What is 16/31 plus 9/13?
16/31 plus 9/13 equals 487/403 (or 1 84/403 as a mixed number) (or 1.208437 in decimal form). Learn the step-by-step solution to add 16/31 and 9/13 using Least Common Denominator and simplification.
Exact Answer
16/31 + 9/13 = 487/403
Simplified Fraction
487/403
Mixed Number
1 84/403
Decimal Value
1.208437
Percentage
120.8437%
Step-by-Step Solution: 16/31 + 9/13
Step 1
Find the Least Common Denominator (LCD)
The denominators 31 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 31 × 13 = 403.
LCD(31, 13) = 403
Step 2
Convert to Equivalent Fractions with Common Denominator 403
Multiply the numerator and denominator of 16/31 by 13, and multiply the numerator and denominator of 9/13 by 31 so both fractions share the common base 403.
16 × 13/31 × 13 = 208/403 and 9 × 31/13 × 31 = 279/403
Step 3
Add the Numerators
Now add the numerators (208 + 279 = 487) and keep the common denominator 403 unchanged.
208 + 279/403 = 487/403
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 487 and 403 is 1, confirming that 487/403 cannot be reduced further—it is already in its simplest irreducible form.
487/403
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (487) is greater than the denominator (403), divide 487 by 403: it goes in 1 whole time(s) with a remainder of 84, giving the mixed number 1 84/403.
487/403 = 184/403
Step 6
Decimal & Percentage Representation
Dividing the numerator 487 by denominator 403 produces a repeating decimal (approximately 1.208437, or 120.8437%).
487 ÷ 403 = 1.208437 (120.8437%)
Visual Representation
The diagram below illustrates 16/31 plus 9/13 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 487/403 |
| Mixed Number Form | 1 84/403 |
| Decimal Form | 1.208437 |
| Percentage | 120.8437% |
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Frequently Asked Questions
What is 16/31 plus 9/13 as a fraction?
16/31 + 9/13 in simplest fraction form is 487/403 (or 1 84/403 as a mixed number).
What is 16/31 plus 9/13 as a decimal?
16/31 + 9/13 converted to a decimal is 1.208437.
What is 16/31 plus 9/13 as a percentage?
16/31 + 9/13 expressed as a percentage is 120.8437%.
How do you write 16/31 plus 9/13 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 487/403 can be written as the mixed number 1 84/403.
Does 16/31 plus 9/13 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.208437...) because the denominator contains prime factors other than 2 and 5.