What is 16/33 plus 9/13?
16/33 plus 9/13 equals 505/429 (or 1 76/429 as a mixed number) (or 1.177156 in decimal form). Learn the step-by-step solution to add 16/33 and 9/13 using Least Common Denominator and simplification.
Exact Answer
16/33 + 9/13 = 505/429
Simplified Fraction
505/429
Mixed Number
1 76/429
Decimal Value
1.177156
Percentage
117.7156%
Step-by-Step Solution: 16/33 + 9/13
Step 1
Find the Least Common Denominator (LCD)
The denominators 33 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 33 × 13 = 429.
LCD(33, 13) = 429
Step 2
Convert to Equivalent Fractions with Common Denominator 429
Multiply the numerator and denominator of 16/33 by 13, and multiply the numerator and denominator of 9/13 by 33 so both fractions share the common base 429.
16 × 13/33 × 13 = 208/429 and 9 × 33/13 × 33 = 297/429
Step 3
Add the Numerators
Now add the numerators (208 + 297 = 505) and keep the common denominator 429 unchanged.
208 + 297/429 = 505/429
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 505 and 429 is 1, confirming that 505/429 cannot be reduced further—it is already in its simplest irreducible form.
505/429
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (505) is greater than the denominator (429), divide 505 by 429: it goes in 1 whole time(s) with a remainder of 76, giving the mixed number 1 76/429.
505/429 = 176/429
Step 6
Decimal & Percentage Representation
Dividing the numerator 505 by denominator 429 produces a repeating decimal (approximately 1.177156, or 117.7156%).
505 ÷ 429 = 1.177156 (117.7156%)
Visual Representation
The diagram below illustrates 16/33 plus 9/13 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 505/429 |
| Mixed Number Form | 1 76/429 |
| Decimal Form | 1.177156 |
| Percentage | 117.7156% |
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Frequently Asked Questions
What is 16/33 plus 9/13 as a fraction?
16/33 + 9/13 in simplest fraction form is 505/429 (or 1 76/429 as a mixed number).
What is 16/33 plus 9/13 as a decimal?
16/33 + 9/13 converted to a decimal is 1.177156.
What is 16/33 plus 9/13 as a percentage?
16/33 + 9/13 expressed as a percentage is 117.7156%.
How do you write 16/33 plus 9/13 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 505/429 can be written as the mixed number 1 76/429.
Does 16/33 plus 9/13 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.177156...) because the denominator contains prime factors other than 2 and 5.