You have a piece of lumber that is 4 yards long. You want to cut lengths 2/3 yard long to use in a shelf you are building. How many shelves can you cut? Draw a picture of your solution. Explain your solution in words.

4 / (2/3) = 4 * (3/2) = ?

4 / (2/3)

4 * (3/2)

To determine how many shelves you can cut from a 4-yard long piece of lumber, you need to divide the length of the lumber by the length of each shelf piece.

In this case, the length of each shelf piece is 2/3 yard.

To calculate the number of shelves, you can use the formula:

Number of shelves = Length of lumber / Length of each shelf piece

Plugging in the values:

Number of shelves = 4 yards / (2/3) yard

To divide by a fraction, you can multiply by the reciprocal of the fraction. In this case, the reciprocal of 2/3 is 3/2.

Number of shelves = 4 yards * (3/2)

Multiplying 4 yards by 3/2:

Number of shelves = 12/2 = 6

So, you can cut a total of 6 shelves from the 4-yard long lumber piece.

To draw a picture of the solution, you can represent the 4-yard long piece of lumber as a horizontal line segment and divide it into six equal parts, each representing a 2/3 yard shelf piece.