What is 4/9 plus 5/11?
4/9 plus 5/11 equals 89/99 (or 0.89899 in decimal form). Learn the step-by-step solution to add 4/9 and 5/11 using Least Common Denominator and simplification.
Exact Answer
4/9 + 5/11 = 89/99
Simplified Fraction
89/99
Mixed Number
Proper (89/99)
Decimal Value
0.89899
Percentage
89.899%
Step-by-Step Solution: 4/9 + 5/11
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 5/11 by 9 so both fractions share the common base 99.
4 × 11/9 × 11 = 44/99 and 5 × 9/11 × 9 = 45/99
Step 3
Add the Numerators
Now add the numerators (44 + 45 = 89) and keep the common denominator 99 unchanged.
44 + 45/99 = 89/99
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 89 and 99 is 1, confirming that 89/99 cannot be reduced further—it is already in its simplest irreducible form.
89/99
Step 5
Decimal & Percentage Representation
Dividing the numerator 89 by denominator 99 produces a repeating decimal (approximately 0.89899, or 89.899%).
89 ÷ 99 = 0.89899 (89.899%)
Visual Representation
The diagram below illustrates 4/9 plus 5/11 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 89/99 |
| Mixed Number Form | 89/99 |
| Decimal Form | 0.89899 |
| Percentage | 89.899% |
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Frequently Asked Questions
What is 4/9 plus 5/11 as a fraction?
4/9 + 5/11 in simplest fraction form is 89/99.
What is 4/9 plus 5/11 as a decimal?
4/9 + 5/11 converted to a decimal is 0.89899.
What is 4/9 plus 5/11 as a percentage?
4/9 + 5/11 expressed as a percentage is 89.899%.
Does 4/9 plus 5/11 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 0.89899...) because the denominator contains prime factors other than 2 and 5.