4/12 + 8/5
Understand the Problem
The question is asking to perform the addition of two fractions, 4/12 and 8/5. The process involves finding a common denominator and then adding the numerators.
Answer
The answer is $\frac{29}{15}$.
Answer for screen readers
The final answer is $\frac{29}{15}$.
Steps to Solve
- Find the Least Common Denominator (LCD)
To add the fractions $\frac{4}{12}$ and $\frac{8}{5}$, we first need to find the least common denominator. The denominators are 12 and 5. The smallest multiple of both is 60.
- Convert the Fractions
Now, we need to convert both fractions to have the common denominator of 60.
For $\frac{4}{12}$, we multiply both the numerator and denominator by 5: $$ \frac{4}{12} = \frac{4 \times 5}{12 \times 5} = \frac{20}{60} $$
For $\frac{8}{5}$, we multiply both the numerator and denominator by 12: $$ \frac{8}{5} = \frac{8 \times 12}{5 \times 12} = \frac{96}{60} $$
- Add the Fractions
Now that we have both fractions with a common denominator, we can add them: $$ \frac{20}{60} + \frac{96}{60} = \frac{20 + 96}{60} = \frac{116}{60} $$
- Simplify the Result
Finally, we simplify $\frac{116}{60}$. To do this, we find the greatest common divisor (GCD) of 116 and 60, which is 4. Now, divide both the numerator and the denominator by 4: $$ \frac{116 \div 4}{60 \div 4} = \frac{29}{15} $$
The final answer is $\frac{29}{15}$.
More Information
The resulting fraction $\frac{29}{15}$ is an improper fraction, which means that the numerator is larger than the denominator. It can also be converted into a mixed number: $1 \frac{14}{15}$. This indicates it is slightly more than 1 and less than 2.
Tips
- Forgetting to find a common denominator before adding fractions.
- Not simplifying the fraction at the end. Always check for the GCD to simplify.
AI-generated content may contain errors. Please verify critical information
