Common Core: 5th Grade Math : Multiply Decimals

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

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Example Questions

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Example Question #681 : Number & Operations In Base Ten

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 11.49.12 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 11.49.15 am

 

Multiply  . We will place the  underneath in the product's area because there are no more digits to multiply in the top row. Screen shot 2020 09 16 at 11.49.18 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 11.49.22 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 11.49.27 am

 

Continue multiplying, .  Add the  to the  and place the sum of  in the product's area. Screen shot 2020 09 16 at 11.49.30 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 11.49.34 am

 

Now we add our partial products together. Screen shot 2020 09 16 at 11.49.39 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 11.49.43 am

 

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

Example Question #691 : Number & Operations In Base Ten

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 above the next digit. Screen shot 2020 09 16 at 12.06.12 pm

 

Now we will continue multiplying using the  until we have exhausted all digits in the first row. Next is . Add the  to  for a total sum of . The  is placed in the product area since there are no more numbers to multiply. Screen shot 2020 09 16 at 12.06.15 pm

 

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 green. Screen shot 2020 09 16 at 12.06.19 pm

 

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

Example Question #692 : Number & Operations In Base Ten

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, we only have two digits. . The  is placed under the problem in the product's area because there are no other digits to multiply. Screen shot 2020 09 16 at 12.15.51 pm

 

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 green. Screen shot 2020 09 16 at 12.16.03 pm

 

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

Example Question #693 : Number & Operations In Base Ten

Multiply:

Possible Answers:

Correct answer:

Explanation:

When we multiply decimals, we can first think of the problem as regular numbers: . In this problem, we have 2 numbers after each decimal, thus our answer has to have two numbers after the decimal point, so we add a zero as a place holder:

We start counting out the two-place values needed to the right of the . As you can see, the decimal moves from the right of the , to the left of the , and then finally moves another place value to the left of the  and we fill it in with a zero. The image below shows the movement.

Screen shot 2020 10 14 at 4.31.54 pm

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