What is 21/41 plus 9/13?
21/41 plus 9/13 equals 642/533 (or 1 109/533 as a mixed number) (or 1.204503 in decimal form). Learn the step-by-step solution to add 21/41 and 9/13 using Least Common Denominator and simplification.
Exact Answer
21/41 + 9/13 = 642/533
Simplified Fraction
642/533
Mixed Number
1 109/533
Decimal Value
1.204503
Percentage
120.4503%
Step-by-Step Solution: 21/41 + 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 21/41 by 13, and multiply the numerator and denominator of 9/13 by 41 so both fractions share the common base 533.
21 × 13/41 × 13 = 273/533 and 9 × 41/13 × 41 = 369/533
Step 3
Add the Numerators
Now add the numerators (273 + 369 = 642) and keep the common denominator 533 unchanged.
273 + 369/533 = 642/533
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 642 and 533 is 1, confirming that 642/533 cannot be reduced further—it is already in its simplest irreducible form.
642/533
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (642) is greater than the denominator (533), divide 642 by 533: it goes in 1 whole time(s) with a remainder of 109, giving the mixed number 1 109/533.
642/533 = 1109/533
Step 6
Decimal & Percentage Representation
Dividing the numerator 642 by denominator 533 produces a repeating decimal (approximately 1.204503, or 120.4503%).
642 ÷ 533 = 1.204503 (120.4503%)
Visual Representation
The diagram below illustrates 21/41 plus 9/13 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 642/533 |
| Mixed Number Form | 1 109/533 |
| Decimal Form | 1.204503 |
| Percentage | 120.4503% |
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Frequently Asked Questions
What is 21/41 plus 9/13 as a fraction?
21/41 + 9/13 in simplest fraction form is 642/533 (or 1 109/533 as a mixed number).
What is 21/41 plus 9/13 as a decimal?
21/41 + 9/13 converted to a decimal is 1.204503.
What is 21/41 plus 9/13 as a percentage?
21/41 + 9/13 expressed as a percentage is 120.4503%.
How do you write 21/41 plus 9/13 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 642/533 can be written as the mixed number 1 109/533.
Does 21/41 plus 9/13 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.204503...) because the denominator contains prime factors other than 2 and 5.