simplify 27 1/3
Understand the Problem
The question is asking to simplify the mixed number 27 1/3 into an improper fraction or a simpler form.
Answer
The mixed number 27 1/3 as an improper fraction is $\frac{82}{3}$.
Answer for screen readers
The final answer is $\frac{82}{3}$.
Steps to Solve
- Identify the whole number and the fractional part
The mixed number is composed of a whole number part and a fractional part. Here, the whole number is 27 and the fractional part is $\frac{1}{3}$.
- Convert the whole number to an improper fraction
To convert the whole number to a fraction, write it as a fraction over 1. Thus, we convert 27 to $\frac{27}{1}$.
- Find a common denominator
The denominator of the fractional part is 3, so we need to convert $\frac{27}{1}$ to have the same denominator: $$ \frac{27}{1} = \frac{27 \times 3}{1 \times 3} = \frac{81}{3} $$ This gives us an improper fraction with a denominator of 3.
- Add the two fractions
Now, we can add the improper fraction obtained from the whole number to the fractional part: $$ \frac{81}{3} + \frac{1}{3} = \frac{81 + 1}{3} = \frac{82}{3} $$
- Write the final answer
The mixed number 27 1/3 simplified as an improper fraction is $\frac{82}{3}$.
The final answer is $\frac{82}{3}$.
More Information
When converting a mixed number to an improper fraction, remember that the whole number is multiplied by the denominator of the fractional part and then added to the numerator of the fractional part. This method can be applied to any mixed number.
Tips
- Forgetting to convert the whole number to a fraction before adding it to the fraction.
- Not finding a common denominator when needed.
