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 #33 : 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 59 go into 460

59 can go into 460 seven times times so we write a 7 over the 0 in the dividend:

Next, we multiply 7 and 59 and write that product underneath the 460 and subtract:

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

Think: how many times can 59 go into 473?

59 can go into 473 eight times so we write a 8 above the 3 in the dividend:

Next, we multiply 8 and 59 and write that product underneath the 473 and subtract:

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

Think: how many times can 59 go into 18?

59 can go into 18 zero so we write a 0 above the 8 in the dividend:

Next, we multiply 0 and 59 and write that product underneath the 18 and subtract:

Now we bring down the 5 from the dividend to make the 18 into a 185.

Think: how many times can 59 go into 185?

59 can go into 185 three times so we write a 3 above the 5 in the dividend:

Next, we multiply 3 and 59 and write that product underneath the 185 and subtract:

Notice our remainder is 8 so our answer is 7.803R8.

 

Example Question #34 : 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 68 go into 405

68 can go into 405 five times times so we write a 5 over the 5 in the dividend:

Next, we multiply 5 and 68 and write that product underneath the 405 and subtract:

Now we bring down the 9 from the dividend to make the 65 into a 659.

Think: how many times can 68 go into 659?

68 can go into 659 nine times so we write a 9 above the 9 in the dividend:

Next, we multiply 9 and 68 and write that product underneath the 659 and subtract:

Now we bring down the 4 from the dividend to make the 47 into a 474.

Think: how many times can 68 go into 474?

68 can go into 474 six times so we write a 6 above the 4 in the dividend:

Next, we multiply 6 and 68 and write that product underneath the 474 and subtract:

Now we bring down the 5 from the dividend to make the 66 into a 665.

Think: how many times can 68 go into 665?

68 can go into 665 nine times so we write a 9 above the 5 in the dividend:

Next, we multiply 9 and 68 and write that product underneath the 665 and subtract:

Notice our remainder is 53 so our answer is 5.969R53.

 

Example Question #35 : 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 65 go into 486

65 can go into 486 seven times times so we write a 7 over the 6 in the dividend:

Next, we multiply 7 and 65 and write that product underneath the 486 and subtract:

Now we bring down the 7 from the dividend to make the 31 into a 317.

Think: how many times can 65 go into 317?

65 can go into 317 four times so we write a 4 above the 7 in the dividend:

Next, we multiply 4 and 65 and write that product underneath the 317 and subtract:

Now we bring down the 2 from the dividend to make the 57 into a 572.

Think: how many times can 65 go into 572?

65 can go into 572 eight times so we write a 8 above the 2 in the dividend:

Next, we multiply 8 and 65 and write that product underneath the 572 and subtract:

Now we bring down the 1 from the dividend to make the 52 into a 521.

Think: how many times can 65 go into 521?

65 can go into 521 eight times so we write a 8 above the 1 in the dividend:

Next, we multiply 8 and 65 and write that product underneath the 521 and subtract:

Notice our remainder is 1 so our answer is 7.488R1.

 

Example Question #36 : 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 59 go into 234

59 can go into 234 three times times so we write a 3 over the 4 in the dividend:

Next, we multiply 3 and 59 and write that product underneath the 234 and subtract:

Now we bring down the 6 from the dividend to make the 57 into a 576.

Think: how many times can 59 go into 576?

59 can go into 576 nine times so we write a 9 above the 6 in the dividend:

Next, we multiply 9 and 59 and write that product underneath the 576 and subtract:

Now we bring down the 1 from the dividend to make the 45 into a 451.

Think: how many times can 59 go into 451?

59 can go into 451 seven times so we write a 7 above the 1 in the dividend:

Next, we multiply 7 and 59 and write that product underneath the 451 and subtract:

Now we bring down the 3 from the dividend to make the 38 into a 383.

Think: how many times can 59 go into 383?

59 can go into 383 six times so we write a 6 above the 3 in the dividend:

Next, we multiply 6 and 59 and write that product underneath the 383 and subtract:

Notice our remainder is 29 so our answer is 3.976R29.

 

Example Question #37 : 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 76 go into 129

76 can go into 129 one time times so we write a 1 over the 9 in the dividend:

Next, we multiply 1 and 76 and write that product underneath the 129 and subtract:

Now we bring down the 8 from the dividend to make the 53 into a 538.

Think: how many times can 76 go into 538?

76 can go into 538 seven times so we write a 7 above the 8 in the dividend:

Next, we multiply 7 and 76 and write that product underneath the 538 and subtract:

Now we bring down the 0 from the dividend to make the 6 into a 60.

Think: how many times can 76 go into 60?

76 can go into 60 zero so we write a 0 above the 0 in the dividend:

Next, we multiply 0 and 76 and write that product underneath the 60 and subtract:

Now we bring down the 8 from the dividend to make the 60 into a 608.

Think: how many times can 76 go into 608?

76 can go into 608 eight times so we write a 8 above the 8 in the dividend:

Next, we multiply 8 and 76 and write that product underneath the 608 and subtract:

Notice our remainder is 0 so our answer is 1.708R0.

 

Example Question #38 : 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 88 go into 189

88 can go into 189 two times times so we write a 2 over the 9 in the dividend:

Next, we multiply 2 and 88 and write that product underneath the 189 and subtract:

Now we bring down the 0 from the dividend to make the 13 into a 130.

Think: how many times can 88 go into 130?

88 can go into 130 one time so we write a 1 above the 0 in the dividend:

Next, we multiply 1 and 88 and write that product underneath the 130 and subtract:

Now we bring down the 0 from the dividend to make the 42 into a 420.

Think: how many times can 88 go into 420?

88 can go into 420 four times so we write a 4 above the 0 in the dividend:

Next, we multiply 4 and 88 and write that product underneath the 420 and subtract:

Now we bring down the 2 from the dividend to make the 68 into a 682.

Think: how many times can 88 go into 682?

88 can go into 682 seven times so we write a 7 above the 2 in the dividend:

Next, we multiply 7 and 88 and write that product underneath the 682 and subtract:

Notice our remainder is 66 so our answer is 2.147R66.

 

Example Question #39 : 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 309

73 can go into 309 four times times so we write a 4 over the 9 in the dividend:

Next, we multiply 4 and 73 and write that product underneath the 309 and subtract:

Now we bring down the 7 from the dividend to make the 17 into a 177.

Think: how many times can 73 go into 177?

73 can go into 177 two times so we write a 2 above the 7 in the dividend:

Next, we multiply 2 and 73 and write that product underneath the 177 and subtract:

Now we bring down the 0 from the dividend to make the 31 into a 310.

Think: how many times can 73 go into 310?

73 can go into 310 four times so we write a 4 above the 0 in the dividend:

Next, we multiply 4 and 73 and write that product underneath the 310 and subtract:

Now we bring down the 5 from the dividend to make the 18 into a 185.

Think: how many times can 73 go into 185?

73 can go into 185 two times so we write a 2 above the 5 in the dividend:

Next, we multiply 2 and 73 and write that product underneath the 185 and subtract:

Notice our remainder is 39 so our answer is 4.242R39.

 

Example Question #81 : 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 80 go into 215

80 can go into 215 two times times so we write a 2 over the 5 in the dividend:

Next, we multiply 2 and 80 and write that product underneath the 215 and subtract:

Now we bring down the 8 from the dividend to make the 55 into a 558.

Think: how many times can 80 go into 558?

80 can go into 558 six times so we write a 6 above the 8 in the dividend:

Next, we multiply 6 and 80 and write that product underneath the 558 and subtract:

Now we bring down the 0 from the dividend to make the 78 into a 780.

Think: how many times can 80 go into 780?

80 can go into 780 nine times so we write a 9 above the 0 in the dividend:

Next, we multiply 9 and 80 and write that product underneath the 780 and subtract:

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

Think: how many times can 80 go into 605?

80 can go into 605 seven times so we write a 7 above the 5 in the dividend:

Next, we multiply 7 and 80 and write that product underneath the 605 and subtract:

Notice our remainder is 45 so our answer is 2.697R45.

 

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.

 

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