$\frac{4}{5} = \frac{4}{5} \times \frac{8}{8} =$
We are asked to complete the equation \(\frac{4}{5} = \frac{4}{5} \times \frac{8}{8} = \boxed{\phantom{00}}\). The problem involves multiplying the fraction \(\frac{4}{5}\) by another fraction, \(\frac{8}{8}\), which is equal to \(1\). Since multiplying any number by \(1\) does not change its value, we are essentially finding an equivalent fraction for \(\frac{4}{5}\).
To find the value that goes into the box, we perform the multiplication \(\frac{4}{5} \times \frac{8}{8}\).
Multiplying fractions involves multiplying the numerators together and the denominators together:
\[\frac{4 \times 8}{5 \times 8} = \frac{32}{40}\]
Thus, the value of the expression is \(\frac{32}{40}\). Note that \(\frac{32}{40}\) simplifies back to \(\frac{4}{5}\), confirming the equivalence.
We have determined that \(\frac{4}{5} \times \frac{8}{8} = \frac{32}{40}\). Therefore, the value to fill in the box is \(\frac{32}{40}\).
The final answer is \(\boxed{\frac{32}{40}}\).
Equivalent fractions are essential in everyday life, such as when adjusting recipes. If a recipe calls for \(\frac{4}{5}\) of a cup of flour, but you only have a measuring cup marked in fortieths, you can use the calculation \(\frac{4}{5} \times \frac{8}{8} = \frac{32}{40}\) to realize you need 32 parts of the 40-part cup. Understanding how to create equivalent fractions helps in resizing ingredients, scaling architectural designs, or comparing different amounts of materials.