What is 27/41 plus 9/13? (Answer: 720/533)

Exact Answer

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Problem: What is 27/41 plus 9/13?
Formula / Expression: 27/41 + 9/13
Final Answer: 1 187/533 (720/533)
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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 27/41 by 13, and multiply the numerator and denominator of 9/13 by 41 so both fractions share the common base 533.
Working: 27 × 13/41 × 13 = 351/533 and 9 × 41/13 × 41 = 369/533

Step 3: Add the Numerators
Now add the numerators (351 + 369 = 720) and keep the common denominator 533 unchanged.
Working: 351 + 369/533 = 720/533

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 720 and 533 is 1, confirming that 720/533 cannot be reduced further—it is already in its simplest irreducible form.
Working: 720/533

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (720) is greater than the denominator (533), divide 720 by 533: it goes in 1 whole time(s) with a remainder of 187, giving the mixed number 1 187/533.
Working: 720/533 = 1 187/533

Step 6: Decimal & Percentage Representation
Dividing the numerator 720 by denominator 533 produces a repeating decimal (approximately 1.350844, or 135.0844%).
Working: 720 ÷ 533 = 1.350844 (135.0844%)

Key Values:
- Simplified Fraction: 720/533
- Mixed Number Form: 1 187/533
- Decimal Value: 1.350844
- Percentage: 135.0844%

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Solved with FractionsCalc:
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27/41 + 9/13 = 720/533

Simplified Fraction

720/533

Mixed Number

1 187/533

Decimal Value

1.350844

Percentage

135.0844%

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Step-by-Step Solution: 27/41 + 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 27/41 by 13, and multiply the numerator and denominator of 9/13 by 41 so both fractions share the common base 533.

27 × 13/41 × 13 = 351/533 and 9 × 41/13 × 41 = 369/533

Step 3

Add the Numerators

Now add the numerators (351 + 369 = 720) and keep the common denominator 533 unchanged.

351 + 369/533 = 720/533

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 720 and 533 is 1, confirming that 720/533 cannot be reduced further—it is already in its simplest irreducible form.

720/533

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (720) is greater than the denominator (533), divide 720 by 533: it goes in 1 whole time(s) with a remainder of 187, giving the mixed number 1 187/533.

720/533 = 1187/533

Step 6

Decimal & Percentage Representation

Dividing the numerator 720 by denominator 533 produces a repeating decimal (approximately 1.350844, or 135.0844%).

720 ÷ 533 = 1.350844 (135.0844%)

Visual Representation

The diagram below illustrates 27/41 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`720/533`
Mixed Number Form	`1 187/533`
Decimal Form	`1.350844`
Percentage	`135.0844%`

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Frequently Asked Questions

What is 27/41 plus 9/13 as a fraction?

27/41 + 9/13 in simplest fraction form is 720/533 (or 1 187/533 as a mixed number).

What is 27/41 plus 9/13 as a decimal?

27/41 + 9/13 converted to a decimal is 1.350844.

What is 27/41 plus 9/13 as a percentage?

27/41 + 9/13 expressed as a percentage is 135.0844%.

How do you write 27/41 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 720/533 can be written as the mixed number 1 187/533.

Does 27/41 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.350844...) because the denominator contains prime factors other than 2 and 5.