Question

Celia has some cakes.

Answer 1

The carrot cakes are the fraction of the cake given by $1 - \frac{6}{7}$ multiplied by $\frac{1}{3}$

• The fraction of the cakes that are carrot cakes is $\underline {\dfrac{1}{21}}$

How are the cakes evaluated as fractions?

The fraction of the cake that are chocolate cake = $\dfrac{2}{3}$

The fraction of the remaining cake that cheesecakes = $\dfrac{6}{7}$

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 = $1 - \dfrac{2}{3} = \mathbf{ \dfrac{1}{3}}$

The fraction of the remaining cakes that are cheesecake = $\dfrac{6}{7} \times \dfrac{1}{3} = \mathbf{ \dfrac{6}{21}}$

The fraction of the cake that are carrot cake = $\dfrac{1}{3} - \dfrac{6}{7} \times \dfrac{1}{3} = \mathbf{\dfrac{1}{21}}$

• The fraction of the cakes that are carrot cake is $\underline{\dfrac{1}{21}}$

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