# More Complicated Expressions

## Negative numbers and expressions

Use the grid and the slider to find the value of \$2x-3\$ for each value of \$x\$ shown in the table below. Notice that \$x\$, \$2x-3\$, or both may be negative.

\$x\$\$2x-3\$

When \$x=0\$, notice that we draw a black line of length 2 at the bottom of the grid in place of the rectangle for \$2x\$. This is to remind you that the expression \$2x-3\$ includes \$2x\$, but the current value of \$2x\$ is zero.

Use the grid and the slider to find the value of the expression \$-y+2\$ for each value of \$y\$ shown in the table below. (Remember that a negative number times a negative number is positive.)

\$y\$\$-y+2\$

Use the grid and the slider to find the value of \$-2y-6\$ for each value of \$y\$ shown in the table below.

\$y\$\$-2y-6\$
For each row of this table, the top grid to the left illustrates some expression that depends on the variable \$x\$. Find that expression by looking at the grid and sliding the slider. The expression you type in will be shown on the bottom grid.

## Expressions with division

The Mathscribe Fruit Stand has decided to give away bananas to their first \$3\$ customers. If they set aside a total of \$b\$ bananas to give away, they can give each customer \$\$b/3\$\$ bananas.

For each value of \$b\$ in the table below, slide the slider, look at the grid, and find the number of bananas that each customer gets. (Remember that the height of a rectangle equals its area divided by its width.)

\$b\$ = total number of bananas \$\$b/3\$\$ = number of bananas
each customer gets

Now the fruit stand is giving away fruit pies. They want to give away a total of 6 pies. So, if \$c\$ customers show up, they can give each customer \$\$6/c\$\$ pies.

For each value of \$c\$ in the table below, slide the slider, look at the grid, and find the number of pies each customer gets.

\$c\$ = number of customers \$\$6/c\$\$ = number of pies
each customer gets
 If the fruit stand decides instead to give away 9 pies to \$c\$ customers, what is an expression for the number of pies each customer will get?

Now the fruit stand is giving away a total of 9 pies. If \$c\$ customers show up, that means they can give each customer \$\$9/c\$\$ pies. The fruit stand might give each customer a fractional number of pies, depending on what \$c\$ is. For example, if 2 customers show up, each customer will get \$\$9/2=4.5\$\$ pies.

For each value of \$c\$ in the table below, find the number of pies each customer gets. If each customer gets a fractional number of pies, write that number as a decimal.

\$c\$ = number of customers \$\$9/c\$\$ = number of pies
each customer gets