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 #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 #71 : How To Do Other Word Problems

On a particular November day, it is  and sunny in Tucson, Arizona. On the eastern side of the United States, it is  and sleeting in New Castle, Pennsylvania. How many degrees warmer is it in Tucson than New Castle?

Possible Answers:

Correct answer:

Explanation:

There are several ways that we could solve this problem. First, we can say that the temperature in New Castle is  below zero and in Tucson it is  above zero; therefore we can say:

Also, we can solve this problem by using a number line. New Castle’s temperature is  units away from zero and Tucson’s is  units away.  

Temp1

We can see that Tucson is  warmer than New Castle.

Example Question #71 : How To Do Other Word Problems

On a particular November day, it is  and sunny in Tucson, Arizona. On the eastern side of the United States, it is  and sleeting in New Castle, Pennsylvania. How many degrees warmer is it in Tucson than New Castle?

Possible Answers:

Correct answer:

Explanation:

There are several ways that we could solve this problem. First, we can say that the temperature in New Castle is  below zero and in Tucson it is  above zero; therefore we can say:

Also, we can solve this problem by using a number line. New Castle’s temperature is  units away from zero and Tucson’s is  units away.  

Temp2

We can see that Tucson is  warmer than New Castle.

Example Question #73 : How To Do Other Word Problems

On a particular November day, it is  and sunny in Tucson, Arizona. On the eastern side of the United States, it is  and sleeting in New Castle, Pennsylvania. How many degrees warmer is it in Tucson than New Castle?

Possible Answers:

Correct answer:

Explanation:

There are several ways that we could solve this problem. First, we can say that the temperature in New Castle is  below zero and in Tucson it is  above zero; therefore we can say:

Also, we can solve this problem by using a number line. New Castle’s temperature is  units away from zero and Tucson’s is  units away.  

Temp3

We can see that Tucson is  warmer than New Castle.

Example Question #1 : Understand The Value Of Positive And Negative Numbers: Ccss.Math.Content.6.Ns.C.5

On a particular November day, it is  and sunny in Tucson, Arizona. On the eastern side of the United States, it is  and sleeting in New Castle, Pennsylvania. How many degrees warmer is it in Tucson than New Castle?

Possible Answers:

Correct answer:

Explanation:

There are several ways that we could solve this problem. First, we can say that the temperature in New Castle is  below zero and in Tucson it is  above zero; therefore we can say:

Also, we can solve this problem by using a number line. New Castle’s temperature is  units away from zero and Tucson’s is  units away.  

Temp4

We can see that Tucson is  warmer than New Castle.

Example Question #1 : Understand The Value Of Positive And Negative Numbers: Ccss.Math.Content.6.Ns.C.5

On a particular November day, it is  and sunny in Tucson, Arizona. On the eastern side of the United States, it is  and sleeting in New Castle, Pennsylvania. How many degrees warmer is it in Tucson than New Castle?

Possible Answers:

Correct answer:

Explanation:

There are several ways that we could solve this problem. First, we can say that the temperature in New Castle is  below zero and in Tucson it is  above zero; therefore we can say:

Also, we can solve this problem by using a number line. New Castle’s temperature is  units away from zero and Tucson’s is  units away.  

Temp5

We can see that Tucson is  warmer than New Castle.

Example Question #2 : Understand The Value Of Positive And Negative Numbers: Ccss.Math.Content.6.Ns.C.5

On a particular November day, it is  and sunny in Tucson, Arizona. On the eastern side of the United States, it is  and sleeting in New Castle, Pennsylvania. How many degrees warmer is it in Tucson than New Castle?

Possible Answers:

Correct answer:

Explanation:

There are several ways that we could solve this problem. First, we can say that the temperature in New Castle is  below zero and in Tucson it is  above zero; therefore we can say:

Also, we can solve this problem by using a number line. New Castle’s temperature is  units away from zero and Tucson’s is  units away.  

Temp6

We can see that Tucson is  warmer than New Castle.

Example Question #81 : How To Do Other Word Problems

On a particular November day, it is  and sunny in Tucson, Arizona. On the eastern side of the United States, it is  and sleeting in New Castle, Pennsylvania. How many degrees warmer is it in Tucson than New Castle?

Possible Answers:

Correct answer:

Explanation:

There are several ways that we could solve this problem. First, we can say that the temperature in New Castle is  below zero and in Tucson it is  above zero; therefore we can say:

Also, we can solve this problem by using a number line. New Castle’s temperature is  units away from zero and Tucson’s is  units away.  

Temp7

We can see that Tucson is  warmer than New Castle.

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