What is 16/35 plus 9/13?
16/35 plus 9/13 equals 523/455 (or 1 68/455 as a mixed number) (or 1.149451 in decimal form). Learn the step-by-step solution to add 16/35 and 9/13 using Least Common Denominator and simplification.
Exact Answer
16/35 + 9/13 = 523/455
Simplified Fraction
523/455
Mixed Number
1 68/455
Decimal Value
1.149451
Percentage
114.9451%
Step-by-Step Solution: 16/35 + 9/13
Step 1
Find the Least Common Denominator (LCD)
The denominators 35 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 35 × 13 = 455.
LCD(35, 13) = 455
Step 2
Convert to Equivalent Fractions with Common Denominator 455
Multiply the numerator and denominator of 16/35 by 13, and multiply the numerator and denominator of 9/13 by 35 so both fractions share the common base 455.
16 × 13/35 × 13 = 208/455 and 9 × 35/13 × 35 = 315/455
Step 3
Add the Numerators
Now add the numerators (208 + 315 = 523) and keep the common denominator 455 unchanged.
208 + 315/455 = 523/455
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 523 and 455 is 1, confirming that 523/455 cannot be reduced further—it is already in its simplest irreducible form.
523/455
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (523) is greater than the denominator (455), divide 523 by 455: it goes in 1 whole time(s) with a remainder of 68, giving the mixed number 1 68/455.
523/455 = 168/455
Step 6
Decimal & Percentage Representation
Dividing the numerator 523 by denominator 455 produces a repeating decimal (approximately 1.149451, or 114.9451%).
523 ÷ 455 = 1.149451 (114.9451%)
Visual Representation
The diagram below illustrates 16/35 plus 9/13 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 523/455 |
| Mixed Number Form | 1 68/455 |
| Decimal Form | 1.149451 |
| Percentage | 114.9451% |
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Frequently Asked Questions
What is 16/35 plus 9/13 as a fraction?
16/35 + 9/13 in simplest fraction form is 523/455 (or 1 68/455 as a mixed number).
What is 16/35 plus 9/13 as a decimal?
16/35 + 9/13 converted to a decimal is 1.149451.
What is 16/35 plus 9/13 as a percentage?
16/35 + 9/13 expressed as a percentage is 114.9451%.
How do you write 16/35 plus 9/13 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 523/455 can be written as the mixed number 1 68/455.
Does 16/35 plus 9/13 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.149451...) because the denominator contains prime factors other than 2 and 5.