Question

kareems cheese recipe requires salt. he has \\(\frac{3}{5}\\) bags of salt. he uses \\(\frac{1}{9}\\) bags of salt for each kilogram of cheese that he makes. complete the following to help kareem find how many kilograms of cheese he has the salt to make.

(a) fill in the blanks to write an expression that gives the number of kilograms of cheese kareem has the salt to make. choose only from \\(\frac{3}{5}\\), \\(\frac{1}{9}\\), +, -, \\(\times\\), or \\(\div\\).

expression: \\(\square\\ \square\\ \square\\)

(b) here is a figure that represents 1 whole bag of salt.

choose the figure that can be used to model how many kilograms of cheese kareem has the salt to make.

(options with figures showing different segmentations for salt per kilogram of cheese)

Explanation:

Step1: Identify operation for quantity

To find the number of kilograms, we divide total salt by salt per kg.
Expression: $\frac{3}{5} \div \frac{1}{9}$

Step2: Calculate the value

Dividing by a fraction is multiplying by its reciprocal.
$\frac{3}{5} \times \frac{9}{1} = \frac{27}{5} = 5.4$

Step3: Match to the model

The total salt is $\frac{3}{5}$, and each kg uses $\frac{1}{9}$. The correct model divides the total into $\frac{1}{9}$ segments: the third option (with 7 shaded small parts, where the whole is split into 9 parts, and $\frac{3}{5}$ of the whole equals $\frac{27}{45}$, while $\frac{1}{9}$ is $\frac{5}{45}$, so $\frac{27}{5}=5.4$ matches 5 full $\frac{1}{9}$ segments plus a partial one, which is the third figure).

Answer:

(a) Expression: $\boldsymbol{\frac{3}{5} \div \frac{1}{9}}$
(b) The correct figure is the third option (bottom-left, with 7 shaded small segments, where each full kg's salt is 2 small segments, and the total shaded represents $\frac{3}{5}$ of the whole bag, matching the calculation of 5.4 kg of cheese).