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?
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).
To understand the meaning and solve the equation 1/3 Y ÷ 1/2 X = 4, let's break it down step by step:
1. Equation Meaning:
The equation states that when you divide 1/3 of the value of Y by 1/2 of the value of X, the result is 4. In other words, if you take one-third of the value of Y and divide it by one-half of the value of X, the quotient will be 4.
2. Creating Shapes:
To visually represent the values of X and Y, we can use shapes. Let's assume X is represented by a triangle and Y is represented by a square.
3. Illustrating the Quotient:
To illustrate how the quotient is obtained, we can represent the division visually. For example, by splitting the square (Y) into three equal parts (1/3) and the triangle (X) into two equal parts (1/2), we can show that when we divide one of the parts of Y by one of the parts of X, the result is 4.
4. Use of Tangram for X and Y:
A traditional tangram consists of seven flat puzzle pieces that can be arranged to form various shapes. While it is possible to use individual pieces of a traditional tangram to represent X and Y, it would be challenging to demonstrate the specific relationship of dividing 1/3 of Y by 1/2 of X using these pieces.
5. Balancing the Scale:
If we draw a scale with one Y on the left side, to balance the scale, we cannot simply put one Y on the right side since it would create an imbalance. However, if we put two-thirds of Y on the right side, it would balance the scale with one-third on the left side.
In summary, the equation 1/3 Y ÷ 1/2 X = 4 represents the relationship of dividing one-third of Y by one-half of X to obtain a quotient of 4. By visually representing X and Y using shapes and illustrating the division process, you can better understand the equation. However, using individual pieces of a tangram may not be the best choice to represent X and Y or to demonstrate the given relationship. Finally, to balance a scale with one Y on the left side, you would need to put two-thirds of Y on the right side.