What is 17/25 plus 9/13?
17/25 plus 9/13 equals 446/325 (or 1 121/325 as a mixed number) (or 1.372308 in decimal form). Learn the step-by-step solution to add 17/25 and 9/13 using Least Common Denominator and simplification.
Exact Answer
17/25 + 9/13 = 446/325
Simplified Fraction
446/325
Mixed Number
1 121/325
Decimal Value
1.372308
Percentage
137.2308%
Step-by-Step Solution: 17/25 + 9/13
Step 1
Find the Least Common Denominator (LCD)
The denominators 25 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 25 × 13 = 325.
LCD(25, 13) = 325
Step 2
Convert to Equivalent Fractions with Common Denominator 325
Multiply the numerator and denominator of 17/25 by 13, and multiply the numerator and denominator of 9/13 by 25 so both fractions share the common base 325.
17 × 13/25 × 13 = 221/325 and 9 × 25/13 × 25 = 225/325
Step 3
Add the Numerators
Now add the numerators (221 + 225 = 446) and keep the common denominator 325 unchanged.
221 + 225/325 = 446/325
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 446 and 325 is 1, confirming that 446/325 cannot be reduced further—it is already in its simplest irreducible form.
446/325
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (446) is greater than the denominator (325), divide 446 by 325: it goes in 1 whole time(s) with a remainder of 121, giving the mixed number 1 121/325.
446/325 = 1121/325
Step 6
Decimal & Percentage Representation
Dividing the numerator 446 by denominator 325 produces a repeating decimal (approximately 1.372308, or 137.2308%).
446 ÷ 325 = 1.372308 (137.2308%)
Visual Representation
The diagram below illustrates 17/25 plus 9/13 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 446/325 |
| Mixed Number Form | 1 121/325 |
| Decimal Form | 1.372308 |
| Percentage | 137.2308% |
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Frequently Asked Questions
What is 17/25 plus 9/13 as a fraction?
17/25 + 9/13 in simplest fraction form is 446/325 (or 1 121/325 as a mixed number).
What is 17/25 plus 9/13 as a decimal?
17/25 + 9/13 converted to a decimal is 1.372308.
What is 17/25 plus 9/13 as a percentage?
17/25 + 9/13 expressed as a percentage is 137.2308%.
How do you write 17/25 plus 9/13 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 446/325 can be written as the mixed number 1 121/325.
Does 17/25 plus 9/13 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.372308...) because the denominator contains prime factors other than 2 and 5.