What is 14/25 plus 9/13?
14/25 plus 9/13 equals 407/325 (or 1 82/325 as a mixed number) (or 1.252308 in decimal form). Learn the step-by-step solution to add 14/25 and 9/13 using Least Common Denominator and simplification.
Exact Answer
14/25 + 9/13 = 407/325
Simplified Fraction
407/325
Mixed Number
1 82/325
Decimal Value
1.252308
Percentage
125.2308%
Step-by-Step Solution: 14/25 + 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 14/25 by 13, and multiply the numerator and denominator of 9/13 by 25 so both fractions share the common base 325.
14 × 13/25 × 13 = 182/325 and 9 × 25/13 × 25 = 225/325
Step 3
Add the Numerators
Now add the numerators (182 + 225 = 407) and keep the common denominator 325 unchanged.
182 + 225/325 = 407/325
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 407 and 325 is 1, confirming that 407/325 cannot be reduced further—it is already in its simplest irreducible form.
407/325
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (407) is greater than the denominator (325), divide 407 by 325: it goes in 1 whole time(s) with a remainder of 82, giving the mixed number 1 82/325.
407/325 = 182/325
Step 6
Decimal & Percentage Representation
Dividing the numerator 407 by denominator 325 produces a repeating decimal (approximately 1.252308, or 125.2308%).
407 ÷ 325 = 1.252308 (125.2308%)
Visual Representation
The diagram below illustrates 14/25 plus 9/13 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 407/325 |
| Mixed Number Form | 1 82/325 |
| Decimal Form | 1.252308 |
| Percentage | 125.2308% |
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Frequently Asked Questions
What is 14/25 plus 9/13 as a fraction?
14/25 + 9/13 in simplest fraction form is 407/325 (or 1 82/325 as a mixed number).
What is 14/25 plus 9/13 as a decimal?
14/25 + 9/13 converted to a decimal is 1.252308.
What is 14/25 plus 9/13 as a percentage?
14/25 + 9/13 expressed as a percentage is 125.2308%.
How do you write 14/25 plus 9/13 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 407/325 can be written as the mixed number 1 82/325.
Does 14/25 plus 9/13 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.252308...) because the denominator contains prime factors other than 2 and 5.