What is 3/41 plus 3/9? (Answer: 50/123)

Exact Answer

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Problem: What is 3/41 plus 3/9?
Formula / Expression: 3/41 + 3/9
Final Answer: 50/123
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 41 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 41 × 9 = 369.
Working: LCD(41, 9) = 369

Step 2: Convert to Equivalent Fractions with Common Denominator 369
Multiply the numerator and denominator of 3/41 by 9, and multiply the numerator and denominator of 3/9 by 41 so both fractions share the common base 369.
Working: 3 × 9/41 × 9 = 27/369 and 3 × 41/9 × 41 = 123/369

Step 3: Add the Numerators
Now add the numerators (27 + 123 = 150) and keep the common denominator 369 unchanged.
Working: 27 + 123/369 = 150/369

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 150 and 369, which is 3. Divide both the numerator and denominator by 3.
Working: 150 ÷ 3/369 ÷ 3 = 50/123

Step 5: Decimal & Percentage Representation
Dividing the numerator 50 by denominator 123 produces a repeating decimal (approximately 0.406504, or 40.6504%).
Working: 50 ÷ 123 = 0.406504 (40.6504%)

Key Values:
- Simplified Fraction: 50/123
- Mixed Number Form: 50/123
- Decimal Value: 0.406504
- Percentage: 40.6504%

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Solved with FractionsCalc:
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3/41 + 3/9 = 50/123

Simplified Fraction

50/123

Mixed Number

Proper (50/123)

Decimal Value

0.406504

Percentage

40.6504%

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Step-by-Step Solution: 3/41 + 3/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 41 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 41 × 9 = 369.

LCD(41, 9) = 369

Step 2

Convert to Equivalent Fractions with Common Denominator 369

Multiply the numerator and denominator of 3/41 by 9, and multiply the numerator and denominator of 3/9 by 41 so both fractions share the common base 369.

3 × 9/41 × 9 = 27/369 and 3 × 41/9 × 41 = 123/369

Step 3

Add the Numerators

Now add the numerators (27 + 123 = 150) and keep the common denominator 369 unchanged.

27 + 123/369 = 150/369

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 150 and 369, which is 3. Divide both the numerator and denominator by 3.

150 ÷ 3/369 ÷ 3 = 50/123

Step 5

Decimal & Percentage Representation

Dividing the numerator 50 by denominator 123 produces a repeating decimal (approximately 0.406504, or 40.6504%).

50 ÷ 123 = 0.406504 (40.6504%)

Visual Representation

The diagram below illustrates 3/41 plus 3/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`50/123`
Mixed Number Form	`50/123`
Decimal Form	`0.406504`
Percentage	`40.6504%`

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Frequently Asked Questions

What is 3/41 plus 3/9 as a fraction?

3/41 + 3/9 in simplest fraction form is 50/123.

What is 3/41 plus 3/9 as a decimal?

3/41 + 3/9 converted to a decimal is 0.406504.

What is 3/41 plus 3/9 as a percentage?

3/41 + 3/9 expressed as a percentage is 40.6504%.

Does 3/41 plus 3/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.406504...) because the denominator contains prime factors other than 2 and 5.