Multiplying Whole Numbers

Multiplication is where whole numbers take on a new light. Multiplying whole numbers is simply a faster way to add, yet it does not resemble adding. Instead, for many it’s a convoluted practice that’s best done on the calculator.

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Necessary Skills

Depending on the problem, you may need the following skill. However, it’s unlikely you will need it on the actual math GED® exam.

The Different Methods

There are many ways to multiply whole numbers. In fact, there are more than 25 different ways to accomplish the goal. However, you do not need to know all of them. You simply need to find the one that works for you.

Steps for Multiplying Whole Numbers (Traditional)

Traditional multiplication is the mainstay from the USA education system going back decades. Unfortunately, this method of multiplying whole numbers requires that you keep track of your steps in your head. It tends not to work well for visual learners.

The first step with multiplying whole numbers is to line the numbers up based on the ones spot. Proper columns will help you keep track of each step, so make sure everything lines up. It’s also good practice so you can check your math later. It does not matter which number is on top, though many people prefer to place the biggest number up there.

Traditional Multiplication Problem Layout

Take the bottom number in the ones column. Then multiply that number against the top number in the ones column. If the answer is less then 10, just write the answer under the ones column. If it is more than ten, write the answer value from the ones spot under the ones column and carry the tens spot to the tens column, just like carrying in addition.

Then you take the same bottom number from the ones spot and multiply it against the tens column value from that top number. The same principles apply to writing down the answer value as above. Then you do the hundreds spot the same way, and so on until you run out of digits in the top value.

Now it gets tricky, since you have a row of answer under the column. When you move to the next step, you will start a new row. The first thing you do before any math is place a 0 in the ones column of the new answer row. In fact, every time you drop to a new row, you’ll drop another 0 on more column to the left.

Now that you’ve dropped a row and dropped a 0, you can resume multiplying. Take the tens column digit from the bottom row and multiply it against the ones column digit in the top value. The same rules for writing down apply as before, except this time you’ll start by placing the ones column of the answer underneath the tens column.

Next you multiply the digit from the bottom value tens column against that of the top value tens column with the same writing down rules. Then the bottom tens digit against the top hundreds digit. Continue doing so until you complete the row.

If there is a hundreds value in the bottom number, you will continue in the same fashion. The only difference is instead of only placing one 0 in the ones column when you drop a row, you will place 0s in the ones and tens column. This will inform you to begin writing answers under the hundred column.

When you run out of column values in the bottom value, you should have a series of neatly lined rows under the original problem. You then add the numbers in the rows just like a normal addition problem. The answer to that addition is the problem solution.

Steps for Multiplying Whole Numbers (Visual)

A visual method for multiplying numbers is generally easy to keep track of, and the steps are not kept in your head. You may know this as lattice method from school.

To begin, you’re going to draw a square or rectangle on a piece of paper. Then you will divide this shape into rows and columns that match the place values in your problem. For example, AB times ED would get a square with two rows and two columns. It does not matter which number gets the rows or the columns.

Once you have divided the shape into rows and columns, it’s time to slash each box in half. This slashing starts in the upper right corner of each box and ends in the lower left. Each box should be done individually, but you will see longer diagonals form across your shape.

Visual Multiplication Layout

Now you need to fill in the boxes. Each box is the intersection of a row and a column. You will multiply the row by the column for each box. Then you will write the number in the ones place value underneath the box slash and the tens place value on top of the box slash. Repeat until all the boxes are full.

Next is the fun part, since you are going to add down the slides. You will start with the slide in the bottom right corner of your overall shape. There should only be one value in this slide, so write it down outside your shape and move to the next one to the left. This one should have more than one value, so you add down the slide.

During this addition, if the adding yields a number higher than 10, write only the ones place value under the slide. Then write the tens place value on top of the next slide to the left. That tens value you just wrote is now part of the addition problem for that next slide.

Continue adding the slides until there are no more slides. Then you have your answer written around the left and bottom of your visual grid.

Example Problems for Multiplying Whole Numbers

Let’s jump into some example problems to clear this up.

Example 1

Let’s start by doing 3 times 17. In the traditional method, the 17 would be the top value, and the 3 would be the bottom value. The 3 sits under the 7 for the columns. You would begin by multiplying 3 and 7, which is 21. We would write the 1 under the ones column and the 2 above the 1 in the ten column. Then we would multiply the 3 and the 1, which is 3, and add the 2 we carried earlier. The answer would be 51.

In the visual method, you would need a rectangle that holds 2 columns for the 17 and 1 row for the 3. Then you do the multiplication and place the numbers in the appropriate boxes. From there, you’ll add the bottom right corner slide, followed by the one to the left. The answer is 51.

Multiplying Whole Numbers Example 1

Example 2

Let’s do another with 21 times 34. We’ll line up the 1 and 4 in the ones column, while the 2 and 3 sit in the sit in the tens column. Now we’ll take the 4 and multiply it by the 1, which leads us to write 4 into the ones column. Then we multiply 4 and 2, which leads to an 8 in the tens column. Then we drop a row and a 0. From there, we multiple 3 times 1, which puts a 3 under the tens column in the new row. This is followed by 3 times 2, which leads to a 6 in the hundreds column. Add down and you get 714 as the final solution.

In the visual method, you need a box with 2 rows and 2 columns. Go through and fill all the boxes with all the intersecting multiplication problems. Then start adding the slides from that bottom right corner. You should come up with 714 as the final answer.

Multiplying Whole Numbers Example 2

Example 3

Let’s look at 45 times 23. The 2 goes under the 4 and the 3 goes under the 5. First step is multiplying 3 by 5, for 15, which means write the 5 and carry the 1 to the tens column. Then do 3 by 4 and add the collected 1 for a total of 13, written with the 3 in the tens column. Drop a row, drop a zero. Now take 2 times 5, for a total of ten. Write the 0 in the tens column and carry the 1. Then multiply 2 by 4 and add the extra 1 for a total of 9. Final answer is 1,035.

In the visual method, you need a box with 2 rows and 2 columns. Go through and fill all the boxes using your multiplication facts. Then start adding the slides, beginning from the bottom righthand corner. You should come up with a final answer of 1,035.

Multiplying whole numbers example 3