What is 16/33 plus 15/21?
16/33 plus 15/21 equals 277/231 (or 1 46/231 as a mixed number) (or 1.199134 in decimal form). Learn the step-by-step solution to add 16/33 and 15/21 using Least Common Denominator and simplification.
Exact Answer
16/33 + 15/21 = 277/231
Simplified Fraction
277/231
Mixed Number
1 46/231
Decimal Value
1.199134
Percentage
119.9134%
Step-by-Step Solution: 16/33 + 15/21
Step 1
Find the Least Common Denominator (LCD)
The denominators 33 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 231 (which is smaller than their product 33 × 21 = 693, keeping the calculation simpler).
LCD(33, 21) = 231
Step 2
Convert to Equivalent Fractions with Common Denominator 231
Multiply the numerator and denominator of 16/33 by 7, and multiply the numerator and denominator of 15/21 by 11 so both fractions share the common base 231.
16 × 7/33 × 7 = 112/231 and 15 × 11/21 × 11 = 165/231
Step 3
Add the Numerators
Now add the numerators (112 + 165 = 277) and keep the common denominator 231 unchanged.
112 + 165/231 = 277/231
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 277 and 231 is 1, confirming that 277/231 cannot be reduced further—it is already in its simplest irreducible form.
277/231
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (277) is greater than the denominator (231), divide 277 by 231: it goes in 1 whole time(s) with a remainder of 46, giving the mixed number 1 46/231.
277/231 = 146/231
Step 6
Decimal & Percentage Representation
Dividing the numerator 277 by denominator 231 produces a repeating decimal (approximately 1.199134, or 119.9134%).
277 ÷ 231 = 1.199134 (119.9134%)
Visual Representation
The diagram below illustrates 16/33 plus 15/21 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 277/231 |
| Mixed Number Form | 1 46/231 |
| Decimal Form | 1.199134 |
| Percentage | 119.9134% |
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Frequently Asked Questions
What is 16/33 plus 15/21 as a fraction?
16/33 + 15/21 in simplest fraction form is 277/231 (or 1 46/231 as a mixed number).
What is 16/33 plus 15/21 as a decimal?
16/33 + 15/21 converted to a decimal is 1.199134.
What is 16/33 plus 15/21 as a percentage?
16/33 + 15/21 expressed as a percentage is 119.9134%.
How do you write 16/33 plus 15/21 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 277/231 can be written as the mixed number 1 46/231.
Does 16/33 plus 15/21 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.199134...) because the denominator contains prime factors other than 2 and 5.