The Number System

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6th Grade Math › The Number System

Questions 1 - 10
1

Hydraulic fracturing is a process used by gas companies to rupture and collects pockets of gas trapped within pockets of shale rock. A particular shale fracking site is in length and occupies an area of . How wide is this particular site?

Explanation

In order to solve this question, we need to first recall how to find the area of a rectangle.

Substitute in the given values in the equation and solve for .

Divide both sides by

Dividing by a fraction is the same as multiplying by its inverse or reciprocal.

Find the reciprocal of

Simplify and rewrite.

Multiply and solve.

Reduce.

The width of the fracking site is

2

Find the product.

Steven bought 4 cheeseburgers to share. Each cheeseburger costs $0.79. How much did Steven pay for the 4 cheeseburgers?

Explanation

The easiest way to do this problem is to multiply .

Another option is to add .

Either way, the correct answer is .

3

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 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.

4

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:

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

5

Solve:

Explanation

When we add with multi-digit numbers with decimals, we start with the numbers furthest to the right and work our way towards the left.

Add the numbers in the hundredths place:

Your work should look something like this:

Add the numbers in the tenths place:

Because this sum is greater than 9, we write the 1 from the ones place and carry the 1 from the tens place over to the left. Your work should look something like this:

Your work should look something like this:

*Notice that the decimal moves directly down when we are adding decimal numbers.

Add the numbers in the ones place including the one carried over:

Your work should look something like this:

Add the numbers in the tens place:

Your final answer should be:

6

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?

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.

Temp10

We can see that Tucson is warmer than New Castle.

7

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?

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.

8

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?

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.

9

Menu 1

The above is a menu at the concession stand at a drive-in movie.

Gary wants to order two hamburgers and two small orders of fries. He wants to order two sodas of the same size. If he has just a twenty-dollar bill on hand, what is the largest size soda of which he can order two?

Gary can afford two large sodas

Gary can afford two medium sodas, but not two large sodas

Gary can afford two small sodas, but not two medium or large sodas

Gary cannot afford two sodas

Explanation

The easiest way to think of this is to note that Gary seems to be ordering for two people, himself and a friend. He has $20, so half of this will be for himself and half for his friend - and half of $20 is $10.

Each hamburger costs $4.89, and each small order of fries costs $2.29. This leaves

to spend on a soda for each person. This will enable to him to buy both himself and his friend a large soda.

10

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?

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.

Temp10

We can see that Tucson is warmer than New Castle.

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