# Common Core: 6th Grade Math : Dividing Multi-Digit Decimals

## Example Questions

### Example Question #1 : Dividing Multi Digit Decimals

Solve:

Explanation:

The first thing that we want to do when dividing decimals is to turn the divisor into a whole number. We do this by moving the decimal place to the right:

If we move the decimal over one place in the divisor, we must also move the decimal over one place in the dividend:

The new division problem should look as follows:

*Notice how we've already placed the decimal in our answer. When we divide decimals, we place the decimal directly above the decimal in the dividend, but only after we've completed the first two steps of moving the decimal point in the divisor and dividend.

Now we can divide like normal:

Think: how many times can 76 go into 197

76 can go into 197 two times so we write a 2 over the 7 in the dividend:

Next, we multiply 2 and 76 and write that product underneath the 197 and subtract:

Now we bring down the 6 from the dividend to make the 45 into a 456.

Think: how many times can 76 go into 456?

76 can go into 465 six times so we write a 6 above the 6 in the dividend:

Next, we multiply 6 and 76 and write that product underneath the 456 and subtract:

We are left with no remainder and a final quotient of 2.6

### Example Question #1 : Dividing Multi Digit Decimals

Explanation:

The first thing that we want to do when dividing decimals is to turn the divisor into a whole number. In this case, the divisor is already a whole number so no change is needed.

The division problem should look as follows:

*Notice how we've already placed the decimal in our answer. When we divide decimals, we place the decimal directly above the decimal in the dividend, but only after we've completed the first two steps of moving the decimal point in the divisor and dividend.

Now we can divide like normal:

Think: how many times can 12 go into 8

12 cannot go into 8 so we write a 0 over the 8 in the dividend:

Since 12 could not go into 8 we combine the ones place and tenths place and think of how many times 12 can go into 85. The number is split with the decimal but for multiplication's sake, we think of it as just an 85.

Think: how many times can 12 go into 85

12 can go into 85 seven times so we write a 7 above the 5 in the dividend:

Next, we multiply 12 and 7 and write that product underneath the 85 and subtract:

Now we bring down the 8 from the dividend to make the 1 into an 18.

Think: how many times can 12 go into 18?

12 can go into 18 one times so we write a 1 above the 8 in the dividend:

Next, we multiply 12 and 1 and write that product underneath the 18 and subtract:

Now we are left with 6 in our dividend and we cannot multiply 12 by anything to make a 6. We annex or add a zero to our dividend which we can carry down beside the 6 and it will now be a 60. We did no change the value of our dividend, we added a zero to make the number divisible by 12.

Think: how many times can 12 go into 60?

12 can go into 60 five times so we write a 5 above the 0 in the dividend:

Next, we multiply 12 and 5 and write that product underneath the 60 and subtract:

We are left with no remainder and a final quotient of 0.715

### Example Question #2 : Dividing Multi Digit Decimals

Explanation:

The first thing that we want to do when dividing decimals is to turn the divisor into a whole number. In this case, the divisor is already a whole number so no change is needed.

The division problem should look as follows:

*Notice how we've already placed the decimal in our answer. When we divide decimals, we place the decimal directly above the decimal in the dividend, but only after we've completed the first two steps of moving the decimal point in the divisor and dividend.

Now we can divide like normal:

Think: how many times can 9 go into 8

9 cannot go into 8 so we write a 0 over the 8 in the dividend:

Since 9 could not go into 8 we combine the ones place and tenths place and think of how many times 9 can go into 87. The number is split with the decimal but for multiplication's sake, we think of it as just an 87.

Think: how many times can 9 go into 87

9 can go into 87 nine times so we write a 9 above the 7 in the dividend:

Next, we multiply 9 and 9 and write that product underneath the 87 and subtract:

Now we bring down the 3 from the dividend to make the 6 into an 63.

Think: how many times can 9 go into 63?

9 can go into 63 seven times so we write a 7 above the 3 in the dividend:

Next, we multiply 9 and 7 and write that product underneath the 63 and subtract:

We are left with no remainder and a final quotient of 0.97

### Example Question #3 : Dividing Multi Digit Decimals

Explanation:

The first thing that we want to do when dividing decimals is to turn the divisor into a whole number. We do this by moving the decimal place to the right:

If we move the decimal over one place in the divisor, we must also move the decimal over one place in the dividend:

The new division problem should look as follows:

*Notice how we've already placed the decimal in our answer. When we divide decimals, we place the decimal directly above the decimal in the dividend, but only after we've completed the first two steps of moving the decimal point in the divisor and dividend.

Now we can divide like normal:

Think: how many times can 18 go into 45

18 can go into 45 two times so we write a 2 over the 5 in the dividend:

Next, we multiply 2 and 18 and write that product underneath the 45 and subtract:

Now 18 cannot be multiplied by a whole number to create a 9 so annex or add a zero to the dividend to create a number divisible by 18. We are not changing the value of the dividend by adding a zero. Bring that 0 down next to the 9 to create 90.

Think: how many times can 18 go into 90?

18 can go into 90 five times so we write a 5 above the 0 in the dividend:

Next, we multiply 5 and 18 and write that product underneath the 90 and subtract:

We are left with no remainder and a final quotient of 2.5

### Example Question #1 : Dividing Multi Digit Decimals

Solve:

Explanation:

The first thing that we want to do when dividing decimals is to turn the divisor into a whole number. We do this by moving the decimal place to the right:

If we move the decimal over one place in the divisor, we must also move the decimal over one place in the dividend:

The new division problem should look as follows:

*Notice how we've already placed the decimal in our answer. When we divide decimals, we place the decimal directly above the decimal in the dividend, but only after we've completed the first two steps of moving the decimal point in the divisor and dividend.

Now we can divide like normal:

Think: how many times can 52 go into 1

52 cannot go into 1 so we write a 0 over the 1 in the dividend:

We did not use the 1 in the hundreds place so now we bring in the 0 in the tens place and attempt to divide it by 52

Think: how many times can 52 go into 10

52 cannot go into 10 so we write a 0 over the 0 in the dividend:

We did not use the 10 so we now bring in the 1 from the ones place and attempt to divide it by 52

Think: how many times can 52 go into 101

52 can go into 101 one time so we write a 1 over the 1 in the dividend:

Next, we multiply 52 and 1 and write that product underneath the 101 and subtract:

Now we bring down the 4 from the dividend to make the 49 into a 494.

Think: how many times can 52 go into 494

52 can go into 494 nine times so we write a 9 over the 4 in the dividend:

Next, we multiply 52 and 9 and write that product underneath the 494 and subtract:

Now 52 cannot be multiplied by a whole number to create a 26 so annex or add a zero to the dividend to create a number divisible by 52. We are not changing the value of the dividend by adding a zero. Bring that 0 down next to the 26 to create 260.

Think: how many times can 52 go into 260?

52 can go into 260 five times so we write a 5 above the 0 in the dividend:

Next, we multiply 52 and 5 and write that product underneath the 260 and subtract:

We are left with no remainder and a final quotient of 1.95

### Example Question #1 : Dividing Multi Digit Decimals

Solve:

Explanation:

The first thing that we want to do when dividing decimals is to turn the divisor into a whole number. We do this by moving the decimal place to the right:

If we move the decimal over one place in the divisor, we must also move the decimal over one place in the dividend:

The new division problem should look as follows:

*Notice how we've already placed the decimal in our answer. When we divide decimals, we place the decimal directly above the decimal in the dividend, but only after we've completed the first two steps of moving the decimal point in the divisor and dividend.

Now we can divide like normal:

Think: how many times can 2 go into 4

2 can go into 4 two times so we write a 2 over the 4 in the dividend:

Next, we multiply 2 and 2 and write that product underneath the 4 and subtract:

Now we bring down the 0 from the dividend to make the 0 into 00.

Think: how many times can 2 go into 0

2 can go into 0 zero times so we write a 0 over the 0 in the dividend:

Next, we multiply 2 and 0 and write that product underneath the 0 and subtract:

Now we bring down the 9 from the dividend to make the 0 into 9.

2 can go into 9 four times so we write a 4 over the 9 in the dividend:

Next, we multiply 2 and 4 and write that product underneath the 9 and subtract:

Now 2 cannot be multiplied by a whole number to create a 1 so annex or add a zero to the dividend to create a number divisible by 2. We are not changing the value of the dividend by adding a zero. Bring that 0 down next to the 1 to create 10.

Think: how many times can 2 go into 10?

2 can go into 10 five times so we write a 5 above the 0 in the dividend:

Next, we multiply 2 and 5 and write that product underneath the 10 and subtract:

We are left with no remainder and a final quotient of 204.5

### Example Question #1 : Dividing Multi Digit Decimals

In the problem  which number is the dividend?

None of the answer choices are correct.

Explanation:

A dividend is what you are splitting up or breaking up in a division problem. It is the amount that you want to divide up. In this problem  is the dividend. In a division problem, the dividend is listed first.

### Example Question #2 : Dividing Multi Digit Decimals

Which model correctly represents  on the hundreds block?

Explanation:

Models are often used to help represent the division of decimals and help connect the related equation with a visual representation.

You need to shade a rectangle with an area of 0.24. So, shade 24 small squares, in a decimal model.

There are many rectangles with an area of 0.24. You need to shade one that has a length of 0.6.

The missing factor is 0.4 which we can see is represented on the y-axis of the hundreds block.

The area if a 0.4 by 0.6 rectangle is 0.24. Therefore, 0.24 ÷ 0.6 = 0.4

### Example Question #2 : Dividing Multi Digit Decimals

Solve the problem using the area model provided.

Explanation:

Models are often used to help represent the division of decimals and help connect the related equation with a visual representation.

You need to shade a rectangle with an area of 0.12. So, shade 12 small squares, in a decimal model.

There are many rectangles with an area of 0.12. You need to shade one that has a length of 0.3.

The missing factor is 0.4 which we can see is represented on the y-axis of the hundreds block.

The area if a 0.4 by 0.3 rectangle is 0.12. Therefore, 0.12 ÷ 0.3 = 0.4

### Example Question #1 : Dividing Multi Digit Decimals

Which model correctly represents  on the hundreds block?