Given

1/3 Y÷1/2 X=4

Discuss its meaning.
Create a shape for X and for Y that will make this true. Draw and label the shapes, then illustrate how the quotient was obtained. Your drawing must be neat and accurate.
Can individual pieces of a traditional tangram be used to represent X and Y and to support the given relationship? Explain why or why not.
Draw a scale with one Y on the left side. What should you put on the right side for the scale to balance? (Note: You cannot put one Y).

1/3 Y / 1/2 x= 2/3 y/x

2/3 y /x=4
2y=12x
y= 6x

Looks like a line to me.

Can tangrams be use to represent x and y?

To understand the meaning of the equation 1/3 Y ÷ 1/2 X = 4, let's break it down step by step.

First, we have the division symbol "÷" which represents the operation of division. In this equation, we are dividing a variable Y by another variable X.

Next, we have the fractions 1/3 and 1/2. These fractions indicate that we are dividing Y by two-thirds and X by one-half, respectively.

Lastly, we have the result of this division, which is 4. This means that the ratio of Y divided by two-thirds of X is equal to 4.

To create a shape for X and Y that satisfies this equation, we can use rectangles as an example. Let's represent X as a rectangle with a length of 6 units (since one-half of X is equal to 6), and Y as a rectangle with a length of 8 units (since two-thirds of Y is equal to 8).

To illustrate how the quotient was obtained, we can divide the length of Y (8 units) by the length of X (6 units). In this case, the division gives us a result of 4, which matches the value in the equation.

Regarding the traditional tangram pieces, they may not be suitable for representing X and Y in this equation since the tangram pieces are fixed shapes with specific dimensions. They cannot be easily adjusted to satisfy the equation or represent fractions.

If we draw a scale with one Y on the left side, in order to balance the scale, we need to put a value on the right side that is equal to or proportional to Y. Since we cannot put just one Y (as specified in the question), we can choose a value that satisfies the equation. From the given equation, we have 1/3 Y ÷ 1/2 X = 4. If we multiply both sides of the equation by 1/4, we get Y ÷ (1/6)X = 1. In this case, we would need a value of 1/6X on the right side of the scale to balance it.