What is 13/36 plus 15/21?
13/36 plus 15/21 equals 271/252 (or 1 19/252 as a mixed number) (or 1.075397 in decimal form). Learn the step-by-step solution to add 13/36 and 15/21 using Least Common Denominator and simplification.
Exact Answer
13/36 + 15/21 = 271/252
Simplified Fraction
271/252
Mixed Number
1 19/252
Decimal Value
1.075397
Percentage
107.5397%
Step-by-Step Solution: 13/36 + 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 13/36 by 7, and multiply the numerator and denominator of 15/21 by 12 so both fractions share the common base 252.
13 × 7/36 × 7 = 91/252 and 15 × 12/21 × 12 = 180/252
Step 3
Add the Numerators
Now add the numerators (91 + 180 = 271) and keep the common denominator 252 unchanged.
91 + 180/252 = 271/252
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 271 and 252 is 1, confirming that 271/252 cannot be reduced further—it is already in its simplest irreducible form.
271/252
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (271) is greater than the denominator (252), divide 271 by 252: it goes in 1 whole time(s) with a remainder of 19, giving the mixed number 1 19/252.
271/252 = 119/252
Step 6
Decimal & Percentage Representation
Dividing the numerator 271 by denominator 252 produces a repeating decimal (approximately 1.075397, or 107.5397%).
271 ÷ 252 = 1.075397 (107.5397%)
Visual Representation
The diagram below illustrates 13/36 plus 15/21 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 271/252 |
| Mixed Number Form | 1 19/252 |
| Decimal Form | 1.075397 |
| Percentage | 107.5397% |
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Frequently Asked Questions
What is 13/36 plus 15/21 as a fraction?
13/36 + 15/21 in simplest fraction form is 271/252 (or 1 19/252 as a mixed number).
What is 13/36 plus 15/21 as a decimal?
13/36 + 15/21 converted to a decimal is 1.075397.
What is 13/36 plus 15/21 as a percentage?
13/36 + 15/21 expressed as a percentage is 107.5397%.
How do you write 13/36 plus 15/21 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 271/252 can be written as the mixed number 1 19/252.
Does 13/36 plus 15/21 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.075397...) because the denominator contains prime factors other than 2 and 5.