What is 4/11 plus 7/9?
4/11 plus 7/9 equals 113/99 (or 1 14/99 as a mixed number) (or 1.141414 in decimal form). Learn the step-by-step solution to add 4/11 and 7/9 using Least Common Denominator and simplification.
Exact Answer
4/11 + 7/9 = 113/99
Simplified Fraction
113/99
Mixed Number
1 14/99
Decimal Value
1.141414
Percentage
114.1414%
Step-by-Step Solution: 4/11 + 7/9
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 7/9 by 11 so both fractions share the common base 99.
4 × 9/11 × 9 = 36/99 and 7 × 11/9 × 11 = 77/99
Step 3
Add the Numerators
Now add the numerators (36 + 77 = 113) and keep the common denominator 99 unchanged.
36 + 77/99 = 113/99
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 113 and 99 is 1, confirming that 113/99 cannot be reduced further—it is already in its simplest irreducible form.
113/99
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (113) is greater than the denominator (99), divide 113 by 99: it goes in 1 whole time(s) with a remainder of 14, giving the mixed number 1 14/99.
113/99 = 114/99
Step 6
Decimal & Percentage Representation
Dividing the numerator 113 by denominator 99 produces a repeating decimal (approximately 1.141414, or 114.1414%).
113 ÷ 99 = 1.141414 (114.1414%)
Visual Representation
The diagram below illustrates 4/11 plus 7/9 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 113/99 |
| Mixed Number Form | 1 14/99 |
| Decimal Form | 1.141414 |
| Percentage | 114.1414% |
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Frequently Asked Questions
What is 4/11 plus 7/9 as a fraction?
4/11 + 7/9 in simplest fraction form is 113/99 (or 1 14/99 as a mixed number).
What is 4/11 plus 7/9 as a decimal?
4/11 + 7/9 converted to a decimal is 1.141414.
What is 4/11 plus 7/9 as a percentage?
4/11 + 7/9 expressed as a percentage is 114.1414%.
How do you write 4/11 plus 7/9 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 113/99 can be written as the mixed number 1 14/99.
Does 4/11 plus 7/9 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.141414...) because the denominator contains prime factors other than 2 and 5.