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 given equation 1/3 Y ÷ 1/2 X = 4, let's break it down step by step:
Step 1: Simplify the equation.
When you divide one fraction by another fraction, you can multiply the first fraction by the reciprocal of the second fraction. So, we can rewrite the equation as follows:
(1/3 Y) * (2/1 X) = 4
Step 2: Multiply the fractions.
When you multiply fractions, multiply the numerators together, and multiply the denominators together. Therefore, we have:
(1 * 2) / (3 * 1) * (Y * X) = 4
Simplifying further, we get:
2/3 * YX = 4
Step 3: Solve for YX.
To find the value of YX, we need to divide both sides of the equation by the coefficient 2/3. Dividing by a fraction is equivalent to multiplying by its reciprocal, so we get:
(YX) = 4 / (2/3)
To simplify the expression on the right side, we can multiply the numerator by the reciprocal of the denominator:
(YX) = 4 * (3/2)
Simplifying further, we obtain:
(YX) = 12/2
Simplifying the fraction, we find:
(YX) = 6
So, the value of YX is 6.
To create shapes for X and Y, you can use any geometric figures or objects you prefer. For example, you can draw a square to represent X and a circle to represent Y.
For the X shape, draw a square and label it as X. Then, for the Y shape, draw a circle and label it as Y. Additionally, you can write the value "6" inside the Y shape to represent the value for YX, which we obtained earlier.
Now, regarding the use of traditional tangram pieces to represent X and Y, it is not directly possible to use them to support the given relationship. Tangram pieces are geometric shapes that can be combined to form other shapes, but they do not incorporate numerical values or allow for mathematical operations such as division.
If you draw a scale with one Y on the left side, for the scale to balance, you will need to put 6X on the right side. This means that the weight of one Y is equal to the weight of 6X.