# Two-Digit Subtraction and Multiplication

In this lesson, we will continue with the two-digit arithmetic we were studying in the last lesson, now looking at subtraction and multiplication.

## Two-digit subtraction

The subtraction problem in the first row of this table is illustrated on the grid to the left. How many green squares are there? (Ignore all gray squares in your count.) Type in your answer, and continue to the following rows, clicking each Next button in turn.
For each row of this table, the top grid illustrates a simple subtraction problem, of the type you just solved. Type this subtraction problem into the table to the right. Your equation will be illustrated on the bottom grid as you type.
For each row of this table, enter the subtraction problem that the example on the top grid illustrates. These problems involve slightly larger numbers than in the last question; you do not have to solve them. Again, your equation will be illustrated on the bottom grid as you type.

How many green squares are there on each of these grids? As in the last lesson, use the button to make them easier to count. For example: in the first row of the table, the button splits the 79 into 70 + 9, and groups the 4 from the 34 with the 9.

How many green squares are there on each grid? Again, use the Rearrange button if it is helpful. For example: in the first row of the table, the button splits the 86 into 70 + 16, and groups the 8 from the 18 with the 16 from the 86.

Solve these subtraction problems in the standard way, using columns instead of the grid.

 \$79\$ \$-\$ \$34\$ \$=\$
 \$86\$ \$-\$ \$18\$ \$=\$
 \$77\$ \$-\$ \$39\$ \$=\$

As in the addition lesson, notice that the normal “column” method of subtracting two numbers involves exactly the same steps as the grid illustrates! That is, the grid allows you to see why the normal method works.

## Two-digit multiplication

How many green squares are there in each of these examples? (Remember that we use parentheses for multiplication in this course. When you see “4(3),” think “4 copies of 3,” or “4 times 3.”)
For each row of the table to the right, enter the multiplication problem shown on the top grid.

Each of these multiplication problems is illustrated on the grid. Count the number of small green squares in each example. Use the Rearrange button to switch between the original picture and an equivalent picture where the squares are easier to count.

Solve these multiplication problems in the standard way, using columns instead of the grid.

 \$12\$ \$×\$ \$3\$ \$=\$
 \$21\$ \$×\$ \$4\$ \$=\$
 \$37\$ \$×\$ \$2\$ \$=\$

As with the addition and subtraction methods, notice that the Rearrange button illustrates on the grid the steps you perform when multiplying.