What is 19/28 plus 9/13?
19/28 plus 9/13 equals 499/364 (or 1 135/364 as a mixed number) (or 1.370879 in decimal form). Learn the step-by-step solution to add 19/28 and 9/13 using Least Common Denominator and simplification.
Exact Answer
19/28 + 9/13 = 499/364
Simplified Fraction
499/364
Mixed Number
1 135/364
Decimal Value
1.370879
Percentage
137.0879%
Step-by-Step Solution: 19/28 + 9/13
Step 1
Find the Least Common Denominator (LCD)
The denominators 28 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 28 × 13 = 364.
LCD(28, 13) = 364
Step 2
Convert to Equivalent Fractions with Common Denominator 364
Multiply the numerator and denominator of 19/28 by 13, and multiply the numerator and denominator of 9/13 by 28 so both fractions share the common base 364.
19 × 13/28 × 13 = 247/364 and 9 × 28/13 × 28 = 252/364
Step 3
Add the Numerators
Now add the numerators (247 + 252 = 499) and keep the common denominator 364 unchanged.
247 + 252/364 = 499/364
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 499 and 364 is 1, confirming that 499/364 cannot be reduced further—it is already in its simplest irreducible form.
499/364
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (499) is greater than the denominator (364), divide 499 by 364: it goes in 1 whole time(s) with a remainder of 135, giving the mixed number 1 135/364.
499/364 = 1135/364
Step 6
Decimal & Percentage Representation
Dividing the numerator 499 by denominator 364 produces a repeating decimal (approximately 1.370879, or 137.0879%).
499 ÷ 364 = 1.370879 (137.0879%)
Visual Representation
The diagram below illustrates 19/28 plus 9/13 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 499/364 |
| Mixed Number Form | 1 135/364 |
| Decimal Form | 1.370879 |
| Percentage | 137.0879% |
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Frequently Asked Questions
What is 19/28 plus 9/13 as a fraction?
19/28 + 9/13 in simplest fraction form is 499/364 (or 1 135/364 as a mixed number).
What is 19/28 plus 9/13 as a decimal?
19/28 + 9/13 converted to a decimal is 1.370879.
What is 19/28 plus 9/13 as a percentage?
19/28 + 9/13 expressed as a percentage is 137.0879%.
How do you write 19/28 plus 9/13 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 499/364 can be written as the mixed number 1 135/364.
Does 19/28 plus 9/13 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.370879...) because the denominator contains prime factors other than 2 and 5.