Ms. Sherman is preparing 5 5/8 cups of rice. She is using a fixed amount of 1/4 cup for each serving. Since we know the total amount of rice she is using and the amount per serving, we divide these to determine the number of servings.
It might be easier to see if we used friendlier numbers. If she has 10 cups total and uses 2 cups per serving she would have 10 / 2 = 5 servings.
Now, back to the numbers we were given. We need to divide 5 5/8 by 1/4. Let's first re-write 5 5/8 as an improper fraction (multiply 8 by 5 and add 5 to get 45 then place this over the already existing denominator of 8). 5 5/8 = 45 / 8.
The division we need to undertake is [tex] \frac{45}{8} / \frac{1}{4} [/tex]
To divide by a fraction we multiply by the reciprocal (what you get when you flip the fraction over) so our problem becomes [tex]( \frac{45}{8} )( \frac{4}{1} )[/tex]
We multiply across to get [tex]( \frac{45}{8} )( \frac{4}{1} ) = \frac{(45)(4)}{(8)(1)}= \frac{180}{8}=22.5 [/tex]
That is, she is making 22.5 servings. As a fraction this is 22 1/2
