Multiply Decimals - Common Core: 5th Grade Math

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:

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:

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:

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

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:

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:

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:

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

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:

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.

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:

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.

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 .

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.

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.

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.

Continue multiplying, and add the on top, . Place the in the prodict's area and carry your .

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.

Now we add our partial products together.

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.

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

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.

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 .

Multiply and add the on top . We will place the underneath in the product's area.

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.

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.

Continue multiplying, . Place the in the product's area.

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.

Now we add our partial products together.

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.

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

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.

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 .

Multiply and add the on top . We will place the underneath in the product's area.

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.

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

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.

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.

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.

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

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.

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.

Finally, multiply . There are no more digits to multiply so we place the entire in the product's area.

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.

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

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.

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.

Multiply . We will place the underneath in the product's area because there are no more digits to multiply in the top row.

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.

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.

Continue multiplying, . Add the to the and place the sum of in the product's area.

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.

Now we add our partial products together.

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.

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

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.

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.

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.

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

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.

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.

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