Question

the model below represents a division problem. which equation is represented by the model? answer options: $1\frac{3}{5} \div \frac{2}{5} = 4$, $\frac{1}{5} \div 8 = 1\frac{3}{5}$, $\frac{2}{5} \div 1\frac{3}{5} = 4$, $\frac{2}{5} \div 4 = 1\frac{3}{5}$

Explanation:

Step1: Analyze the model

The model shows a total length (let's consider the blue part and the white part, but focusing on the division context). The blue segments are each \( \frac{2}{5} \)? Wait, no, looking at the labels: the blue parts are labeled \( \frac{2}{5} \)? Wait, no, the problem says "a division problem" and the model has segments. Wait, maybe the total of the blue parts is \( 1\frac{3}{5} \) (since \( 1 + \frac{3}{5} \))? Wait, no, let's re-express. Wait, the equation options: let's check each.

First, let's parse the model. The blue area: let's see, the total of the blue parts: if each blue segment is \( \frac{2}{5} \), and how many? Wait, no, the options: let's check \( \frac{2}{5} \div \frac{1}{5} = 4 \)? Wait, no, let's look at the options:

Option 1: \( 1\frac{3}{5} \div \frac{2}{5} = 4 \)

Option 2: \( \frac{2}{5} \div 1\frac{3}{5} = 4 \) (no, that can't be, since \( 1\frac{3}{5} > \frac{2}{5} \), division would be less than 1)

Option 3: \( \frac{1}{5} \div 8 = 1\frac{3}{5} \) (no, \( \frac{1}{5} \div 8 = \frac{1}{40} \), not \( 1\frac{3}{5} \))

Option 4: \( \frac{2}{5} \div 4 = 1\frac{3}{5} \) (no, \( \frac{2}{5} \div 4 = \frac{1}{10} \), not \( 1\frac{3}{5} \))

Wait, maybe the total of the blue parts is \( 1\frac{3}{5} \) (which is \( \frac{8}{5} \)) and each segment is \( \frac{2}{5} \). Then \( \frac{8}{5} \div \frac{2}{5} = 4 \), which is \( 1\frac{3}{5} \div \frac{2}{5} = 4 \) (since \( 1\frac{3}{5} = \frac{8}{5} \), \( \frac{8}{5} \div \frac{2}{5} = \frac{8}{5} \times \frac{5}{2} = 4 \)). So that's the first option.

Step2: Verify each option

• Option 1: \( 1\frac{3}{5} \div \frac{2}{5} = \frac{8}{5} \div \frac{2}{5} = \frac{8}{5} \times \frac{5}{2} = 4 \). Correct.
• Option 2: \( \frac{2}{5} \div 1\frac{3}{5} = \frac{2}{5} \div \frac{8}{5} = \frac{2}{5} \times \frac{5}{8} = \frac{1}{4}

eq 4 \). Incorrect.

• Option 3: \( \frac{1}{5} \div 8 = \frac{1}{40}

eq 1\frac{3}{5} \). Incorrect.

• Option 4: \( \frac{2}{5} \div 4 = \frac{1}{10}

eq 1\frac{3}{5} \). Incorrect.

Answer:

\( 1\frac{3}{5} \div \frac{2}{5} = 4 \) (the first option, assuming the first option is labeled as, say, A: \( 1\frac{3}{5} \div \frac{2}{5} = 4 \))