What is 11/21 plus 21/40?
11/21 plus 21/40 equals 881/840 (or 1 41/840 as a mixed number) (or 1.04881 in decimal form). Learn the step-by-step solution to add 11/21 and 21/40 using Least Common Denominator and simplification.
Exact Answer
11/21 + 21/40 = 881/840
Simplified Fraction
881/840
Mixed Number
1 41/840
Decimal Value
1.04881
Percentage
104.881%
Step-by-Step Solution: 11/21 + 21/40
Step 1
Find the Least Common Denominator (LCD)
The denominators 21 and 40 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 40 = 840.
LCD(21, 40) = 840
Step 2
Convert to Equivalent Fractions with Common Denominator 840
Multiply the numerator and denominator of 11/21 by 40, and multiply the numerator and denominator of 21/40 by 21 so both fractions share the common base 840.
11 × 40/21 × 40 = 440/840 and 21 × 21/40 × 21 = 441/840
Step 3
Add the Numerators
Now add the numerators (440 + 441 = 881) and keep the common denominator 840 unchanged.
440 + 441/840 = 881/840
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 881 and 840 is 1, confirming that 881/840 cannot be reduced further—it is already in its simplest irreducible form.
881/840
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (881) is greater than the denominator (840), divide 881 by 840: it goes in 1 whole time(s) with a remainder of 41, giving the mixed number 1 41/840.
881/840 = 141/840
Step 6
Decimal & Percentage Representation
Dividing the numerator 881 by denominator 840 produces a repeating decimal (approximately 1.04881, or 104.881%).
881 ÷ 840 = 1.04881 (104.881%)
Visual Representation
The diagram below illustrates 11/21 plus 21/40 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 881/840 |
| Mixed Number Form | 1 41/840 |
| Decimal Form | 1.04881 |
| Percentage | 104.881% |
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Frequently Asked Questions
What is 11/21 plus 21/40 as a fraction?
11/21 + 21/40 in simplest fraction form is 881/840 (or 1 41/840 as a mixed number).
What is 11/21 plus 21/40 as a decimal?
11/21 + 21/40 converted to a decimal is 1.04881.
What is 11/21 plus 21/40 as a percentage?
11/21 + 21/40 expressed as a percentage is 104.881%.
How do you write 11/21 plus 21/40 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 881/840 can be written as the mixed number 1 41/840.
Does 11/21 plus 21/40 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.04881...) because the denominator contains prime factors other than 2 and 5.