Multiplying Decimals

Multiplying decimals tends to be where most people start questioning their math ability. Fortunately, multiplying decimals does not need to remain mysterious. It simply requires you practice.

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Necessary Skills

Depending on the problem, you may need the following skill. You will probably need it on the actual math GED® exam.

The Different Methods

There are many ways to multiply decimals. 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 decimals (Traditional)

Traditional multiplication is the mainstay from the USA education system going back decades. Unfortunately, this method of multiplying decimals 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 decimals is to line the numbers up based on the decimal. 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.

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

Then you take the same bottom number you began manipulating and multiply it against the column value to the left from the top number. The same principles apply to writing down the answer value as above. Then you do the next spot to the left 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 problem. 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 column furthest right of the new answer row. In fact, every time you drop to a new row, you’ll drop another 0 on more columns to the left.

Now that you’ve dropped a row and dropped a 0, you can resume multiplying. Take the next rightmost column digit from the bottom number in your original problem. Multiply it against the column digit furthest right 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 by the 0 you added when you dropped a row.

Next you multiply the digit from the bottom value column against that of the top value nest to the left column with the same writing down rules. Continue following the procedure until you complete the row.

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. Then you count how many spots were to the right of the decimal (include any 0s you added). From there place your pencil on the right hand of the answer and go in that many places.

Steps for Multiplying decimals (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, A.B times E.D 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.

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. Count how many decimal places there were in the initial problem. Then place you pencil on the righthand side of the problem and move in that many.

Example Problems for Multiplying decimals

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

Example 1

Let’s start by doing 3 times 1.7. In the traditional method, the 1.7 would be the top value, and the 3 would be the bottom value. The 3 sits under the 1 for the columns. You would begin by multiplying 3 and 7, which is 21. We would write the 1 under the tenths column and the 2 above the 1 in the ones column. Then we would multiply the 3 and the 1, which is 3, and add the 2 we carried earlier. Remember to move the decimal in one from the right. The answer would be 5.1.

In the visual method, you would need a rectangle that holds 2 columns for the 1.7 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. Remember to move the decimal. The answer is 5.1.

multiplying decimals example 1

Example 2

Let’s do another with 2.1 times 3.4. We’ll line up the 1 and 4 in the tenths column, while the 2 and 3 sit in the sit in the ones column. Now we’ll take the 4 and multiply it by the 1, which leads us to write 4 into the tenths column. Then we multiply 4 and 2, which leads to an 8 in the ones column. Then we drop a row and a 0. From there, we multiple 3 times 1, which puts a 3 under the ones column in the new row. This is followed by 3 times 2, which leads to a 6 in the tens column. Add down, move the decimal, and you get 7.14 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. Remember the decimal. You should come up with 7.14 as the final answer.

Multiplying decimals example 2

Example 3

Let’s look at 45 times 2.3. The 2 goes under the 5 and the 3 goes under the .0 you need to add to the top value. 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. Remember your decimal. Final answer is 103.5.

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. Remember to add your decimal at the end. You should come up with a final answer of 103.5.

Decimal multiplying example 3