What is 4/9 plus 8/11?
4/9 plus 8/11 equals 116/99 (or 1 17/99 as a mixed number) (or 1.171717 in decimal form). Learn the step-by-step solution to add 4/9 and 8/11 using Least Common Denominator and simplification.
Exact Answer
4/9 + 8/11 = 116/99
Simplified Fraction
116/99
Mixed Number
1 17/99
Decimal Value
1.171717
Percentage
117.1717%
Step-by-Step Solution: 4/9 + 8/11
Step 1
Find the Least Common Denominator (LCD)
The denominators 9 and 11 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 11 = 99.
LCD(9, 11) = 99
Step 2
Convert to Equivalent Fractions with Common Denominator 99
Multiply the numerator and denominator of 4/9 by 11, and multiply the numerator and denominator of 8/11 by 9 so both fractions share the common base 99.
4 × 11/9 × 11 = 44/99 and 8 × 9/11 × 9 = 72/99
Step 3
Add the Numerators
Now add the numerators (44 + 72 = 116) and keep the common denominator 99 unchanged.
44 + 72/99 = 116/99
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 116 and 99 is 1, confirming that 116/99 cannot be reduced further—it is already in its simplest irreducible form.
116/99
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (116) is greater than the denominator (99), divide 116 by 99: it goes in 1 whole time(s) with a remainder of 17, giving the mixed number 1 17/99.
116/99 = 117/99
Step 6
Decimal & Percentage Representation
Dividing the numerator 116 by denominator 99 produces a repeating decimal (approximately 1.171717, or 117.1717%).
116 ÷ 99 = 1.171717 (117.1717%)
Visual Representation
The diagram below illustrates 4/9 plus 8/11 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 116/99 |
| Mixed Number Form | 1 17/99 |
| Decimal Form | 1.171717 |
| Percentage | 117.1717% |
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Frequently Asked Questions
What is 4/9 plus 8/11 as a fraction?
4/9 + 8/11 in simplest fraction form is 116/99 (or 1 17/99 as a mixed number).
What is 4/9 plus 8/11 as a decimal?
4/9 + 8/11 converted to a decimal is 1.171717.
What is 4/9 plus 8/11 as a percentage?
4/9 + 8/11 expressed as a percentage is 117.1717%.
How do you write 4/9 plus 8/11 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 116/99 can be written as the mixed number 1 17/99.
Does 4/9 plus 8/11 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.171717...) because the denominator contains prime factors other than 2 and 5.