What is 9/13 plus 16/23?
9/13 plus 16/23 equals 415/299 (or 1 116/299 as a mixed number) (or 1.38796 in decimal form). Learn the step-by-step solution to add 9/13 and 16/23 using Least Common Denominator and simplification.
Exact Answer
9/13 + 16/23 = 415/299
Simplified Fraction
415/299
Mixed Number
1 116/299
Decimal Value
1.38796
Percentage
138.796%
Step-by-Step Solution: 9/13 + 16/23
Step 1
Find the Least Common Denominator (LCD)
The denominators 13 and 23 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 23 = 299.
LCD(13, 23) = 299
Step 2
Convert to Equivalent Fractions with Common Denominator 299
Multiply the numerator and denominator of 9/13 by 23, and multiply the numerator and denominator of 16/23 by 13 so both fractions share the common base 299.
9 × 23/13 × 23 = 207/299 and 16 × 13/23 × 13 = 208/299
Step 3
Add the Numerators
Now add the numerators (207 + 208 = 415) and keep the common denominator 299 unchanged.
207 + 208/299 = 415/299
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 415 and 299 is 1, confirming that 415/299 cannot be reduced further—it is already in its simplest irreducible form.
415/299
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (415) is greater than the denominator (299), divide 415 by 299: it goes in 1 whole time(s) with a remainder of 116, giving the mixed number 1 116/299.
415/299 = 1116/299
Step 6
Decimal & Percentage Representation
Dividing the numerator 415 by denominator 299 produces a repeating decimal (approximately 1.38796, or 138.796%).
415 ÷ 299 = 1.38796 (138.796%)
Visual Representation
The diagram below illustrates 9/13 plus 16/23 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 415/299 |
| Mixed Number Form | 1 116/299 |
| Decimal Form | 1.38796 |
| Percentage | 138.796% |
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Frequently Asked Questions
What is 9/13 plus 16/23 as a fraction?
9/13 + 16/23 in simplest fraction form is 415/299 (or 1 116/299 as a mixed number).
What is 9/13 plus 16/23 as a decimal?
9/13 + 16/23 converted to a decimal is 1.38796.
What is 9/13 plus 16/23 as a percentage?
9/13 + 16/23 expressed as a percentage is 138.796%.
How do you write 9/13 plus 16/23 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 415/299 can be written as the mixed number 1 116/299.
Does 9/13 plus 16/23 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.38796...) because the denominator contains prime factors other than 2 and 5.