Common Core: 6th Grade Math : The Number System

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

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Example Questions

Example Question #21 : 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 81 go into 336

81 can go into 336 four times times so we write a 4 over the 6 in the dividend:

Next, we multiply 4 and 81 and write that product underneath the 336 and subtract:

Now we bring down the 3 from the dividend to make the 12 into a 123.

Think: how many times can 81 go into 123?

81 can go into 123 one time so we write a 1 above the 3 in the dividend:

Next, we multiply 1 and 81 and write that product underneath the 123 and subtract:

Now we bring down the 1 from the dividend to make the 42 into a 421.

Think: how many times can 81 go into 421?

81 can go into 421 five times so we write a 5 above the 1 in the dividend:

Next, we multiply 5 and 81 and write that product underneath the 421 and subtract:

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

Think: how many times can 81 go into 165?

81 can go into 165 two times so we write a 2 above the 5 in the dividend:

Next, we multiply 2 and 81 and write that product underneath the 165 and subtract:

Notice our remainder is 3 so our answer is 4.152R3.

 

Example Question #22 : 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 84 go into 205

84 can go into 205 two times times so we write a 2 over the 5 in the dividend:

Next, we multiply 2 and 84 and write that product underneath the 205 and subtract:

Now we bring down the 6 from the dividend to make the 37 into a 376.

Think: how many times can 84 go into 376?

84 can go into 376 four times so we write a 4 above the 6 in the dividend:

Next, we multiply 4 and 84 and write that product underneath the 376 and subtract:

Now we bring down the 1 from the dividend to make the 40 into a 401.

Think: how many times can 84 go into 401?

84 can go into 401 four times so we write a 4 above the 1 in the dividend:

Next, we multiply 4 and 84 and write that product underneath the 401 and subtract:

Now we bring down the 2 from the dividend to make the 65 into a 652.

Think: how many times can 84 go into 652?

84 can go into 652 seven times so we write a 7 above the 2 in the dividend:

Next, we multiply 7 and 84 and write that product underneath the 652 and subtract:

Notice our remainder is 64 so our answer is 2.447R64.

 

Example Question #71 : 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 40 go into 104

40 can go into 104 two times times so we write a 2 over the 4 in the dividend:

Next, we multiply 2 and 40 and write that product underneath the 104 and subtract:

Now we bring down the 8 from the dividend to make the 24 into a 248.

Think: how many times can 40 go into 248?

40 can go into 248 six times so we write a 6 above the 8 in the dividend:

Next, we multiply 6 and 40 and write that product underneath the 248 and subtract:

Now we bring down the 7 from the dividend to make the 8 into a 87.

Think: how many times can 40 go into 87?

40 can go into 87 two times so we write a 2 above the 7 in the dividend:

Next, we multiply 2 and 40 and write that product underneath the 87 and subtract:

Now we bring down the 5 from the dividend to make the 7 into a 75.

Think: how many times can 40 go into 75?

40 can go into 75 one time so we write a 1 above the 5 in the dividend:

Next, we multiply 1 and 40 and write that product underneath the 75 and subtract:

Notice our remainder is 35 so our answer is 2.621R35.

 

Example Question #24 : 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 78 go into 415

78 can go into 415 five times times so we write a 5 over the 5 in the dividend:

Next, we multiply 5 and 78 and write that product underneath the 415 and subtract:

Now we bring down the 7 from the dividend to make the 25 into a 257.

Think: how many times can 78 go into 257?

78 can go into 257 three times so we write a 3 above the 7 in the dividend:

Next, we multiply 3 and 78 and write that product underneath the 257 and subtract:

Now we bring down the 9 from the dividend to make the 23 into a 239.

Think: how many times can 78 go into 239?

78 can go into 239 three times so we write a 3 above the 9 in the dividend:

Next, we multiply 3 and 78 and write that product underneath the 239 and subtract:

Now we bring down the 2 from the dividend to make the 5 into a 52.

Think: how many times can 78 go into 52?

78 can go into 52 zero so we write a 0 above the 2 in the dividend:

Next, we multiply 0 and 78 and write that product underneath the 52 and subtract:

Notice our remainder is 52 so our answer is 5.330R52.

 

Example Question #25 : 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 89 go into 289

89 can go into 289 three times times so we write a 3 over the 9 in the dividend:

Next, we multiply 3 and 89 and write that product underneath the 289 and subtract:

Now we bring down the 5 from the dividend to make the 22 into a 225.

Think: how many times can 89 go into 225?

89 can go into 225 two times so we write a 2 above the 5 in the dividend:

Next, we multiply 2 and 89 and write that product underneath the 225 and subtract:

Now we bring down the 3 from the dividend to make the 47 into a 473.

Think: how many times can 89 go into 473?

89 can go into 473 five times so we write a 5 above the 3 in the dividend:

Next, we multiply 5 and 89 and write that product underneath the 473 and subtract:

Now we bring down the 1 from the dividend to make the 28 into a 281.

Think: how many times can 89 go into 281?

89 can go into 281 three times so we write a 3 above the 1 in the dividend:

Next, we multiply 3 and 89 and write that product underneath the 281 and subtract:

Notice our remainder is 14 so our answer is 3.253R14.

 

Example Question #26 : 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 79 go into 333

79 can go into 333 four times times so we write a 4 over the 3 in the dividend:

Next, we multiply 4 and 79 and write that product underneath the 333 and subtract:

Now we bring down the 5 from the dividend to make the 17 into a 175.

Think: how many times can 79 go into 175?

79 can go into 175 two times so we write a 2 above the 5 in the dividend:

Next, we multiply 2 and 79 and write that product underneath the 175 and subtract:

Now we bring down the 3 from the dividend to make the 17 into a 173.

Think: how many times can 79 go into 173?

79 can go into 173 two times so we write a 2 above the 3 in the dividend:

Next, we multiply 2 and 79 and write that product underneath the 173 and subtract:

Now we bring down the 3 from the dividend to make the 15 into a 153.

Think: how many times can 79 go into 153?

79 can go into 153 one time so we write a 1 above the 3 in the dividend:

Next, we multiply 1 and 79 and write that product underneath the 153 and subtract:

Notice our remainder is 74 so our answer is 4.221R74.

 

Example Question #27 : 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 87 go into 234

87 can go into 234 two times times so we write a 2 over the 4 in the dividend:

Next, we multiply 2 and 87 and write that product underneath the 234 and subtract:

Now we bring down the 5 from the dividend to make the 60 into a 605.

Think: how many times can 87 go into 605?

87 can go into 605 six times so we write a 6 above the 5 in the dividend:

Next, we multiply 6 and 87 and write that product underneath the 605 and subtract:

Now we bring down the 7 from the dividend to make the 83 into a 837.

Think: how many times can 87 go into 837?

87 can go into 837 nine times so we write a 9 above the 7 in the dividend:

Next, we multiply 9 and 87 and write that product underneath the 837 and subtract:

Now we bring down the 1 from the dividend to make the 54 into a 541.

Think: how many times can 87 go into 541?

87 can go into 541 six times so we write a 6 above the 1 in the dividend:

Next, we multiply 6 and 87 and write that product underneath the 541 and subtract:

Notice our remainder is 19 so our answer is 2.696R19.

 

Example Question #28 : 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 71 go into 298

71 can go into 298 four times times so we write a 4 over the 8 in the dividend:

Next, we multiply 4 and 71 and write that product underneath the 298 and subtract:

Now we bring down the 1 from the dividend to make the 14 into a 141.

Think: how many times can 71 go into 141?

71 can go into 141 one time so we write a 1 above the 1 in the dividend:

Next, we multiply 1 and 71 and write that product underneath the 141 and subtract:

Now we bring down the 1 from the dividend to make the 70 into a 701.

Think: how many times can 71 go into 701?

71 can go into 701 nine times so we write a 9 above the 1 in the dividend:

Next, we multiply 9 and 71 and write that product underneath the 701 and subtract:

Now we bring down the 7 from the dividend to make the 62 into a 627.

Think: how many times can 71 go into 627?

71 can go into 627 eight times so we write a 8 above the 7 in the dividend:

Next, we multiply 8 and 71 and write that product underneath the 627 and subtract:

Notice our remainder is 59 so our answer is 4.198R59.

 

Example Question #31 : 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 73 go into 345

73 can go into 345 four times times so we write a 4 over the 5 in the dividend:

Next, we multiply 4 and 73 and write that product underneath the 345 and subtract:

Now we bring down the 7 from the dividend to make the 53 into a 537.

Think: how many times can 73 go into 537?

73 can go into 537 seven times so we write a 7 above the 7 in the dividend:

Next, we multiply 7 and 73 and write that product underneath the 537 and subtract:

Now we bring down the 7 from the dividend to make the 26 into a 267.

Think: how many times can 73 go into 267?

73 can go into 267 three times so we write a 3 above the 7 in the dividend:

Next, we multiply 3 and 73 and write that product underneath the 267 and subtract:

Now we bring down the 7 from the dividend to make the 48 into a 487.

Think: how many times can 73 go into 487?

73 can go into 487 six times so we write a 6 above the 7 in the dividend:

Next, we multiply 6 and 73 and write that product underneath the 487 and subtract:

Notice our remainder is 49 so our answer is 4.736R49.

 

Example Question #32 : 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 78 go into 347

78 can go into 347 four times times so we write a 4 over the 7 in the dividend:

Next, we multiply 4 and 78 and write that product underneath the 347 and subtract:

Now we bring down the 2 from the dividend to make the 35 into a 352.

Think: how many times can 78 go into 352?

78 can go into 352 four times so we write a 4 above the 2 in the dividend:

Next, we multiply 4 and 78 and write that product underneath the 352 and subtract:

Now we bring down the 6 from the dividend to make the 40 into a 406.

Think: how many times can 78 go into 406?

78 can go into 406 five times so we write a 5 above the 6 in the dividend:

Next, we multiply 5 and 78 and write that product underneath the 406 and subtract:

Now we bring down the 8 from the dividend to make the 16 into a 168.

Think: how many times can 78 go into 168?

78 can go into 168 two times so we write a 2 above the 8 in the dividend:

Next, we multiply 2 and 78 and write that product underneath the 168 and subtract:

Notice our remainder is 12 so our answer is 4.452R12.

 

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