What is 19/36 plus 15/21?
19/36 plus 15/21 equals 313/252 (or 1 61/252 as a mixed number) (or 1.242063 in decimal form). Learn the step-by-step solution to add 19/36 and 15/21 using Least Common Denominator and simplification.
Exact Answer
19/36 + 15/21 = 313/252
Simplified Fraction
313/252
Mixed Number
1 61/252
Decimal Value
1.242063
Percentage
124.2063%
Step-by-Step Solution: 19/36 + 15/21
Step 1
Find the Least Common Denominator (LCD)
The denominators 36 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 252 (which is smaller than their product 36 × 21 = 756, keeping the calculation simpler).
LCD(36, 21) = 252
Step 2
Convert to Equivalent Fractions with Common Denominator 252
Multiply the numerator and denominator of 19/36 by 7, and multiply the numerator and denominator of 15/21 by 12 so both fractions share the common base 252.
19 × 7/36 × 7 = 133/252 and 15 × 12/21 × 12 = 180/252
Step 3
Add the Numerators
Now add the numerators (133 + 180 = 313) and keep the common denominator 252 unchanged.
133 + 180/252 = 313/252
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 313 and 252 is 1, confirming that 313/252 cannot be reduced further—it is already in its simplest irreducible form.
313/252
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (313) is greater than the denominator (252), divide 313 by 252: it goes in 1 whole time(s) with a remainder of 61, giving the mixed number 1 61/252.
313/252 = 161/252
Step 6
Decimal & Percentage Representation
Dividing the numerator 313 by denominator 252 produces a repeating decimal (approximately 1.242063, or 124.2063%).
313 ÷ 252 = 1.242063 (124.2063%)
Visual Representation
The diagram below illustrates 19/36 plus 15/21 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 313/252 |
| Mixed Number Form | 1 61/252 |
| Decimal Form | 1.242063 |
| Percentage | 124.2063% |
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Frequently Asked Questions
What is 19/36 plus 15/21 as a fraction?
19/36 + 15/21 in simplest fraction form is 313/252 (or 1 61/252 as a mixed number).
What is 19/36 plus 15/21 as a decimal?
19/36 + 15/21 converted to a decimal is 1.242063.
What is 19/36 plus 15/21 as a percentage?
19/36 + 15/21 expressed as a percentage is 124.2063%.
How do you write 19/36 plus 15/21 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 313/252 can be written as the mixed number 1 61/252.
Does 19/36 plus 15/21 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.242063...) because the denominator contains prime factors other than 2 and 5.