 converted to a decimal is 0.481998.

What is 5/21 plus 10/41 as a percentage?

5/21 + 10/41 expressed as a percentage is 48.1998%.

Does 5/21 plus 10/41 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.481998...) because the denominator contains prime factors other than 2 and 5.