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# Multiplying & Dividing Decimals : Concept, Practice & Rules

Christian Killian, Yuanxin (Amy) Yang Alcocer
• Author
Christian Killian

Christian has a bachelor's degree in business administration, a master's degree in media communication and psychology, and credits toward a PhD in social psychology. They excel at math and science and enjoy explaining things to others. They are also OSHA 30 certified.

• Instructor
Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has been teaching math for over 9 years. Amy has worked with students at all levels from those with special needs to those that are gifted.

Learn about the operations of multiplying and dividing decimals. Discover decimal multiplication and division word problems with walkthroughs and solutions. Updated: 12/31/2021

## Multiplying and Dividing Decimals

Multiplying and dividing decimals is similar to multiplying and dividing whole numbers with one small difference: decimal placement, which is the place value in a number where the decimal is. For both multiplication and division, there is a strategy to place the decimal that adds one simple step to the process.

For multiplication, that extra step is placing the decimal the same number of places as the decimal placements in all factors combined. Because of this, the decimal placement can be determined before calculating the answer. If we have one factor with two decimal places and another with one, our answer will have three decimal places.

Example: 3.8 x .007. 38 x 7 is 266. 3.8 has one decimal place and 0.007 has three, giving us four total. Since 266 only has three decimal placements available, we will need to add a zero as the fourth. Therefore, 3.8 x 0.007 = 0.0266.

Division is similar, only we move the decimal placements before the calculation. Decimal placements are removed until the number we are dividing by (the divisor) is a whole number. Then, we use the same decimal place of the number into which we are dividing (the dividend) for our answer.

Example: 50.22 / 3.1. 3.1 is a decimal, so we'll move everything over one decimal place to make it a whole number. This gives us 502.2 / 31. Without any decimal, our answer is 162. Since 502.2 has one decimal place, so will our answer. 50.22 / 3.1 = 16.2.

## Multiplying Decimals

Decimal numbers, those numbers with a decimal point in them, aren't scary or difficult to work with if you know the shortcuts that I will show you. In this video, we are specifically talking about multiplication and division of decimal numbers. I will show you that multiplying and dividing decimal numbers is exactly the same as multiplying and dividing whole numbers with just one difference.

In the real world, multiplying and dividing decimals happens all the time, so being able to multiply and divide decimals is an essential skill to have. For example, when you are shopping, you may need to quickly find out how much tax you can expect to pay for your purchase so that you can keep an eye out so you are not overcharged.

Let's first look at multiplying decimal numbers. Let's say we want to multiply 1.25 and 3.5. What do we do? We proceed by first multiplying the two numbers while ignoring the decimal. So we go ahead and multiply 125 with 35. We get 4,375.

Now this is where the one difference comes in and where we can apply our trick. The trick here is to count the number of decimal places we have in total. We have two from 1.25 and we have one from 3.5. We have a total of three decimal places, so that tells us that we need to count three decimal places, and that is where we put our decimal point. So our decimal goes between the 4 and the 3. Our final answer is 4.375.

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## Multiplying Decimals from Word Problems

The most common use of multiplying decimals, outside of statistics and advanced mathematics, is calculating money. Tax, interest, dividends, and even everyday prices use decimals. In United States currency, dollars are whole numbers and cents are decimals. Multiplying one price by another involves multiplying decimals.

Example: Maia lost her job and deferred her student loans for one year. She owes \$59,847.19 with an interest rate of 5.875% (0.05875). How much interest will be added by the end of her deferment?

The equation we need to solve here is 59,847.19 x .05875. Using our strategy for multiplying decimals, we will first multiply the numbers without decimals. 59,84719 x 5875 is 35,160,224,125. Then we add the decimal places. \$59,847.19 has two decimal places and .05875 has five. This gives us seven decimal places for our answer. 59,847.19 x .05875 = 3,516.0224125. Rounded to the hundredths place for cents, Maia's added interest will be \$3,156.02.

## Dividing Decimals from Word Problems

Dividing decimals typically occurs when we have to split a decimal amount by another decimal amount. It can apply to money, distance, time, food; anything that can be divided can also be divided again.

Example: Trey made chili for his big game night. After everyone has had their fill, there are 12.5 cups left in his crockpot. How many 2.5 cup containers can he fill for leftovers?

This equation is 12.5 / 2.5. Our strategy tells us to move the decimal until both numbers are whole. Since 12.5 and 2.5 both have one decimal place, we end up with 125 / 25, which is 5. Trey will have 5 containers of leftovers.

## Sales Tax: A Multiplication Example

Now let's look at a real-world example. You are shopping, and you want to buy two pairs of shoes. The total for the two shoes is \$62.18. The sales tax in your area is 6 percent. How much should you expect to pay in sales tax?

To solve this problem, you need to multiply your total of \$62.18 with the sales tax of 0.06 percent. Yes, we are multiplying the two decimals together. Remember what we just learned? First, go ahead and multiply as if there are no decimals. We multiply 6,218 with 6 to get 37,308. Then we count the total number of decimal places we have between our two numbers. We have four.

Now we count four decimal places in our answer to find where we should put our decimal point. We place it between the beginning 3 and the 7. Our final answer is 3.7308. We can expect to pay around \$3.73 in sales tax.

## Dividing Decimals

Let's move onto division now. Division is also similar to dividing whole numbers. The only difference here is that if the number we are dividing by is a decimal, then we will want to convert it to a whole number before we divide. If we are dividing 7.24 by 0.2, we would first change the 0.2 to a 2. To do that, we move the decimal place over one space to the right.

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Video Transcript

## Multiplying Decimals

Decimal numbers, those numbers with a decimal point in them, aren't scary or difficult to work with if you know the shortcuts that I will show you. In this video, we are specifically talking about multiplication and division of decimal numbers. I will show you that multiplying and dividing decimal numbers is exactly the same as multiplying and dividing whole numbers with just one difference.

In the real world, multiplying and dividing decimals happens all the time, so being able to multiply and divide decimals is an essential skill to have. For example, when you are shopping, you may need to quickly find out how much tax you can expect to pay for your purchase so that you can keep an eye out so you are not overcharged.

Let's first look at multiplying decimal numbers. Let's say we want to multiply 1.25 and 3.5. What do we do? We proceed by first multiplying the two numbers while ignoring the decimal. So we go ahead and multiply 125 with 35. We get 4,375.

Now this is where the one difference comes in and where we can apply our trick. The trick here is to count the number of decimal places we have in total. We have two from 1.25 and we have one from 3.5. We have a total of three decimal places, so that tells us that we need to count three decimal places, and that is where we put our decimal point. So our decimal goes between the 4 and the 3. Our final answer is 4.375.

## Sales Tax: A Multiplication Example

Now let's look at a real-world example. You are shopping, and you want to buy two pairs of shoes. The total for the two shoes is \$62.18. The sales tax in your area is 6 percent. How much should you expect to pay in sales tax?

To solve this problem, you need to multiply your total of \$62.18 with the sales tax of 0.06 percent. Yes, we are multiplying the two decimals together. Remember what we just learned? First, go ahead and multiply as if there are no decimals. We multiply 6,218 with 6 to get 37,308. Then we count the total number of decimal places we have between our two numbers. We have four.

Now we count four decimal places in our answer to find where we should put our decimal point. We place it between the beginning 3 and the 7. Our final answer is 3.7308. We can expect to pay around \$3.73 in sales tax.

## Dividing Decimals

Let's move onto division now. Division is also similar to dividing whole numbers. The only difference here is that if the number we are dividing by is a decimal, then we will want to convert it to a whole number before we divide. If we are dividing 7.24 by 0.2, we would first change the 0.2 to a 2. To do that, we move the decimal place over one space to the right.

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#### What is an example of a decimal word problem?

The laptop KC wants is \$809.97. Their state tax is 6%, or \$1.06 times the sale price. How much should KC expect to spend total?

The equation here is \$809.97 x \$1.06. The strategy for multiplying decimals tells us to multiply without decimals, so 80997 x 106 = 8,585,682. Next, we add the number of decimal places in the factors. Both 809.97 and 1.06 have two decimal places, giving us four total. Then, we move the decimal point four places in on our previous product. 809.97 x 1.06 = 858.5682. KC can expect to spend \$858.57 on their new laptop.

#### How do you divide decimals in word problems?

First, change the decimal placement in both numbers so that the divisor is a whole number. Then, divide like usual. The decimal place in the dividend will be the same in the answer.

#### How do you solve word problems involving multiplying decimals?

First, determine the equation using the numbers and context provided in the problem. Then, multiply the factors without decimal points. Next, add the decimal places of all factors together. Finally, move the decimal point on the previous answer the same number of spaces as the added total.

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