How do you divide a whole number by a fraction?

To divide a whole number by a fraction, multiply the whole number by the fraction's reciprocal.

When you divide a whole number by a fraction, you essentially want to see how many times that fraction fits into the whole number. To do this, you use the reciprocal of the fraction. The reciprocal of a fraction is simply flipping the numerator (top number) and the denominator (bottom number). For example, the reciprocal of \( \frac{3}{4} \) is \( \frac{4}{3} \).

Let's say you want to divide 6 by \( \frac{2}{3} \). First, find the reciprocal of \( \frac{2}{3} \), which is \( \frac{3}{2} \). Then, multiply 6 by \( \frac{3}{2} \). To multiply a whole number by a fraction, you multiply the whole number by the numerator and then divide by the denominator. So, \( 6 \times \frac{3}{2} = \frac{6 \times 3}{2} = \frac{18}{2} = 9 \).

In another example, if you want to divide 8 by \( \frac{5}{6} \), first find the reciprocal of \( \frac{5}{6} \), which is \( \frac{6}{5} \). Then, multiply 8 by \( \frac{6}{5} \). This gives \( 8 \times \frac{6}{5} = \frac{8 \times 6}{5} = \frac{48}{5} = 9.6 \).

Remember, dividing by a fraction is the same as multiplying by its reciprocal. This method simplifies the process and helps you understand the relationship between division and multiplication in the context of fractions.