Tarique drew this model for a problem : 2/5 2/5 2/5 2/5 2/5 2/5 (5 2/5 ) write 2 problems that can be solved using the model one of the problems should involve multiplying a whole number by a fraction. The other should involve multiplying a fraction by a whole number.

Here's one.

The five children in the Smith family each spend 2/5 of an hour doing household chores on Saturday. How much time did the spend all together on their chores?

*they spend . . .

Problem 1:

Multiply a whole number by a fraction using the given model.

Step 1: Determine the whole number and the fraction to be multiplied.
Let's take the whole number as 3 and the fraction as 2/5.

Step 2: Write the model and multiply.
We can write the model as 2/5 2/5 2/5 2/5 2/5 2/5 (5 2/5).
To multiply, we can add the fraction 2/5 repeatedly 3 times, since we are multiplying by 3.

Result: 2/5 2/5 2/5 2/5 2/5 2/5 (5 2/5) multiplied by 3 equals to 6/5 6/5 6/5 6/5 6/5 6/5 (16 1/5).

Problem 2:
Multiply a fraction by a whole number using the given model.

Step 1: Determine the whole number and the fraction to be multiplied.
Let's take the fraction as 1/5 and the whole number as 4.

Step 2: Write the model and multiply.
We can write the model as 2/5 2/5 2/5 2/5 2/5 2/5 (5 2/5).
To multiply, we can add the fraction 1/5 repeatedly 4 times, since we are multiplying by 4.

Result: 2/5 2/5 2/5 2/5 2/5 2/5 (5 2/5) multiplied by 4 equals to 8/5 8/5 8/5 8/5 8/5 8/5 (21 2/5).

To solve the two problems using the given model, we need to understand how the numbers in the model correspond to the operations mentioned — multiplying a whole number by a fraction and multiplying a fraction by a whole number.

The model depicts the repeated fraction (2/5) six times, followed by the mixed number (5 2/5). This implies that multiplying a whole number by a fraction refers to multiplying 5 by 2/5, while multiplying a fraction by a whole number means multiplying 2/5 by 5.

Let's break down the two problems step by step:

1. Problem: Multiplying a whole number by a fraction.
- Number 1 in the model: 2/5
- Number 2 in the model: 2/5
- Number 3 in the model: 2/5
- Number 4 in the model: 2/5
- Number 5 in the model: 2/5
- Number 6 in the model: 2/5
- Mixed number: 5 2/5

To solve this problem, we need to multiply 5 (the whole number) by 2/5 (the fraction) or, mathematically, 5 * 2/5.

Solution:
5 * 2/5 = (5 * 2) / 5 = 10/5 = 2

Therefore, the solution to this problem is 2.

2. Problem: Multiplying a fraction by a whole number.
- Number 1-6 in the model: 2/5
- Mixed number: 5 2/5

In this case, we need to multiply 2/5 (the fraction) by 5 (the whole number) or, mathematically, 2/5 * 5.

Solution:
2/5 * 5 = (2 * 5) / 5 = 10/5 = 2

Again, the solution to this problem is 2.

Therefore, both problems involve multiplying numbers using the given model, with the first problem being about multiplying a whole number by a fraction, and the second problem being about multiplying a fraction by a whole number.