Common Core: 6th Grade Math : Fluently Add, Subtract, Multiply, and Divide Multi-Digit Decimals: CCSS.Math.Content.6.NS.B.3

Study concepts, example questions & explanations for Common Core: 6th Grade Math

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Example Questions

Example Question #41 : Fluently Add, Subtract, Multiply, And Divide Multi Digit Decimals: Ccss.Math.Content.6.Ns.B.3

Solve:

Possible Answers:

Correct answer:

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 two places in the divisor, we must also move the decimal over two places 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 423

52 can go into 423 eight times times so we write a 8 over the 3 in the dividend:

Next, we multiply 8 and 52 and write that product underneath the 423 and subtract:

Now we bring down the 4 from the dividend to make the 7 into a 74.

Think: how many times can 52 go into 74?

52 can go into 74 one time so we write a 1 above the 4 in the dividend:

Next, we multiply 1 and 52 and write that product underneath the 74 and subtract:

Now we bring down the 4 from the dividend to make the 22 into a 224.

Think: how many times can 52 go into 224?

52 can go into 224 four times so we write a 4 above the 4 in the dividend:

Next, we multiply 4 and 52 and write that product underneath the 224 and subtract:

Now we bring down the 5 from the dividend to make the 16 into a 165.

Think: how many times can 52 go into 165?

52 can go into 165 three times so we write a 3 above the 5 in the dividend:

Next, we multiply 3 and 52 and write that product underneath the 165 and subtract:

Notice our remainder is 9 so our answer is 8.143R9.

 

Example Question #42 : Fluently Add, Subtract, Multiply, And Divide Multi Digit Decimals: Ccss.Math.Content.6.Ns.B.3

Solve:

Possible Answers:

Correct answer:

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 two places in the divisor, we must also move the decimal over two places 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 75 go into 278

75 can go into 278 three times times so we write a 3 over the 8 in the dividend:

Next, we multiply 3 and 75 and write that product underneath the 278 and subtract:

Now we bring down the 2 from the dividend to make the 53 into a 532.

Think: how many times can 75 go into 532?

75 can go into 532 seven times so we write a 7 above the 2 in the dividend:

Next, we multiply 7 and 75 and write that product underneath the 532 and subtract:

Now we bring down the 4 from the dividend to make the 7 into a 74.

Think: how many times can 75 go into 74?

75 can go into 74 zero so we write a 0 above the 4 in the dividend:

Next, we multiply 0 and 75 and write that product underneath the 74 and subtract:

Now we bring down the 9 from the dividend to make the 74 into a 749.

Think: how many times can 75 go into 749?

75 can go into 749 nine times so we write a 9 above the 9 in the dividend:

Next, we multiply 9 and 75 and write that product underneath the 749 and subtract:

Notice our remainder is 74 so our answer is 3.709R74.

 

Example Question #91 : The Number System

Solve:

Possible Answers:

Correct answer:

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 two places in the divisor, we must also move the decimal over two places 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 43 go into 238

43 can go into 238 five times times so we write a 5 over the 8 in the dividend:

Next, we multiply 5 and 43 and write that product underneath the 238 and subtract:

Now we bring down the 2 from the dividend to make the 23 into a 232.

Think: how many times can 43 go into 232?

43 can go into 232 five times so we write a 5 above the 2 in the dividend:

Next, we multiply 5 and 43 and write that product underneath the 232 and subtract:

Now we bring down the 9 from the dividend to make the 17 into a 179.

Think: how many times can 43 go into 179?

43 can go into 179 four times so we write a 4 above the 9 in the dividend:

Next, we multiply 4 and 43 and write that product underneath the 179 and subtract:

Now we bring down the 3 from the dividend to make the 7 into a 73.

Think: how many times can 43 go into 73?

43 can go into 73 one time so we write a 1 above the 3 in the dividend:

Next, we multiply 1 and 43 and write that product underneath the 73 and subtract:

Notice our remainder is 30 so our answer is 5.541R30.

 

Example Question #92 : The Number System

Solve:

Possible Answers:

Correct answer:

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 two places in the divisor, we must also move the decimal over two places 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 78 go into 440

78 can go into 440 five times times so we write a 5 over the 0 in the dividend:

Next, we multiply 5 and 78 and write that product underneath the 440 and subtract:

Now we bring down the 6 from the dividend to make the 50 into a 506.

Think: how many times can 78 go into 506?

78 can go into 506 six times so we write a 6 above the 6 in the dividend:

Next, we multiply 6 and 78 and write that product underneath the 506 and subtract:

Now we bring down the 4 from the dividend to make the 38 into a 384.

Think: how many times can 78 go into 384?

78 can go into 384 four times so we write a 4 above the 4 in the dividend:

Next, we multiply 4 and 78 and write that product underneath the 384 and subtract:

Now we bring down the 8 from the dividend to make the 72 into a 728.

Think: how many times can 78 go into 728?

78 can go into 728 nine times so we write a 9 above the 8 in the dividend:

Next, we multiply 9 and 78 and write that product underneath the 728 and subtract:

Notice our remainder is 26 so our answer is 5.649R26.

 

Example Question #93 : The Number System

Solve:

Possible Answers:

Correct answer:

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 two places in the divisor, we must also move the decimal over two places 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 69 go into 454

69 can go into 454 six times times so we write a 6 over the 4 in the dividend:

Next, we multiply 6 and 69 and write that product underneath the 454 and subtract:

Now we bring down the 4 from the dividend to make the 40 into a 404.

Think: how many times can 69 go into 404?

69 can go into 404 five times so we write a 5 above the 4 in the dividend:

Next, we multiply 5 and 69 and write that product underneath the 404 and subtract:

Now we bring down the 3 from the dividend to make the 59 into a 593.

Think: how many times can 69 go into 593?

69 can go into 593 eight times so we write a 8 above the 3 in the dividend:

Next, we multiply 8 and 69 and write that product underneath the 593 and subtract:

Now we bring down the 9 from the dividend to make the 41 into a 419.

Think: how many times can 69 go into 419?

69 can go into 419 six times so we write a 6 above the 9 in the dividend:

Next, we multiply 6 and 69 and write that product underneath the 419 and subtract:

Notice our remainder is 5 so our answer is 6.586R5.

 

Example Question #1 : Dividing Multi Digit Decimals

Solve:

Possible Answers:

Correct answer:

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: 

Screen shot 2020 10 08 at 11.52.33 am

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

Screen shot 2020 10 08 at 11.52.37 am

The new division problem should look as follows:  

Screen shot 2020 10 08 at 11.52.40 am

*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:

Screen shot 2020 10 08 at 11.52.40 am

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:

Screen shot 2020 10 08 at 11.52.50 am

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

Screen shot 2020 10 08 at 11.52.54 am

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:

Screen shot 2020 10 08 at 11.52.59 am

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

Screen shot 2020 10 08 at 11.53.02 am

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

Example Question #2 : Dividing Multi Digit Decimals

Possible Answers:

Correct answer:

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:

Screen shot 2020 10 08 at 12.52.51 pm

*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:

Screen shot 2020 10 08 at 12.52.51 pm

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:

Screen shot 2020 10 08 at 12.54.09 pm

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:

Screen shot 2020 10 08 at 12.57.21 pm

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

Screen shot 2020 10 08 at 12.59.16 pm

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:

Screen shot 2020 10 08 at 1.03.31 pm

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

Screen shot 2020 10 08 at 1.04.46 pm

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.

Screen shot 2020 10 08 at 1.08.23 pm

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:

Screen shot 2020 10 08 at 1.14.33 pm

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

Screen shot 2020 10 08 at 1.13.05 pm

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

Example Question #3 : Dividing Multi Digit Decimals

Possible Answers:

Correct answer:

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:

Screen shot 2020 10 08 at 1.33.03 pm

*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:

Screen shot 2020 10 08 at 1.33.03 pm

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:

Screen shot 2020 10 08 at 1.41.57 pm

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:

Screen shot 2020 10 08 at 1.43.11 pm

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

Screen shot 2020 10 08 at 1.44.18 pm

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

Screen shot 2020 10 08 at 1.46.26 pm

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:

Screen shot 2020 10 08 at 1.47.10 pm

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

Screen shot 2020 10 08 at 1.48.18 pm

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

Example Question #4 : Dividing Multi Digit Decimals

Possible Answers:

Correct answer:

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: 

Screen shot 2020 10 08 at 1.51.20 pm

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

Screen shot 2020 10 08 at 1.51.24 pm

The new division problem should look as follows:  

Screen shot 2020 10 08 at 1.53.06 pm

*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:

Screen shot 2020 10 08 at 1.53.06 pm

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:

Screen shot 2020 10 08 at 1.54.01 pm

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

Screen shot 2020 10 08 at 1.55.14 pm

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.

Screen shot 2020 10 08 at 1.57.35 pm

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:

Screen shot 2020 10 08 at 1.58.34 pm

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

Screen shot 2020 10 08 at 2.00.06 pm

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

Example Question #5 : Dividing Multi Digit Decimals

Solve:

Possible Answers:

Correct answer:

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: 

Screen shot 2020 10 08 at 2.03.55 pm

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

Screen shot 2020 10 08 at 2.03.36 pm

The new division problem should look as follows:  

Screen shot 2020 10 08 at 2.05.19 pm

*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:

Screen shot 2020 10 08 at 2.05.19 pm

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:

Screen shot 2020 10 08 at 2.06.28 pm

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:

Screen shot 2020 10 08 at 2.07.59 pm

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:

Screen shot 2020 10 08 at 2.09.18 pm

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

Screen shot 2020 10 08 at 2.11.00 pm

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

Screen shot 2020 10 08 at 2.12.43 pm

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:

Screen shot 2020 10 08 at 2.14.13 pm

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

Screen shot 2020 10 08 at 2.15.56 pm

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.

Screen shot 2020 10 08 at 2.18.40 pm

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:

Screen shot 2020 10 08 at 2.19.43 pm

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

Screen shot 2020 10 08 at 2.21.08 pm

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

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