The carrot cakes are the fraction of the cake given by [tex]1 - \frac{6}{7}[/tex] multiplied by [tex]\frac{1}{3}[/tex]
- The fraction of the cakes that are carrot cakes is [tex]\underline {\dfrac{1}{21}}[/tex]
How are the cakes evaluated as fractions?
The fraction of the cake that are chocolate cake = [tex]\dfrac{2}{3}[/tex]
The fraction of the remaining cake that cheesecakes = [tex]\dfrac{6}{7}[/tex]
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 = [tex]1 - \dfrac{2}{3} = \mathbf{ \dfrac{1}{3}}[/tex]
The fraction of the remaining cakes that are cheesecake = [tex]\dfrac{6}{7} \times \dfrac{1}{3} = \mathbf{ \dfrac{6}{21}}[/tex]
The fraction of the cake that are carrot cake = [tex]\dfrac{1}{3} - \dfrac{6}{7} \times \dfrac{1}{3} = \mathbf{\dfrac{1}{21}}[/tex]
- The fraction of the cakes that are carrot cake is [tex]\underline{\dfrac{1}{21}}[/tex]
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