What is 16/27 plus 9/13?
16/27 plus 9/13 equals 451/351 (or 1 100/351 as a mixed number) (or 1.2849 in decimal form). Learn the step-by-step solution to add 16/27 and 9/13 using Least Common Denominator and simplification.
Exact Answer
16/27 + 9/13 = 451/351
Simplified Fraction
451/351
Mixed Number
1 100/351
Decimal Value
1.2849
Percentage
128.49%
Step-by-Step Solution: 16/27 + 9/13
Step 1
Find the Least Common Denominator (LCD)
The denominators 27 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 27 × 13 = 351.
LCD(27, 13) = 351
Step 2
Convert to Equivalent Fractions with Common Denominator 351
Multiply the numerator and denominator of 16/27 by 13, and multiply the numerator and denominator of 9/13 by 27 so both fractions share the common base 351.
16 × 13/27 × 13 = 208/351 and 9 × 27/13 × 27 = 243/351
Step 3
Add the Numerators
Now add the numerators (208 + 243 = 451) and keep the common denominator 351 unchanged.
208 + 243/351 = 451/351
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 451 and 351 is 1, confirming that 451/351 cannot be reduced further—it is already in its simplest irreducible form.
451/351
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (451) is greater than the denominator (351), divide 451 by 351: it goes in 1 whole time(s) with a remainder of 100, giving the mixed number 1 100/351.
451/351 = 1100/351
Step 6
Decimal & Percentage Representation
Dividing the numerator 451 by denominator 351 produces a repeating decimal (approximately 1.2849, or 128.49%).
451 ÷ 351 = 1.2849 (128.49%)
Visual Representation
The diagram below illustrates 16/27 plus 9/13 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 451/351 |
| Mixed Number Form | 1 100/351 |
| Decimal Form | 1.2849 |
| Percentage | 128.49% |
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Frequently Asked Questions
What is 16/27 plus 9/13 as a fraction?
16/27 + 9/13 in simplest fraction form is 451/351 (or 1 100/351 as a mixed number).
What is 16/27 plus 9/13 as a decimal?
16/27 + 9/13 converted to a decimal is 1.2849.
What is 16/27 plus 9/13 as a percentage?
16/27 + 9/13 expressed as a percentage is 128.49%.
How do you write 16/27 plus 9/13 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 451/351 can be written as the mixed number 1 100/351.
Does 16/27 plus 9/13 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.2849...) because the denominator contains prime factors other than 2 and 5.