Common Core: 5th Grade Math : Multiply Decimals

Study concepts, example questions & explanations for Common Core: 5th Grade Math

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Example Questions

Example Question #1 : Multiply Decimals

Multiply:

Possible Answers:

Correct answer:

Explanation:

When multiplying decimals, we can use our base ten blocks to create an area model. To do this, we want to use our hundreds, or one whole, block:

One whole

 is equal to five tenths. Remember, our one whole block is made up of ten tenths. We can shade in , or five tenths blocks, of the whole. Let's shade  of the vertical tenths blocks. Let's use blue to shade:

5

Next, we want to shade four of the tenths blocks to represent the . Since we shaded vertical for the first step, we need to shade horizontal for this step. Let's use yellow to shade:

4

Notice the green shading. This is where the yellow and the blue shading overlapped. (Remember, yellow and blue make green). The overlapping section is our answer. There are twenty green hundredths blocks; therefore, our answer is  which is equal to two tenths, :

20

 

Example Question #2 : Multiply Decimals

Multiply:

Possible Answers:

Correct answer:

Explanation:

When multiplying decimals, we can use our base ten blocks to create an area model. To do this, we want to use our hundreds, or one whole, block:

One whole

 is equal to three tenths. Remember, our one whole block is made up of ten tenths. We can shade in , or three tenths blocks, of the whole. Let's shade  of the vertical tenths blocks. Let's use blue to shade:

3

Next, we want to shade four of the tenths blocks to represent the . Since we shaded vertical for the first step, we need to shade horizontal for this step. Let's use yellow to shade:

4

Notice the green shading. This is where the yellow and the blue shading overlapped. (Remember, yellow and blue make green). The overlapping section is our answer. There are twelve green hundredths blocks, or one tenths block and two hundredths block; therefore, our answer is 


12

Example Question #3 : Multiply Decimals

Multiply the following:

Possible Answers:

Correct answer:

Explanation:

When multiplying decimals, we can use our base ten blocks to create an area model. To do this, we want to use our hundreds, or one whole, block:

One whole

 is equal to three tenths. Remember, our one whole block is made up of ten tenths. We can shade in , or three tenths blocks, of the whole. Let's shade  of the vertical tenths blocks. Let's use blue to shade:

3

Next, we want to shade two of the tenths blocks to represent the . Since we shaded vertical for the first step, we need to shade horizontal for this step. Let's use yellow to shade:

2

Notice the green shading. This is where the yellow and the blue shading overlapped. (Remember, yellow and blue make green). The overlapping section is our answer. There are six green hundredths blocks and no tenths; therefore, our answer is 

6

Example Question #1 : Multiply Decimals

Multiply:

Possible Answers:

Correct answer:

Explanation:

We can first think of this as , which you should know is . But, we need to remember our decimal point. In the problem we have two number after the decimals, so our answer must have two numbers after the decimal point: 

Example Question #1 : Multiply Decimals

Multiply:

Possible Answers:

Correct answer:

Explanation:

We can first think of this as , which you should know is . But, we need to remember our decimal point. In the problem we have two number after the decimals, so our answer must have two numbers after the decimal point: 

Example Question #6 : Multiply Decimals

Possible Answers:

Correct answer:

Explanation:

The first step when multiplying decimals is lining up the digits on the right-side regardless of place value. It is okay for a tenths place to be in line with a ones place, we want the numbers lined up on the right. 

 

Then, multiply the digits furthest to the right. In this case, it would be . The  is placed under the problem in the product's area and the  is carried to the top of the problem above the next set of digits. Screen shot 2020 09 16 at 9.27.20 am

 

Now we will continue multiplying using the  until we have exhausted all digits in the first row. Next is  we must add the  we carried to the top to our product. . Place the  in the product's area and carry the Screen shot 2020 09 16 at 9.29.36 am

 

Multiply  and add the  on top . There are no other digits in the top number so we will place the entire  underneath in the product's area. Screen shot 2020 09 16 at 9.32.46 am

 

You will notice that we have not placed the decimal, that will come at the end of the solution. Now we can cross out the digits we have exhausted and put a placeholder zero in the product's area to hold the place of the furthest right digit that we have finished with. Screen shot 2020 09 16 at 9.34.56 am

 

It is time to multiply by our final digit,  in , we start back with the furthest right-hand digit, . Place the  in the products area and carry the  above the next digit we will multiply. Screen shot 2020 09 16 at 9.37.03 am

 

Continue multiplying,  and add the  on top, . Place the  in the prodict's area and carry your Screen shot 2020 09 16 at 9.38.40 am

 

Finally, we are at the last multiplication step before we combine our product.  and we add the  that we carried giving us a total of . The entire  is placed in the product's area because we are out of digits to multiply. Screen shot 2020 09 16 at 9.40.37 am

 

Now we add our partial products together. Screen shot 2020 09 16 at 9.41.24 am

 

The last step in a decimal multiplication problem is to place the decimal. Count how many digits are behind the decimal in your problem and we will do the same in the product. This problem has  digits behind the decimal as you can see in pink. Screen shot 2020 09 16 at 9.43.41 am

 

We will place the decimal in the product so that there are  digits behind it. Giving us a final answer of 

Example Question #7 : Multiply Decimals

Possible Answers:

Correct answer:

Explanation:

The first step when multiplying decimals is lining up the digits on the right-side regardless of place value. It is okay for a tenths place to be in line with a ones place, we want the numbers lined up on the right. 

 

Then, multiply the digits furthest to the right. In this case, it would be . The  is placed under the problem in the product's area and the  is carried to the top of the problem above the next set of digits. Screen shot 2020 09 16 at 10.10.14 am

 

Now we will continue multiplying using the  until we have exhausted all digits in the first row. Next is  we must add the  we carried to the top to our product. . Place the  in the product's area and carry the Screen shot 2020 09 16 at 10.10.17 am

 

Multiply  and add the  on top . We will place the  underneath in the product's area. Screen shot 2020 09 16 at 10.10.20 am

 

You will notice that we have not placed the decimal, that will come at the end of the solution. Now we can cross out the digits we have exhausted and put a placeholder zero in the product's area to hold the place of the furthest right digit that we have finished with. Screen shot 2020 09 16 at 10.10.25 am

 

It is time to multiply by our final digit,  in , we start back with the furthest right-hand digit, . Place the  in the products area. Screen shot 2020 09 16 at 10.10.29 am

 

Continue multiplying, . Place the  in the product's area. Screen shot 2020 09 16 at 10.10.33 am

 

Finally, we are at the last multiplication step before we combine our product.  . The  is placed in the product's area and we are out of digits to multiply. Screen shot 2020 09 16 at 10.10.37 am

 

Now we add our partial products together. Screen shot 2020 09 16 at 10.10.43 am

 

The last step in a decimal multiplication problem is to place the decimal. Count how many digits are behind the decimal in your problem and we will do the same in the product. This problem has  digits behind the decimal as you can see in pink. Screen shot 2020 09 16 at 10.10.47 am

 

We will place the decimal in the product so that there are  digits behind it. Giving us a final answer of 

Example Question #8 : Multiply Decimals

Possible Answers:

Correct answer:

Explanation:

The first step when multiplying decimals is lining up the digits on the right-side regardless of place value. It is okay for a tenths place to be in line with a ones place, we want the numbers lined up on the right. 

 

Then, multiply the digits furthest to the right. In this case, it would be . The  is placed under the problem in the product's area and the  is carried to the top of the problem above the next set of digits. Screen shot 2020 09 16 at 10.31.39 am

 

Now we will continue multiplying using the  until we have exhausted all digits in the first row. Next is  we must add the  we carried to the top to our product. . Place the  in the product's area and carry the Screen shot 2020 09 16 at 10.31.42 am

 

Multiply  and add the  on top . We will place the  underneath in the product's area. Screen shot 2020 09 16 at 10.31.51 am

 

You will notice that we have not placed the decimal, that will come at the end of the solution.

 

The last step in a decimal multiplication problem is to place the decimal. Count how many digits are behind the decimal in your problem and we will do the same in the product. This problem has  digits behind the decimal as you can see in pink. Screen shot 2020 09 16 at 10.32.38 am

 

We will place the decimal in the product so that there are  digits behind it. Giving us a final answer of 

Example Question #9 : Multiply Decimals

Possible Answers:

Correct answer:

Explanation:

The first step when multiplying decimals is lining up the digits on the right-side regardless of place value. It is okay for a tenths place to be in line with a ones place, we want the numbers lined up on the right. 

 

Then, multiply the digits furthest to the right. In this case, it would be . The  is placed under the problem in the product's area. Screen shot 2020 09 16 at 10.55.07 am

 

Now we will continue multiplying using the  until we have exhausted all digits in the first row. Next is . Place the  in the product's area. There are no more digits to multiply so we don't need to carry any digits to the next place value. Screen shot 2020 09 16 at 10.55.11 am

 

You will notice that we have not placed the decimal, that will come at the end of the solution.

 

The last step in a decimal multiplication problem is to place the decimal. Count how many digits are behind the decimal in your problem and we will do the same in the product. This problem has  digits behind the decimal as you can see in pink. Screen shot 2020 09 16 at 10.55.28 am

 

We will place the decimal in the product so that there are  digits behind it. Giving us a final answer of 

Example Question #10 : Multiply Decimals

Possible Answers:

Correct answer:

Explanation:

The first step when multiplying decimals is lining up the digits on the right-side regardless of place value. It is okay for a tenths place to be in line with a ones place, we want the numbers lined up on the right. 

 

Then, multiply the digits furthest to the right. In this case, it would be . The  is placed under the problem in the product's area. Screen shot 2020 09 16 at 11.14.01 am

 

Now we will continue multiplying using the  until we have exhausted all digits in the first row. Next is . Place the  in the product's area. Screen shot 2020 09 16 at 11.14.09 am

 

Finally, multiply . There are no more digits to multiply so we place the entire  in the product's area. Screen shot 2020 09 16 at 11.14.17 am

 

You will notice that we have not placed the decimal, that will come at the end of the solution.

 

The last step in a decimal multiplication problem is to place the decimal. Count how many digits are behind the decimal in your problem and we will do the same in the product. This problem has  digits behind the decimal as you can see in pink. Screen shot 2020 09 16 at 11.14.20 am

 

We will place the decimal in the product so that there are  digits behind it. Giving us a final answer of 

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