a rectangle shows counters representing 1 as the black counters and -1 as the red counters
the rectangle shows all red counters (the red counters represent -1)
Which of the following equations is modeled by the counters inside the rectangle?
Responses
A 12 ÷ (-3) = -412 ÷ (-3) = -4
B (-12) ÷ 3 = -4(-12) ÷ 3 = -4
C (-12) ÷ (-3) = 4(-12) ÷ (-3) = 4
D 12 ÷ 3 = 4
C (-12) ÷ (-3) = 4(-12) ÷ (-3) = 4
Based on the description provided, the counters inside the rectangle represent -1, which means they represent the value of -1. Therefore, the correct equation would be:
C) (-12) ÷ (-3) = 4(-12) ÷ (-3) = 4
This equation correctly models the distribution of the counters in the rectangle.
To determine which equation is modeled by the counters inside the rectangle, let's analyze the information given. The rectangle represents all red counters, which represent the value -1.
The area of the rectangle signifies the total sum of the counters. Since all the counters are red, the sum would be equal to the number of counters multiplied by -1.
Now let's evaluate each option based on this information:
A. 12 ÷ (-3) = -4
In this equation, we have 12 counters divided by -3. However, the sum of counters in the rectangle is -1, not 12. So, this option does not match the representation.
B. (-12) ÷ 3 = -4
This equation suggests dividing -12 by 3. Here, we have the correct sign and numbers, but the sum represented in the rectangle is -1, not -12. Thus, this option is also incorrect.
C. (-12) ÷ (-3) = 4
In this equation, we are dividing -12 by -3. The signs align with the representation, as both are negative. Also, the result of the division, 4, matches the sum represented by the rectangle, -1. Therefore, this option matches the representation.
D. 12 ÷ 3 = 4
Here, we find 12 counters divided by 3, resulting in 4. However, the sum depicted by the rectangle is -1, not 4. Hence, this option does not match the representation.
Based on the analysis, option C, (-12) ÷ (-3) = 4, is the equation that matches the counters inside the rectangle.