What is 5 divided by 2/3 as a fraction
The Correct Answer and Explanation is :
To divide 5 by (\frac{2}{3}), follow these steps:
- Rewrite the division as multiplication:
[
5 \div \frac{2}{3} = 5 \times \frac{3}{2}
]
When dividing by a fraction, you multiply by its reciprocal (flip the numerator and denominator). - Multiply:
[
5 \times \frac{3}{2} = \frac{5 \times 3}{1 \times 2} = \frac{15}{2}
]
So, 5 divided by (\frac{2}{3}) equals (\frac{15}{2}).
Explanation (300 words):
Dividing by a fraction can sometimes be confusing, but there’s a simple rule: to divide by a fraction, multiply by its reciprocal. This is because division is the inverse of multiplication. To see why this works, consider the problem 5 divided by (\frac{2}{3}).
Imagine the fraction (\frac{2}{3}) as “two-thirds.” If you are dividing by (\frac{2}{3}), you’re asking how many times two-thirds fit into 5. To simplify this, you can flip the fraction and multiply instead of dividing. This gives us 5 multiplied by (\frac{3}{2}), which makes the calculation straightforward.
Now, when multiplying fractions, you multiply the numerators (top numbers) and the denominators (bottom numbers) separately. In our case, multiplying the whole number 5 by (\frac{3}{2}) means converting 5 into a fraction ((\frac{5}{1})) and performing the multiplication:
[
\frac{5}{1} \times \frac{3}{2} = \frac{5 \times 3}{1 \times 2} = \frac{15}{2}
]
The result, (\frac{15}{2}), is an improper fraction, meaning the numerator is larger than the denominator. This is the correct answer and cannot be simplified further as a fraction.
You could convert (\frac{15}{2}) to a mixed number, but (\frac{15}{2}) itself is the precise fractional result.