What is 6/11 plus 9/13?
6/11 plus 9/13 equals 177/143 (or 1 34/143 as a mixed number) (or 1.237762 in decimal form). Learn the step-by-step solution to add 6/11 and 9/13 using Least Common Denominator and simplification.
Exact Answer
6/11 + 9/13 = 177/143
Simplified Fraction
177/143
Mixed Number
1 34/143
Decimal Value
1.237762
Percentage
123.7762%
Step-by-Step Solution: 6/11 + 9/13
Step 1
Find the Least Common Denominator (LCD)
The denominators 11 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 11 × 13 = 143.
LCD(11, 13) = 143
Step 2
Convert to Equivalent Fractions with Common Denominator 143
Multiply the numerator and denominator of 6/11 by 13, and multiply the numerator and denominator of 9/13 by 11 so both fractions share the common base 143.
6 × 13/11 × 13 = 78/143 and 9 × 11/13 × 11 = 99/143
Step 3
Add the Numerators
Now add the numerators (78 + 99 = 177) and keep the common denominator 143 unchanged.
78 + 99/143 = 177/143
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 177 and 143 is 1, confirming that 177/143 cannot be reduced further—it is already in its simplest irreducible form.
177/143
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (177) is greater than the denominator (143), divide 177 by 143: it goes in 1 whole time(s) with a remainder of 34, giving the mixed number 1 34/143.
177/143 = 134/143
Step 6
Decimal & Percentage Representation
Dividing the numerator 177 by denominator 143 produces a repeating decimal (approximately 1.237762, or 123.7762%).
177 ÷ 143 = 1.237762 (123.7762%)
Visual Representation
The diagram below illustrates 6/11 plus 9/13 visually:
+
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 177/143 |
| Mixed Number Form | 1 34/143 |
| Decimal Form | 1.237762 |
| Percentage | 123.7762% |
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Frequently Asked Questions
What is 6/11 plus 9/13 as a fraction?
6/11 + 9/13 in simplest fraction form is 177/143 (or 1 34/143 as a mixed number).
What is 6/11 plus 9/13 as a decimal?
6/11 + 9/13 converted to a decimal is 1.237762.
What is 6/11 plus 9/13 as a percentage?
6/11 + 9/13 expressed as a percentage is 123.7762%.
How do you write 6/11 plus 9/13 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 177/143 can be written as the mixed number 1 34/143.
Does 6/11 plus 9/13 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.237762...) because the denominator contains prime factors other than 2 and 5.