The given partial fraction divided by the fraction of sugar in a scoop is
equal to multiplying the partial fraction by the reciprocal of the fraction.
- The number of scoops of sugar needed is <u>10 scoops</u>.
Reasons:
The amount of sugar the recipe Emma is making needs = 2 1/2 cups
Amount of sugar in each scoop of sugar = 1/4 cups
Required:
The amount of scoops Emma needs to add for the entire recipe
Solution:
The amount of sugar needed = 2 1/2 cups
Amount of sugar per scoop = 1/4 cups/scoop
Therefore;
Which gives;
![\displaystyle 2 \frac{1}{2} = \frac{5}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%202%20%5Cfrac%7B1%7D%7B2%7D%20%3D%20%5Cfrac%7B5%7D%7B2%7D)
![\displaystyle \frac{ \frac{5}{2}}{\frac{1}{4} } = \mathbf{ \frac{5}{2} \times \frac{4}{1} = \frac{20}{2 }} = 10](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B%20%5Cfrac%7B5%7D%7B2%7D%7D%7B%5Cfrac%7B1%7D%7B4%7D%20%7D%20%3D%20%20%5Cmathbf%7B%20%5Cfrac%7B5%7D%7B2%7D%20%5Ctimes%20%5Cfrac%7B4%7D%7B1%7D%20%3D%20%5Cfrac%7B20%7D%7B2%20%7D%7D%20%3D%2010)
Therefore;
![\displaystyle Number \ of \ scoops \ needed = \mathbf{\frac{2 \frac{1}{2} \ cups \ of \ sugar }{\frac{1}{4} \ cups \ of \ sugar \ per \ scoop}} = 10 \, scoops](https://tex.z-dn.net/?f=%5Cdisplaystyle%20Number%20%5C%20of%20%5C%20scoops%20%5C%20needed%20%20%3D%20%5Cmathbf%7B%5Cfrac%7B2%20%5Cfrac%7B1%7D%7B2%7D%20%20%5C%20cups%20%5C%20of%20%5C%20sugar%20%7D%7B%5Cfrac%7B1%7D%7B4%7D%20%5C%20%20cups%20%5C%20of%20%5C%20sugar%20%5C%20per%20%5C%20scoop%7D%7D%20%3D%2010%20%5C%2C%20scoops)
The number of scoops she needs for the entire recipe is <u>10 scoops</u>
Learn more about division by fractions here:
brainly.com/question/20591763