The carrot cakes are the fraction of the cake given by
multiplied by ![\frac{1}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D)
- The fraction of the cakes that are carrot cakes is
![\underline {\dfrac{1}{21}}](https://tex.z-dn.net/?f=%5Cunderline%20%7B%5Cdfrac%7B1%7D%7B21%7D%7D)
<h3>How are the cakes evaluated as fractions?</h3>
The fraction of the cake that are chocolate cake = ![\dfrac{2}{3}](https://tex.z-dn.net/?f=%5Cdfrac%7B2%7D%7B3%7D)
The fraction of the remaining cake that cheesecakes = ![\dfrac{6}{7}](https://tex.z-dn.net/?f=%5Cdfrac%7B6%7D%7B7%7D)
The rest of the cakes = carrot cakes
Required:
The fraction of the cake that are carrot cakes
Solution:
The fraction of the cakes that are not chocolate cake = ![1 - \dfrac{2}{3} = \mathbf{ \dfrac{1}{3}}](https://tex.z-dn.net/?f=1%20-%20%5Cdfrac%7B2%7D%7B3%7D%20%3D%20%5Cmathbf%7B%20%5Cdfrac%7B1%7D%7B3%7D%7D)
The fraction of the remaining cakes that are cheesecake = ![\dfrac{6}{7} \times \dfrac{1}{3} = \mathbf{ \dfrac{6}{21}}](https://tex.z-dn.net/?f=%5Cdfrac%7B6%7D%7B7%7D%20%5Ctimes%20%5Cdfrac%7B1%7D%7B3%7D%20%3D%20%5Cmathbf%7B%20%5Cdfrac%7B6%7D%7B21%7D%7D)
The fraction of the cake that are carrot cake = ![\dfrac{1}{3} - \dfrac{6}{7} \times \dfrac{1}{3} = \mathbf{\dfrac{1}{21}}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B3%7D%20-%20%5Cdfrac%7B6%7D%7B7%7D%20%5Ctimes%20%5Cdfrac%7B1%7D%7B3%7D%20%3D%20%5Cmathbf%7B%5Cdfrac%7B1%7D%7B21%7D%7D)
- The fraction of the cakes that are carrot cake is
![\underline{\dfrac{1}{21}}](https://tex.z-dn.net/?f=%5Cunderline%7B%5Cdfrac%7B1%7D%7B21%7D%7D)
Learn more about fractions here:
brainly.com/question/3840488