What is 9/59 plus 9/13?
9/59 plus 9/13 equals 648/767 (or 0.84485 in decimal form). Learn the step-by-step solution to add 9/59 and 9/13 using Least Common Denominator and simplification.
Exact Answer
9/59 + 9/13 = 648/767
Simplified Fraction
648/767
Mixed Number
Proper (648/767)
Decimal Value
0.84485
Percentage
84.485%
Step-by-Step Solution: 9/59 + 9/13
Step 1
Find the Least Common Denominator (LCD)
The denominators 59 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 59 × 13 = 767.
LCD(59, 13) = 767
Step 2
Convert to Equivalent Fractions with Common Denominator 767
Multiply the numerator and denominator of 9/59 by 13, and multiply the numerator and denominator of 9/13 by 59 so both fractions share the common base 767.
9 × 13/59 × 13 = 117/767 and 9 × 59/13 × 59 = 531/767
Step 3
Add the Numerators
Now add the numerators (117 + 531 = 648) and keep the common denominator 767 unchanged.
117 + 531/767 = 648/767
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 648 and 767 is 1, confirming that 648/767 cannot be reduced further—it is already in its simplest irreducible form.
648/767
Step 5
Decimal & Percentage Representation
Dividing the numerator 648 by denominator 767 produces a repeating decimal (approximately 0.84485, or 84.485%).
648 ÷ 767 = 0.84485 (84.485%)
Visual Representation
The diagram below illustrates 9/59 plus 9/13 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 648/767 |
| Mixed Number Form | 648/767 |
| Decimal Form | 0.84485 |
| Percentage | 84.485% |
Was this solution helpful?
Help us improve our free step-by-step tools
Frequently Asked Questions
What is 9/59 plus 9/13 as a fraction?
9/59 + 9/13 in simplest fraction form is 648/767.
What is 9/59 plus 9/13 as a decimal?
9/59 + 9/13 converted to a decimal is 0.84485.
What is 9/59 plus 9/13 as a percentage?
9/59 + 9/13 expressed as a percentage is 84.485%.
Does 9/59 plus 9/13 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 0.84485...) because the denominator contains prime factors other than 2 and 5.