What is 20/39 plus 11/21?
20/39 plus 11/21 equals 283/273 (or 1 10/273 as a mixed number) (or 1.03663 in decimal form). Learn the step-by-step solution to add 20/39 and 11/21 using Least Common Denominator and simplification.
Exact Answer
20/39 + 11/21 = 283/273
Simplified Fraction
283/273
Mixed Number
1 10/273
Decimal Value
1.03663
Percentage
103.663%
Step-by-Step Solution: 20/39 + 11/21
Step 1
Find the Least Common Denominator (LCD)
The denominators 39 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 273 (which is smaller than their product 39 × 21 = 819, keeping the calculation simpler).
LCD(39, 21) = 273
Step 2
Convert to Equivalent Fractions with Common Denominator 273
Multiply the numerator and denominator of 20/39 by 7, and multiply the numerator and denominator of 11/21 by 13 so both fractions share the common base 273.
20 × 7/39 × 7 = 140/273 and 11 × 13/21 × 13 = 143/273
Step 3
Add the Numerators
Now add the numerators (140 + 143 = 283) and keep the common denominator 273 unchanged.
140 + 143/273 = 283/273
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 283 and 273 is 1, confirming that 283/273 cannot be reduced further—it is already in its simplest irreducible form.
283/273
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (283) is greater than the denominator (273), divide 283 by 273: it goes in 1 whole time(s) with a remainder of 10, giving the mixed number 1 10/273.
283/273 = 110/273
Step 6
Decimal & Percentage Representation
Dividing the numerator 283 by denominator 273 produces a repeating decimal (approximately 1.03663, or 103.663%).
283 ÷ 273 = 1.03663 (103.663%)
Visual Representation
The diagram below illustrates 20/39 plus 11/21 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 283/273 |
| Mixed Number Form | 1 10/273 |
| Decimal Form | 1.03663 |
| Percentage | 103.663% |
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Frequently Asked Questions
What is 20/39 plus 11/21 as a fraction?
20/39 + 11/21 in simplest fraction form is 283/273 (or 1 10/273 as a mixed number).
What is 20/39 plus 11/21 as a decimal?
20/39 + 11/21 converted to a decimal is 1.03663.
What is 20/39 plus 11/21 as a percentage?
20/39 + 11/21 expressed as a percentage is 103.663%.
How do you write 20/39 plus 11/21 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 283/273 can be written as the mixed number 1 10/273.
Does 20/39 plus 11/21 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.03663...) because the denominator contains prime factors other than 2 and 5.