What is 17/32 plus 9/13?
17/32 plus 9/13 equals 509/416 (or 1 93/416 as a mixed number) (or 1.223558 in decimal form). Learn the step-by-step solution to add 17/32 and 9/13 using Least Common Denominator and simplification.
Exact Answer
17/32 + 9/13 = 509/416
Simplified Fraction
509/416
Mixed Number
1 93/416
Decimal Value
1.223558
Percentage
122.3558%
Step-by-Step Solution: 17/32 + 9/13
Step 1
Find the Least Common Denominator (LCD)
The denominators 32 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 32 × 13 = 416.
LCD(32, 13) = 416
Step 2
Convert to Equivalent Fractions with Common Denominator 416
Multiply the numerator and denominator of 17/32 by 13, and multiply the numerator and denominator of 9/13 by 32 so both fractions share the common base 416.
17 × 13/32 × 13 = 221/416 and 9 × 32/13 × 32 = 288/416
Step 3
Add the Numerators
Now add the numerators (221 + 288 = 509) and keep the common denominator 416 unchanged.
221 + 288/416 = 509/416
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 509 and 416 is 1, confirming that 509/416 cannot be reduced further—it is already in its simplest irreducible form.
509/416
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (509) is greater than the denominator (416), divide 509 by 416: it goes in 1 whole time(s) with a remainder of 93, giving the mixed number 1 93/416.
509/416 = 193/416
Step 6
Decimal & Percentage Representation
Dividing the numerator 509 by denominator 416 produces a repeating decimal (approximately 1.223558, or 122.3558%).
509 ÷ 416 = 1.223558 (122.3558%)
Visual Representation
The diagram below illustrates 17/32 plus 9/13 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 509/416 |
| Mixed Number Form | 1 93/416 |
| Decimal Form | 1.223558 |
| Percentage | 122.3558% |
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Frequently Asked Questions
What is 17/32 plus 9/13 as a fraction?
17/32 + 9/13 in simplest fraction form is 509/416 (or 1 93/416 as a mixed number).
What is 17/32 plus 9/13 as a decimal?
17/32 + 9/13 converted to a decimal is 1.223558.
What is 17/32 plus 9/13 as a percentage?
17/32 + 9/13 expressed as a percentage is 122.3558%.
How do you write 17/32 plus 9/13 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 509/416 can be written as the mixed number 1 93/416.
Does 17/32 plus 9/13 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.223558...) because the denominator contains prime factors other than 2 and 5.