What is 19/33 plus 15/21?
19/33 plus 15/21 equals 298/231 (or 1 67/231 as a mixed number) (or 1.290043 in decimal form). Learn the step-by-step solution to add 19/33 and 15/21 using Least Common Denominator and simplification.
Exact Answer
19/33 + 15/21 = 298/231
Simplified Fraction
298/231
Mixed Number
1 67/231
Decimal Value
1.290043
Percentage
129.0043%
Step-by-Step Solution: 19/33 + 15/21
Step 1
Find the Least Common Denominator (LCD)
The denominators 33 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 231 (which is smaller than their product 33 × 21 = 693, keeping the calculation simpler).
LCD(33, 21) = 231
Step 2
Convert to Equivalent Fractions with Common Denominator 231
Multiply the numerator and denominator of 19/33 by 7, and multiply the numerator and denominator of 15/21 by 11 so both fractions share the common base 231.
19 × 7/33 × 7 = 133/231 and 15 × 11/21 × 11 = 165/231
Step 3
Add the Numerators
Now add the numerators (133 + 165 = 298) and keep the common denominator 231 unchanged.
133 + 165/231 = 298/231
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 298 and 231 is 1, confirming that 298/231 cannot be reduced further—it is already in its simplest irreducible form.
298/231
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (298) is greater than the denominator (231), divide 298 by 231: it goes in 1 whole time(s) with a remainder of 67, giving the mixed number 1 67/231.
298/231 = 167/231
Step 6
Decimal & Percentage Representation
Dividing the numerator 298 by denominator 231 produces a repeating decimal (approximately 1.290043, or 129.0043%).
298 ÷ 231 = 1.290043 (129.0043%)
Visual Representation
The diagram below illustrates 19/33 plus 15/21 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 298/231 |
| Mixed Number Form | 1 67/231 |
| Decimal Form | 1.290043 |
| Percentage | 129.0043% |
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Frequently Asked Questions
What is 19/33 plus 15/21 as a fraction?
19/33 + 15/21 in simplest fraction form is 298/231 (or 1 67/231 as a mixed number).
What is 19/33 plus 15/21 as a decimal?
19/33 + 15/21 converted to a decimal is 1.290043.
What is 19/33 plus 15/21 as a percentage?
19/33 + 15/21 expressed as a percentage is 129.0043%.
How do you write 19/33 plus 15/21 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 298/231 can be written as the mixed number 1 67/231.
Does 19/33 plus 15/21 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.290043...) because the denominator contains prime factors other than 2 and 5.