What is 2/5 plus 9/11?
2/5 plus 9/11 equals 67/55 (or 1 12/55 as a mixed number) (or 1.218182 in decimal form). Learn the step-by-step solution to add 2/5 and 9/11 using Least Common Denominator and simplification.
Exact Answer
2/5 + 9/11 = 67/55
Simplified Fraction
67/55
Mixed Number
1 12/55
Decimal Value
1.218182
Percentage
121.8182%
Step-by-Step Solution: 2/5 + 9/11
Step 1
Find the Least Common Denominator (LCD)
The denominators 5 and 11 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 11 = 55.
LCD(5, 11) = 55
Step 2
Convert to Equivalent Fractions with Common Denominator 55
Multiply the numerator and denominator of 2/5 by 11, and multiply the numerator and denominator of 9/11 by 5 so both fractions share the common base 55.
2 × 11/5 × 11 = 22/55 and 9 × 5/11 × 5 = 45/55
Step 3
Add the Numerators
Now add the numerators (22 + 45 = 67) and keep the common denominator 55 unchanged.
22 + 45/55 = 67/55
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 67 and 55 is 1, confirming that 67/55 cannot be reduced further—it is already in its simplest irreducible form.
67/55
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (67) is greater than the denominator (55), divide 67 by 55: it goes in 1 whole time(s) with a remainder of 12, giving the mixed number 1 12/55.
67/55 = 112/55
Step 6
Decimal & Percentage Representation
Dividing the numerator 67 by denominator 55 produces a repeating decimal (approximately 1.218182, or 121.8182%).
67 ÷ 55 = 1.218182 (121.8182%)
Visual Representation
The diagram below illustrates 2/5 plus 9/11 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 67/55 |
| Mixed Number Form | 1 12/55 |
| Decimal Form | 1.218182 |
| Percentage | 121.8182% |
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Frequently Asked Questions
What is 2/5 plus 9/11 as a fraction?
2/5 + 9/11 in simplest fraction form is 67/55 (or 1 12/55 as a mixed number).
What is 2/5 plus 9/11 as a decimal?
2/5 + 9/11 converted to a decimal is 1.218182.
What is 2/5 plus 9/11 as a percentage?
2/5 + 9/11 expressed as a percentage is 121.8182%.
How do you write 2/5 plus 9/11 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 67/55 can be written as the mixed number 1 12/55.
Does 2/5 plus 9/11 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.218182...) because the denominator contains prime factors other than 2 and 5.