How to Multiply Decimals without using a Calculator
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Key Points
- Multiplying decimals is an essential concept in mathematics that involves taking two or more decimal numbers and multiplying them together to get a product.
- When multiplying decimals, it is important to keep track of the decimal point and the number of decimal places in the factors and the product.
- Multiplying decimals is a crucial skill that can be used in various fields, including finance, engineering, and science.
Multiplying Decimals: A Comprehensive Guide
Multiplying decimals is a fundamental concept in mathematics that is often used in everyday life. It involves taking two or more decimal numbers and multiplying them together to get a product. While the process may seem daunting at first, it is a relatively simple task that can be mastered with practice.
When multiplying decimals, it is important to keep track of the decimal point and the number of decimal places in the factors and the product. Multiplying decimals by whole numbers involves ignoring the decimal point in the whole number and multiplying as usual. On the other hand, multiplying decimals by decimals requires counting the number of decimal places in each factor and placing the decimal point in the product accordingly.
Multiplying decimals by fractions is similar to multiplying decimals by decimals, but it requires converting the fraction to a decimal first. Long multiplication with decimals involves multiplying two or more decimals with multiple digits. Overall, multiplying decimals is a crucial skill that can be used in various fields, including finance, engineering, and science.
Multiplying Decimals is the process of multiplying two numbers that are decimals to each other. When Multiplying Decimals together you will line up the decimals vertically. You do not need to add any zeros for missing spaces. Next, you will Multiply Decimals normally as if they were just integers. The last step for finding How to Multiply Decimals is to place the decimal point in your answer. In order to do this you must count up the numbers of decimal places in the decimals that you multiplied together. This amount will be how many spaces you move the decimal in your final answer.
Common Core Standard: 6.NS.3
Related Topics: Adding Decimals, Subtracting Decimals, Dividing Decimals, Greatest Common Factor, Least Common Multiple
Return To: Home, 6th Grade
Multiplying Decimals by Whole Numbers
Multiplying decimals by whole numbers is an essential skill in mathematics. It is used in many real-life situations, such as calculating sales tax, finding the cost of a certain amount of items, or calculating the total distance traveled given a certain speed and time.
To multiply a decimal by a whole number, you can follow these simple steps:
- Ignore the decimal point and multiply the whole numbers as if they were regular numbers.
- Count the total number of digits to the right of the decimal point in both the decimal and the whole number.
- Place the decimal point in the product by counting that many digits from the right end of the product.
For example, to multiply 0.5 by 4, you would:
- Ignore the decimal point and multiply 5 by 4, which is 20.
- Count the total number of digits to the right of the decimal point in both the decimal and the whole number. In this case, there is one digit to the right of the decimal point in 0.5 and no digits to the right of the whole number 4.
- Place the decimal point in the product by counting that many digits from the right end of the product. In this case, there is one digit to the right of the decimal point, so the answer is 2.0.
Another example is multiplying 0.25 by 6. To do this, you would:
- Ignore the decimal point and multiply 25 by 6, which is 150.
- Count the total number of digits to the right of the decimal point in both the decimal and the whole number. In this case, there are two digits to the right of the decimal point in 0.25 and no digits to the right of the whole number 6.
- Place the decimal point in the product by counting that many digits from the right end of the product. In this case, there are two digits to the right of the decimal point, so the answer is 1.50.
Multiplying decimals by whole numbers is a straightforward process that can be easily mastered with practice. It is an important skill to have, as it is used in many real-life situations.
Multiplying Decimals by Decimals
Multiplying decimals by decimals is similar to multiplying whole numbers, with the added step of counting the decimal places. Here are the steps to multiply decimals by decimals:
- Ignore the decimal points and multiply the numbers as if they were whole numbers.
- Count the total number of decimal places in both factors.
- Place the decimal point in the answer so that it has the same number of decimal places as the total counted in step 2.
For example, to multiply 0.25 by 0.5, follow these steps:
- Multiply 25 by 5, which gives 125.
- Count the total number of decimal places in both factors, which is 2.
- Place the decimal point in the answer so that it has 2 decimal places, which gives 0.125.
It’s important to note that the product of two decimals will always be smaller than the product of their corresponding whole numbers. This is because decimals represent parts of a whole, and multiplying two parts will result in a smaller part.
To further illustrate this concept, consider the following example:
- 3 x 4 = 12
- 0.3 x 0.4 = 0.12
In this example, the product of the decimals is smaller than the product of their corresponding whole numbers.
When multiplying decimals by decimals, it’s important to keep track of the decimal places to ensure that the answer is accurate. Practice with different examples to become more comfortable with this process.
Multiplying Decimals by Fractions
Multiplying a decimal by a fraction can be done in a few simple steps. The same rules apply as when multiplying decimals by whole numbers, but with an additional step to convert the fraction to a decimal.
To multiply a decimal by a fraction, follow these steps:
- Convert the fraction to a decimal by dividing the numerator by the denominator.
- Multiply the decimal by the other decimal number as if it were a whole number.
- Count the total number of decimal places in both numbers and place the decimal point in the answer accordingly.
For example, to multiply 0.6 by 1/5:
- Convert 1/5 to a decimal: 1 ÷ 5 = 0.2
- Multiply 0.6 by 0.2: 0.6 × 0.2 = 0.12
- Place the decimal point in the answer: 0.12 has one decimal place, so the answer is 0.12.
It’s important to note that when multiplying decimals by fractions, the answer will always be smaller than the original decimal. This is because multiplying by a fraction less than 1 reduces the value of the original number.
In some cases, it may be easier to simplify the fraction before converting it to a decimal. For example, to multiply 0.3 by 3/4:
- Simplify the fraction to 3/4 ÷ 4/4 = 3/4 × 1/4 = 3/16
- Convert 3/16 to a decimal: 3 ÷ 16 = 0.1875
- Multiply 0.3 by 0.1875: 0.3 × 0.1875 = 0.05625
- Place the decimal point in the answer: 0.05625 has five decimal places, so the answer is 0.05625.
Overall, multiplying decimals by fractions is a straightforward process that requires a few simple steps. By converting the fraction to a decimal and following the same rules as when multiplying decimals by whole numbers, anyone can easily calculate the product of a decimal and a fraction.
3 Easy Multiplying Decimals Examples
Multiplying decimals is a fundamental operation in mathematics. It involves multiplying two decimal numbers and obtaining the product. Here are a few examples of multiplying decimals:
Example 1: Multiplying Decimal with Whole Number
Suppose you want to find the product of 0.5 and 2. To do this, you can follow these steps:
- Ignore the decimal point and multiply 5 and 2. You get 10.
- Count the number of decimal places in the decimal number. Here, 0.5 has one decimal place.
- Place the decimal point in the product obtained in step 1, after one digit from the right. The product is 1.0.
Therefore, the product of 0.5 and 2 is 1.0.
Example 2: Multiplying Decimals with Different Number of Digits
Suppose you want to find the product of 0.25 and 0.4. To do this, you can follow these steps:
- Ignore the decimal point and multiply 25 and 4. You get 100.
- Count the number of decimal places in both decimal numbers. Here, 0.25 has two decimal places, and 0.4 has one decimal place.
- Add the number of decimal places in both decimal numbers. Here, 2 + 1 = 3.
- Place the decimal point in the product obtained in step 1, after three digits from the right. The product is 0.1.
Therefore, the product of 0.25 and 0.4 is 0.1.
Example 3: Multiplying Decimals with the Same Number of Digits
Suppose you want to find the product of 0.6 and 0.3. To do this, you can follow these steps:
- Ignore the decimal point and multiply 6 and 3. You get 18.
- Count the number of decimal places in both decimal numbers. Here, both decimal numbers have one decimal place.
- Place the decimal point in the product obtained in step 1, after one digit from the right. The product is 0.18.
Therefore, the product of 0.6 and 0.3 is 0.18.
These examples show how to multiply decimals with whole numbers, decimals with different numbers of digits, and decimals with the same number of digits. By following these steps, you can easily find the product of any two decimal numbers.
5 Challenging Decimal Multiplication Problems
Long Multiplication with Decimals
When it comes to multiplying decimals, long multiplication is a reliable method that can be used. This method involves multiplying the numbers as if they were whole numbers and then placing the decimal point in the correct position.
Multiplying Decimals by 10
To multiply a decimal by 10, simply move the decimal point one place to the right. For example, 3.45 x 10 would become 34.5. Similarly, to divide a decimal by 10, move the decimal point one place to the left.
Multiplying Decimals with Different Decimal Places
When multiplying decimals with different decimal places, it is important to first ignore the decimal point and multiply the numbers as if they were whole numbers. Then, count the total number of decimal places in both the multiplicand and the multiplier. Finally, place the decimal point in the product so that there are the same number of decimal places as the total counted earlier.
For example, to multiply 3.2 by 0.05, first multiply 32 by 5 to get 160. Then, count the total number of decimal places in both numbers (2 + 2 = 4) and place the decimal point in the product so that there are 4 decimal places: 0.16.
Multiplying Decimals using Long Division
Long division can also be used to multiply decimals. To do this, first ignore the decimal point and multiply the numbers as if they were whole numbers. Then, count the total number of decimal places in both the multiplicand and the multiplier. Finally, place the decimal point in the product so that there are the same number of decimal places as the total counted earlier.
For example, to multiply 4.8 by 0.6 using long division, first multiply 48 by 6 to get 288. Then, count the total number of decimal places in both numbers (1 + 1 = 2) and place the decimal point in the product so that there are 2 decimal places: 2.88.
Long multiplication with decimals can be a bit tricky, but with practice, it can become second nature. Remember to count the total number of decimal places and place the decimal point in the correct position to get the correct product.
FAQ about Decimal Multiplication
How do you multiply decimals step by step?
To multiply decimals, first, multiply the numbers as if there were no decimal point. Next, count the number of digits after the decimal point in each factor. Finally, put the same number of digits behind the decimal point in the product. For example, if you multiply 2.5 by 3.2, you would multiply 25 by 32, which equals 800. Then, since there are 2 digits to the right of the decimal point in the factors, you would put 2 digits to the right of the decimal point in the product, giving you an answer of 8.00.
What is the trick for multiplying decimals?
The trick for multiplying decimals is to ignore the decimal point until the very end of the problem. First, you multiply the numbers as if they were whole numbers, then you count the number of digits to the right of the decimal point in each factor and add them together. Finally, you put the decimal point in the product so that there are the same number of digits to the right of the decimal point as there were in the factors.
Where does the decimal point go when multiplying?
The decimal point goes in the product so that there are the same number of digits to the right of the decimal point as there were in the factors. For example, if you multiply 2.5 by 3.2, you would put the decimal point in the answer so that there are 2 digits to the right of the decimal point, giving you an answer of 8.00.
How do you multiply decimals by whole numbers?
To multiply decimals by whole numbers, you can treat the whole number as a decimal by adding a decimal point to the end of it. For example, if you want to multiply 2.5 by 4, you can treat 4 as 4.0 and multiply 2.5 by 4.0, which gives you an answer of 10.0. You can then remove the extra zero at the end of the answer, giving you a final answer of 10.
How to multiply decimals without a calculator?
To multiply decimals without a calculator, you can follow the same steps as multiplying decimals with a calculator. First, multiply the numbers as if they were whole numbers, then count the number of digits to the right of the decimal point in each factor and add them together. Finally, put the decimal point in the product so that there are the same number of digits to the right of the decimal point as there were in the factors.
When you multiply decimals do you move the decimal to the right or left?
When you multiply decimals, you move the decimal point to the right in the product so that there are the same number of digits to the right of the decimal point as there were in the factors.
Multiplying Decimals Worksheet Video Explanation
Watch our free video on how to Times Decimals. This video shows how to solve problems that are on our free Multiplication with Decimals worksheets that you can get by submitting your email above.
Watch the free Multiplying Decimals video on YouTube here: How to Multiply Decimals Video
Video Transcript:
This video is about how to multiply decimals by whole numbers. You can get the multiplication decimals worksheets used in this video for free by clicking on the link in the description below. The process for multiplying decimals is very similar to the process of just multiplying regular integers except you have to account for the decimal point. Now in order to account for the decimal point you’re going to count how many digits there are behind the decimal point in your problem and then you’re going to move the decimal by that number of digits in your answer.
Just to give you a quick example of this we’re going to solve this multiplying decimals example this problem gives us 3.5 times 9.1. We’re going to multiply these just as though they were integers and didn’t have a decimal. You’re going to start with this one you’re going to do 1 times 5 which is 5 and then 1 times 3 which is 3. Then you move over one spot and you can add a 0 if you want, I’ll put a 0 here. We move over 9 times 5 is 45 and we put a 5 here and we put a 4 over here and then 9 times 3 is 27 and then 27 plus 4 is 31. Then we’re going to add. When you add you just add through regular column addition. Five plus zero is five three plus five is eight and then these would be zero plus one. One and then just three now to figure out your solution you’re going to count how many digits were behind the decimals in your original problem. We have one digit here so everything to the right of the decimal counts. We have one digit to the right and then we have a second digit here to the right. This is two decimal places so I’m going to say two digits which means that we have to move the decimal point two times to account for our two digits. We’re going to move this one time two time and leave it right here and our final solution is going to be 31.85. You can see the process for multiplying decimals is very similar to the process of multiplying integers except you have to account for the decimal place by counting the digits behind the decimal. Let’s do a couple practice problems from our multiplying decimals worksheet
Number one on our multiplying decimals worksheets gives us 1.2 times 8.4. Again, we’re going to take these two numbers and we’re going to multiply them as though they were just regular integer numbers. We’re going to say 1.2 times 8.4 and we’re going to draw our line. 1 then we do four times two, which is eight, four times one which is four, then I’m going to add a zero here eight times two is sixteen. I’m going to put a six here and put a 1 over here and then 8 times 1 is 8 and then 8 plus 1 is 9. 9 goes down here then we’re going to add through regular column addition 8 plus 0 is 8 4 plus 6 is 10 and carry the 1 and then 1 plus 9 is also 10. Now to figure out where our decimal point goes, we have to count how many digits are behind the decimals in our original problem. 1.2 has one digit so that’s one digit and then 8.4 also has one digit. Now we have two total digits. We have to move the decimal two places over so we’re going to go one place two places and it ends up in between the zeros. Our final solution is going to be 10.08.
The next problem we’re going to complete on multiplying with decimals on our multiplying decimals worksheet is number five. This problem gives us 1.75 times 4.93. Again, you’re going to write the decimals out just as though they were regular integers into your multiplication problem. Then you multiply just as though they’re normal numbers. 3 times 5 is 15 carry the 1. 3 times 7 is 21 plus 1 is 22 so we put a 2 here carry the 2. 3 times 1 is three, three plus two is five then we add a zero to move on to our nine. Nine times five is forty-five, carry the four nine times seven is 63. 63 plus 4 67 so we put a 7 down here and then carry the 6 and then 9 times 1 is 9 9 plus 6 is 15. Put a 15 here then we move to the four. We have to do two zeros four times five is twenty. Zero here carry the two four times seven is twenty-eight, twenty-eight plus two is thirty. Another zero carry the 3 and then 4 times 1 is 4 4 plus 3 is 7. Then you add these up through regular column addition. 5 plus 0 plus 0 is 5 2 plus 5 plus 0 is seven five plus seven is twelve, twelve plus zero is two carry the one, one plus five is six and then one plus seven is eight. Now we’re going to move our decimal according to how many digits we have behind our decimal places in our original problem. In this case we have 1 2 3 4 digits behind the decimal point so we’re going to move our decimal four times. It moves one two three four times and it ends up in between the eight and the six. Our final solution is going to be 8.6275 and that’s the answer to our multiplying decimals problem.
The last problem we’re going to complete on our multiplying decimals worksheet to show you how do you multiply decimals is number seven. This problem gives us 7.08 times 1.5. I’m going to go ahead and write these out in our multiplication format. Now you will notice that even though they have a different number of digits behind the decimals I do not line up the decimal points I just line them up as though we have regular integers that we’re multiplying together then you complete the multiplication just as we did in the other problems. You do 5 times 8 which is 40 carry the 4. 5 times 0 is 0 0 plus 4 is 4 5 times 7 is 35. I’m going to have a 35 here add our zero 1 times 8 is 8 1 times 0 is 0 and then 1 times seven is seven. We add those together zero plus zero is zero four plus eight is twelve carry the one five plus one is six and then three plus seven is ten. To figure out how many spaces we move the decimal point we count the digit. We have one two three digits behind the decimal. We’re going to move the decimal point three times one two three times it ends up in between the zero and the six and our final solution is 10.620. Hopefully this video was helpful for teaching you how to multiply decimals. Try the practice problems by downloading the free decimal multiplication worksheets above.
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