What is 6/25 plus 5/13?
6/25 plus 5/13 equals 203/325 (or 0.624615 in decimal form). Learn the step-by-step solution to add 6/25 and 5/13 using Least Common Denominator and simplification.
Exact Answer
6/25 + 5/13 = 203/325
Simplified Fraction
203/325
Mixed Number
Proper (203/325)
Decimal Value
0.624615
Percentage
62.4615%
Step-by-Step Solution: 6/25 + 5/13
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 6/25 by 13, and multiply the numerator and denominator of 5/13 by 25 so both fractions share the common base 325.
6 × 13/25 × 13 = 78/325 and 5 × 25/13 × 25 = 125/325
Step 3
Add the Numerators
Now add the numerators (78 + 125 = 203) and keep the common denominator 325 unchanged.
78 + 125/325 = 203/325
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 203 and 325 is 1, confirming that 203/325 cannot be reduced further—it is already in its simplest irreducible form.
203/325
Step 5
Decimal & Percentage Representation
Dividing the numerator 203 by denominator 325 produces a repeating decimal (approximately 0.624615, or 62.4615%).
203 ÷ 325 = 0.624615 (62.4615%)
Visual Representation
The diagram below illustrates 6/25 plus 5/13 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 203/325 |
| Mixed Number Form | 203/325 |
| Decimal Form | 0.624615 |
| Percentage | 62.4615% |
Was this solution helpful?
Help us improve our free step-by-step tools
Frequently Asked Questions
What is 6/25 plus 5/13 as a fraction?
6/25 + 5/13 in simplest fraction form is 203/325.
What is 6/25 plus 5/13 as a decimal?
6/25 + 5/13 converted to a decimal is 0.624615.
What is 6/25 plus 5/13 as a percentage?
6/25 + 5/13 expressed as a percentage is 62.4615%.
Does 6/25 plus 5/13 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 0.624615...) because the denominator contains prime factors other than 2 and 5.