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