What is 19/37 plus 9/13?
19/37 plus 9/13 equals 580/481 (or 1 99/481 as a mixed number) (or 1.205821 in decimal form). Learn the step-by-step solution to add 19/37 and 9/13 using Least Common Denominator and simplification.
Exact Answer
19/37 + 9/13 = 580/481
Simplified Fraction
580/481
Mixed Number
1 99/481
Decimal Value
1.205821
Percentage
120.5821%
Step-by-Step Solution: 19/37 + 9/13
Step 1
Find the Least Common Denominator (LCD)
The denominators 37 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 37 × 13 = 481.
LCD(37, 13) = 481
Step 2
Convert to Equivalent Fractions with Common Denominator 481
Multiply the numerator and denominator of 19/37 by 13, and multiply the numerator and denominator of 9/13 by 37 so both fractions share the common base 481.
19 × 13/37 × 13 = 247/481 and 9 × 37/13 × 37 = 333/481
Step 3
Add the Numerators
Now add the numerators (247 + 333 = 580) and keep the common denominator 481 unchanged.
247 + 333/481 = 580/481
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 580 and 481 is 1, confirming that 580/481 cannot be reduced further—it is already in its simplest irreducible form.
580/481
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (580) is greater than the denominator (481), divide 580 by 481: it goes in 1 whole time(s) with a remainder of 99, giving the mixed number 1 99/481.
580/481 = 199/481
Step 6
Decimal & Percentage Representation
Dividing the numerator 580 by denominator 481 produces a repeating decimal (approximately 1.205821, or 120.5821%).
580 ÷ 481 = 1.205821 (120.5821%)
Visual Representation
The diagram below illustrates 19/37 plus 9/13 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 580/481 |
| Mixed Number Form | 1 99/481 |
| Decimal Form | 1.205821 |
| Percentage | 120.5821% |
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Frequently Asked Questions
What is 19/37 plus 9/13 as a fraction?
19/37 + 9/13 in simplest fraction form is 580/481 (or 1 99/481 as a mixed number).
What is 19/37 plus 9/13 as a decimal?
19/37 + 9/13 converted to a decimal is 1.205821.
What is 19/37 plus 9/13 as a percentage?
19/37 + 9/13 expressed as a percentage is 120.5821%.
How do you write 19/37 plus 9/13 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 580/481 can be written as the mixed number 1 99/481.
Does 19/37 plus 9/13 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.205821...) because the denominator contains prime factors other than 2 and 5.