Question

Josie is making pizza dough. Complete the double number line by filling in the missing values. Then write an equation that models the relationship between the total cups of flour, c, and number of batches, n. Show your work.

Answer 1

Answer:

First part:

To complete the top number line use the numbers

          $1\dfrac{1}{2}$  

and

          $2\dfrac{1}{4}$

To complete the bottom number line use the numbers:

• 3, and

• 4

Second part:

The relationship between the total cups of flour, c, and number of batches n, is:

        $c=\dfrac{3}{4}n$

Explanation:

Find the complete question if the file attached.

First part.

The number line on top shows the number of cups of flour, c.

Each mark corresponds to 3/4 of cups. Thus the numbers that complete the number line are:

       $\dfrac{3}{4}+\dfrac{3}{4}=\dfrac{6}{4}=\dfrac{4}{4}+\dfrac{2}{4}=1+\dfrac{1}{2}=1\dfrac{1}{2}$

      $1\dfrac{1}{2}+\dfrac{3}{4}=1+\dfrac{1}{2}+\dfrac{3}{4}=\dfrac{4}{4}+\dfrac{2}{4}+\dfrac{3}{4}=\dfrac{9}{4}=\dfrac{8}{4}+\dfrac{1}{4}=2+\dfrac{1}{4}=2\dfrac{1}4}$

The the two numbers that complete the top number line are:

          $1\dfrac{1}{2}$  

and

          $2\dfrac{1}{4}$

The bottom number line models the number of batches of dough, n.

Each mark corresponds to one unit, i.e. one batch.

Thus, the missing values are:

• 2 + 1 = 3, and

• 3 + 1 = 4.

Second part. Find the relationship between the total cups of flour, c, and number of batches n.

The relationship is indicated by the marks that are at equivalent position:

You can notice that you must multiply the number of batches, n, by 3/4 to get the number of cups of flour, c, that correspond to the same position:

 For instance:

         $1\times \dfrac{3}{4}=\dfrac{3}{4}$

        $4\times \dfrac{3}{4}=3$

Therefore,

       $c=\dfrac{3}{4}n$