What is 23/38 plus 9/13?
23/38 plus 9/13 equals 641/494 (or 1 147/494 as a mixed number) (or 1.297571 in decimal form). Learn the step-by-step solution to add 23/38 and 9/13 using Least Common Denominator and simplification.
Exact Answer
23/38 + 9/13 = 641/494
Simplified Fraction
641/494
Mixed Number
1 147/494
Decimal Value
1.297571
Percentage
129.7571%
Step-by-Step Solution: 23/38 + 9/13
Step 1
Find the Least Common Denominator (LCD)
The denominators 38 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 38 × 13 = 494.
LCD(38, 13) = 494
Step 2
Convert to Equivalent Fractions with Common Denominator 494
Multiply the numerator and denominator of 23/38 by 13, and multiply the numerator and denominator of 9/13 by 38 so both fractions share the common base 494.
23 × 13/38 × 13 = 299/494 and 9 × 38/13 × 38 = 342/494
Step 3
Add the Numerators
Now add the numerators (299 + 342 = 641) and keep the common denominator 494 unchanged.
299 + 342/494 = 641/494
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 641 and 494 is 1, confirming that 641/494 cannot be reduced further—it is already in its simplest irreducible form.
641/494
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (641) is greater than the denominator (494), divide 641 by 494: it goes in 1 whole time(s) with a remainder of 147, giving the mixed number 1 147/494.
641/494 = 1147/494
Step 6
Decimal & Percentage Representation
Dividing the numerator 641 by denominator 494 produces a repeating decimal (approximately 1.297571, or 129.7571%).
641 ÷ 494 = 1.297571 (129.7571%)
Visual Representation
The diagram below illustrates 23/38 plus 9/13 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 641/494 |
| Mixed Number Form | 1 147/494 |
| Decimal Form | 1.297571 |
| Percentage | 129.7571% |
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Frequently Asked Questions
What is 23/38 plus 9/13 as a fraction?
23/38 + 9/13 in simplest fraction form is 641/494 (or 1 147/494 as a mixed number).
What is 23/38 plus 9/13 as a decimal?
23/38 + 9/13 converted to a decimal is 1.297571.
What is 23/38 plus 9/13 as a percentage?
23/38 + 9/13 expressed as a percentage is 129.7571%.
How do you write 23/38 plus 9/13 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 641/494 can be written as the mixed number 1 147/494.
Does 23/38 plus 9/13 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.297571...) because the denominator contains prime factors other than 2 and 5.