What is 20/41 plus 9/13? (Answer: 629/533)

Exact Answer

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Problem: What is 20/41 plus 9/13?
Formula / Expression: 20/41 + 9/13
Final Answer: 1 96/533 (629/533)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 41 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 41 × 13 = 533.
Working: LCD(41, 13) = 533

Step 2: Convert to Equivalent Fractions with Common Denominator 533
Multiply the numerator and denominator of 20/41 by 13, and multiply the numerator and denominator of 9/13 by 41 so both fractions share the common base 533.
Working: 20 × 13/41 × 13 = 260/533 and 9 × 41/13 × 41 = 369/533

Step 3: Add the Numerators
Now add the numerators (260 + 369 = 629) and keep the common denominator 533 unchanged.
Working: 260 + 369/533 = 629/533

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 629 and 533 is 1, confirming that 629/533 cannot be reduced further—it is already in its simplest irreducible form.
Working: 629/533

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (629) is greater than the denominator (533), divide 629 by 533: it goes in 1 whole time(s) with a remainder of 96, giving the mixed number 1 96/533.
Working: 629/533 = 1 96/533

Step 6: Decimal & Percentage Representation
Dividing the numerator 629 by denominator 533 produces a repeating decimal (approximately 1.180113, or 118.0113%).
Working: 629 ÷ 533 = 1.180113 (118.0113%)

Key Values:
- Simplified Fraction: 629/533
- Mixed Number Form: 1 96/533
- Decimal Value: 1.180113
- Percentage: 118.0113%

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Solved with FractionsCalc:
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20/41 + 9/13 = 629/533

Simplified Fraction

629/533

Mixed Number

1 96/533

Decimal Value

1.180113

Percentage

118.0113%

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Step-by-Step Solution: 20/41 + 9/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 41 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 41 × 13 = 533.

LCD(41, 13) = 533

Step 2

Convert to Equivalent Fractions with Common Denominator 533

Multiply the numerator and denominator of 20/41 by 13, and multiply the numerator and denominator of 9/13 by 41 so both fractions share the common base 533.

20 × 13/41 × 13 = 260/533 and 9 × 41/13 × 41 = 369/533

Step 3

Add the Numerators

Now add the numerators (260 + 369 = 629) and keep the common denominator 533 unchanged.

260 + 369/533 = 629/533

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 629 and 533 is 1, confirming that 629/533 cannot be reduced further—it is already in its simplest irreducible form.

629/533

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (629) is greater than the denominator (533), divide 629 by 533: it goes in 1 whole time(s) with a remainder of 96, giving the mixed number 1 96/533.

629/533 = 196/533

Step 6

Decimal & Percentage Representation

Dividing the numerator 629 by denominator 533 produces a repeating decimal (approximately 1.180113, or 118.0113%).

629 ÷ 533 = 1.180113 (118.0113%)

Visual Representation

The diagram below illustrates 20/41 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`629/533`
Mixed Number Form	`1 96/533`
Decimal Form	`1.180113`
Percentage	`118.0113%`

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Frequently Asked Questions

What is 20/41 plus 9/13 as a fraction?

20/41 + 9/13 in simplest fraction form is 629/533 (or 1 96/533 as a mixed number).

What is 20/41 plus 9/13 as a decimal?

20/41 + 9/13 converted to a decimal is 1.180113.

What is 20/41 plus 9/13 as a percentage?

20/41 + 9/13 expressed as a percentage is 118.0113%.

How do you write 20/41 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 629/533 can be written as the mixed number 1 96/533.

Does 20/41 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.180113...) because the denominator contains prime factors other than 2 and 5.