What is 3/6 plus 11/21?
3/6 plus 11/21 equals 43/42 (or 1 1/42 as a mixed number) (or 1.02381 in decimal form). Learn the step-by-step solution to add 3/6 and 11/21 using Least Common Denominator and simplification.
Exact Answer
3/6 + 11/21 = 43/42
Simplified Fraction
43/42
Mixed Number
1 1/42
Decimal Value
1.02381
Percentage
102.381%
Step-by-Step Solution: 3/6 + 11/21
Step 1
Find the Least Common Denominator (LCD)
The denominators 6 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 42 (which is smaller than their product 6 × 21 = 126, keeping the calculation simpler).
LCD(6, 21) = 42
Step 2
Convert to Equivalent Fractions with Common Denominator 42
Multiply the numerator and denominator of 3/6 by 7, and multiply the numerator and denominator of 11/21 by 2 so both fractions share the common base 42.
3 × 7/6 × 7 = 21/42 and 11 × 2/21 × 2 = 22/42
Step 3
Add the Numerators
Now add the numerators (21 + 22 = 43) and keep the common denominator 42 unchanged.
21 + 22/42 = 43/42
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 43 and 42 is 1, confirming that 43/42 cannot be reduced further—it is already in its simplest irreducible form.
43/42
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (43) is greater than the denominator (42), divide 43 by 42: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/42.
43/42 = 11/42
Step 6
Decimal & Percentage Representation
Dividing the numerator 43 by denominator 42 produces a repeating decimal (approximately 1.02381, or 102.381%).
43 ÷ 42 = 1.02381 (102.381%)
Visual Representation
The diagram below illustrates 3/6 plus 11/21 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 43/42 |
| Mixed Number Form | 1 1/42 |
| Decimal Form | 1.02381 |
| Percentage | 102.381% |
Was this solution helpful?
Help us improve our free step-by-step tools
Frequently Asked Questions
What is 3/6 plus 11/21 as a fraction?
3/6 + 11/21 in simplest fraction form is 43/42 (or 1 1/42 as a mixed number).
What is 3/6 plus 11/21 as a decimal?
3/6 + 11/21 converted to a decimal is 1.02381.
What is 3/6 plus 11/21 as a percentage?
3/6 + 11/21 expressed as a percentage is 102.381%.
How do you write 3/6 plus 11/21 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 43/42 can be written as the mixed number 1 1/42.
Does 3/6 plus 11/21 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.02381...) because the denominator contains prime factors other than 2 and 5.