What is 5/14 plus 9/13?
5/14 plus 9/13 equals 191/182 (or 1 9/182 as a mixed number) (or 1.049451 in decimal form). Learn the step-by-step solution to add 5/14 and 9/13 using Least Common Denominator and simplification.
Exact Answer
5/14 + 9/13 = 191/182
Simplified Fraction
191/182
Mixed Number
1 9/182
Decimal Value
1.049451
Percentage
104.9451%
Step-by-Step Solution: 5/14 + 9/13
Step 1
Find the Least Common Denominator (LCD)
The denominators 14 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 14 × 13 = 182.
LCD(14, 13) = 182
Step 2
Convert to Equivalent Fractions with Common Denominator 182
Multiply the numerator and denominator of 5/14 by 13, and multiply the numerator and denominator of 9/13 by 14 so both fractions share the common base 182.
5 × 13/14 × 13 = 65/182 and 9 × 14/13 × 14 = 126/182
Step 3
Add the Numerators
Now add the numerators (65 + 126 = 191) and keep the common denominator 182 unchanged.
65 + 126/182 = 191/182
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 191 and 182 is 1, confirming that 191/182 cannot be reduced further—it is already in its simplest irreducible form.
191/182
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (191) is greater than the denominator (182), divide 191 by 182: it goes in 1 whole time(s) with a remainder of 9, giving the mixed number 1 9/182.
191/182 = 19/182
Step 6
Decimal & Percentage Representation
Dividing the numerator 191 by denominator 182 produces a repeating decimal (approximately 1.049451, or 104.9451%).
191 ÷ 182 = 1.049451 (104.9451%)
Visual Representation
The diagram below illustrates 5/14 plus 9/13 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 191/182 |
| Mixed Number Form | 1 9/182 |
| Decimal Form | 1.049451 |
| Percentage | 104.9451% |
Was this solution helpful?
Help us improve our free step-by-step tools
Frequently Asked Questions
What is 5/14 plus 9/13 as a fraction?
5/14 + 9/13 in simplest fraction form is 191/182 (or 1 9/182 as a mixed number).
What is 5/14 plus 9/13 as a decimal?
5/14 + 9/13 converted to a decimal is 1.049451.
What is 5/14 plus 9/13 as a percentage?
5/14 + 9/13 expressed as a percentage is 104.9451%.
How do you write 5/14 plus 9/13 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 191/182 can be written as the mixed number 1 9/182.
Does 5/14 plus 9/13 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.049451...) because the denominator contains prime factors other than 2 and 5.