What is 13/41 plus 15/21? (Answer: 296/287)

Exact Answer

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Problem: What is 13/41 plus 15/21?
Formula / Expression: 13/41 + 15/21
Final Answer: 1 9/287 (296/287)
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 861
Multiply the numerator and denominator of 13/41 by 21, and multiply the numerator and denominator of 15/21 by 41 so both fractions share the common base 861.
Working: 13 × 21/41 × 21 = 273/861 and 15 × 41/21 × 41 = 615/861

Step 3: Add the Numerators
Now add the numerators (273 + 615 = 888) and keep the common denominator 861 unchanged.
Working: 273 + 615/861 = 888/861

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 888 and 861, which is 3. Divide both the numerator and denominator by 3.
Working: 888 ÷ 3/861 ÷ 3 = 296/287

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (296) is greater than the denominator (287), divide 296 by 287: it goes in 1 whole time(s) with a remainder of 9, giving the mixed number 1 9/287.
Working: 296/287 = 1 9/287

Step 6: Decimal & Percentage Representation
Dividing the numerator 296 by denominator 287 produces a repeating decimal (approximately 1.031359, or 103.1359%).
Working: 296 ÷ 287 = 1.031359 (103.1359%)

Key Values:
- Simplified Fraction: 296/287
- Mixed Number Form: 1 9/287
- Decimal Value: 1.031359
- Percentage: 103.1359%

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Solved with FractionsCalc:
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13/41 + 15/21 = 296/287

Simplified Fraction

296/287

Mixed Number

1 9/287

Decimal Value

1.031359

Percentage

103.1359%

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Step-by-Step Solution: 13/41 + 15/21

Step 1

Find the Least Common Denominator (LCD)

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

LCD(41, 21) = 861

Step 2

Convert to Equivalent Fractions with Common Denominator 861

Multiply the numerator and denominator of 13/41 by 21, and multiply the numerator and denominator of 15/21 by 41 so both fractions share the common base 861.

13 × 21/41 × 21 = 273/861 and 15 × 41/21 × 41 = 615/861

Step 3

Add the Numerators

Now add the numerators (273 + 615 = 888) and keep the common denominator 861 unchanged.

273 + 615/861 = 888/861

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 888 and 861, which is 3. Divide both the numerator and denominator by 3.

888 ÷ 3/861 ÷ 3 = 296/287

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (296) is greater than the denominator (287), divide 296 by 287: it goes in 1 whole time(s) with a remainder of 9, giving the mixed number 1 9/287.

296/287 = 19/287

Step 6

Decimal & Percentage Representation

Dividing the numerator 296 by denominator 287 produces a repeating decimal (approximately 1.031359, or 103.1359%).

296 ÷ 287 = 1.031359 (103.1359%)

Visual Representation

The diagram below illustrates 13/41 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`296/287`
Mixed Number Form	`1 9/287`
Decimal Form	`1.031359`
Percentage	`103.1359%`

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Frequently Asked Questions

What is 13/41 plus 15/21 as a fraction?

13/41 + 15/21 in simplest fraction form is 296/287 (or 1 9/287 as a mixed number).

What is 13/41 plus 15/21 as a decimal?

13/41 + 15/21 converted to a decimal is 1.031359.

What is 13/41 plus 15/21 as a percentage?

13/41 + 15/21 expressed as a percentage is 103.1359%.

How do you write 13/41 plus 15/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 296/287 can be written as the mixed number 1 9/287.

Does 13/41 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.031359...) because the denominator contains prime factors other than 2 and 5.