What is 8/5 divided by 3? How do I solve a question with a fraction with a greater numerator?
The Correct Answer and Explanation is:
To solve the problem of dividing ( \frac{8}{5} ) by 3, you need to follow a process for dividing fractions. Here’s how you solve it:
- Rewrite the Whole Number as a Fraction:
Since 3 is a whole number, you can represent it as a fraction by writing it as ( \frac{3}{1} ). Now, the division problem looks like this:
[
\frac{8}{5} \div \frac{3}{1}
] - Invert and Multiply:
When dividing fractions, you multiply by the reciprocal (or the “flipped” version) of the second fraction. The reciprocal of ( \frac{3}{1} ) is ( \frac{1}{3} ). So, the problem becomes:
[
\frac{8}{5} \times \frac{1}{3}
] - Multiply the Numerators and Denominators:
Multiply the numerators together and the denominators together:
[
\frac{8 \times 1}{5 \times 3} = \frac{8}{15}
]
Thus, the answer is ( \frac{8}{15} ).
Detailed Explanation
Fractions can sometimes seem complex, especially when the numerator (top number) is greater than the denominator (bottom number), which makes it an improper fraction. In such cases, you handle them just like you would any other fraction.
When you divide fractions, you’re essentially finding out how many times one fraction fits into another. The key step in dividing fractions is to convert the division into multiplication by flipping (taking the reciprocal of) the second fraction.
For example, in this case, ( \frac{8}{5} ) is the improper fraction, and 3 is a whole number. The division ( \frac{8}{5} \div 3 ) is solved by flipping 3 into ( \frac{1}{3} ) and then multiplying. After that, you simply multiply the numerators together and the denominators together.
The final fraction, ( \frac{8}{15} ), is already in its simplest form since 8 and 15 have no common factors other than 1.
By understanding the steps of converting a whole number to a fraction, inverting and multiplying, and simplifying, you can solve any fraction division problem efficiently.