What is 5/9 plus 7/11?
5/9 plus 7/11 equals 118/99 (or 1 19/99 as a mixed number) (or 1.191919 in decimal form). Learn the step-by-step solution to add 5/9 and 7/11 using Least Common Denominator and simplification.
Exact Answer
5/9 + 7/11 = 118/99
Simplified Fraction
118/99
Mixed Number
1 19/99
Decimal Value
1.191919
Percentage
119.1919%
Step-by-Step Solution: 5/9 + 7/11
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 5/9 by 11, and multiply the numerator and denominator of 7/11 by 9 so both fractions share the common base 99.
5 × 11/9 × 11 = 55/99 and 7 × 9/11 × 9 = 63/99
Step 3
Add the Numerators
Now add the numerators (55 + 63 = 118) and keep the common denominator 99 unchanged.
55 + 63/99 = 118/99
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 118 and 99 is 1, confirming that 118/99 cannot be reduced further—it is already in its simplest irreducible form.
118/99
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (118) is greater than the denominator (99), divide 118 by 99: it goes in 1 whole time(s) with a remainder of 19, giving the mixed number 1 19/99.
118/99 = 119/99
Step 6
Decimal & Percentage Representation
Dividing the numerator 118 by denominator 99 produces a repeating decimal (approximately 1.191919, or 119.1919%).
118 ÷ 99 = 1.191919 (119.1919%)
Visual Representation
The diagram below illustrates 5/9 plus 7/11 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 118/99 |
| Mixed Number Form | 1 19/99 |
| Decimal Form | 1.191919 |
| Percentage | 119.1919% |
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Frequently Asked Questions
What is 5/9 plus 7/11 as a fraction?
5/9 + 7/11 in simplest fraction form is 118/99 (or 1 19/99 as a mixed number).
What is 5/9 plus 7/11 as a decimal?
5/9 + 7/11 converted to a decimal is 1.191919.
What is 5/9 plus 7/11 as a percentage?
5/9 + 7/11 expressed as a percentage is 119.1919%.
How do you write 5/9 plus 7/11 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 118/99 can be written as the mixed number 1 19/99.
Does 5/9 plus 7/11 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.191919...) because the denominator contains prime factors other than 2 and 5.