What is 4/11 plus 4/9?
4/11 plus 4/9 equals 80/99 (or 0.808081 in decimal form). Learn the step-by-step solution to add 4/11 and 4/9 using Least Common Denominator and simplification.
Exact Answer
4/11 + 4/9 = 80/99
Simplified Fraction
80/99
Mixed Number
Proper (80/99)
Decimal Value
0.808081
Percentage
80.8081%
Step-by-Step Solution: 4/11 + 4/9
Step 1
Find the Least Common Denominator (LCD)
The denominators 11 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 11 × 9 = 99.
LCD(11, 9) = 99
Step 2
Convert to Equivalent Fractions with Common Denominator 99
Multiply the numerator and denominator of 4/11 by 9, and multiply the numerator and denominator of 4/9 by 11 so both fractions share the common base 99.
4 × 9/11 × 9 = 36/99 and 4 × 11/9 × 11 = 44/99
Step 3
Add the Numerators
Now add the numerators (36 + 44 = 80) and keep the common denominator 99 unchanged.
36 + 44/99 = 80/99
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 80 and 99 is 1, confirming that 80/99 cannot be reduced further—it is already in its simplest irreducible form.
80/99
Step 5
Decimal & Percentage Representation
Dividing the numerator 80 by denominator 99 produces a repeating decimal (approximately 0.808081, or 80.8081%).
80 ÷ 99 = 0.808081 (80.8081%)
Visual Representation
The diagram below illustrates 4/11 plus 4/9 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 80/99 |
| Mixed Number Form | 80/99 |
| Decimal Form | 0.808081 |
| Percentage | 80.8081% |
Was this solution helpful?
Help us improve our free step-by-step tools
Frequently Asked Questions
What is 4/11 plus 4/9 as a fraction?
4/11 + 4/9 in simplest fraction form is 80/99.
What is 4/11 plus 4/9 as a decimal?
4/11 + 4/9 converted to a decimal is 0.808081.
What is 4/11 plus 4/9 as a percentage?
4/11 + 4/9 expressed as a percentage is 80.8081%.
Does 4/11 plus 4/9 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 0.808081...) because the denominator contains prime factors other than 2 and 5.