What is 9/23 plus 8/13?
9/23 plus 8/13 equals 301/299 (or 1 2/299 as a mixed number) (or 1.006689 in decimal form). Learn the step-by-step solution to add 9/23 and 8/13 using Least Common Denominator and simplification.
Exact Answer
9/23 + 8/13 = 301/299
Simplified Fraction
301/299
Mixed Number
1 2/299
Decimal Value
1.006689
Percentage
100.6689%
Step-by-Step Solution: 9/23 + 8/13
Step 1
Find the Least Common Denominator (LCD)
The denominators 23 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 13 = 299.
LCD(23, 13) = 299
Step 2
Convert to Equivalent Fractions with Common Denominator 299
Multiply the numerator and denominator of 9/23 by 13, and multiply the numerator and denominator of 8/13 by 23 so both fractions share the common base 299.
9 × 13/23 × 13 = 117/299 and 8 × 23/13 × 23 = 184/299
Step 3
Add the Numerators
Now add the numerators (117 + 184 = 301) and keep the common denominator 299 unchanged.
117 + 184/299 = 301/299
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 301 and 299 is 1, confirming that 301/299 cannot be reduced further—it is already in its simplest irreducible form.
301/299
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (301) is greater than the denominator (299), divide 301 by 299: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/299.
301/299 = 12/299
Step 6
Decimal & Percentage Representation
Dividing the numerator 301 by denominator 299 produces a repeating decimal (approximately 1.006689, or 100.6689%).
301 ÷ 299 = 1.006689 (100.6689%)
Visual Representation
The diagram below illustrates 9/23 plus 8/13 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 301/299 |
| Mixed Number Form | 1 2/299 |
| Decimal Form | 1.006689 |
| Percentage | 100.6689% |
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Frequently Asked Questions
What is 9/23 plus 8/13 as a fraction?
9/23 + 8/13 in simplest fraction form is 301/299 (or 1 2/299 as a mixed number).
What is 9/23 plus 8/13 as a decimal?
9/23 + 8/13 converted to a decimal is 1.006689.
What is 9/23 plus 8/13 as a percentage?
9/23 + 8/13 expressed as a percentage is 100.6689%.
How do you write 9/23 plus 8/13 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 301/299 can be written as the mixed number 1 2/299.
Does 9/23 plus 8/13 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.006689...) because the denominator contains prime factors other than 2 and 5.