Common Core: 6th Grade Math : Grade 6

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

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Example Questions

Example Question #3 : How To Multiply And Divide Decimals

Kevin is looking at the blueprint of the house he is building. The scale is 1 inch = 5 feet. On paper, the master bedroom is 2.5 inches by 3 inches. What is the actual size of the bedroom?

Possible Answers:

20 ft x 30 ft

12.5 ft x 15 ft

7.5 ft x 9 ft

15 ft x 25 ft

10 ft x 10 ft

Correct answer:

12.5 ft x 15 ft

Explanation:

The given dimensions must be multiplied by 5, so 2.5 inches becomes 12.5 feet, and 3 inches becomes 15 feet.

Example Question #3 : How To Multiply Decimals

A car has gas mileage of 46 miles per gallon. Assume that gas costs $3.90 per gallon. What would be the total cost of gas if the car traveled 1,150 miles?

Possible Answers:

$179.40

$100.00

$115.60

$125.70

$97.50

Correct answer:

$97.50

Explanation:

First find out how many gallons of gas the car consumed while traveling 1150 miles. This can be found out like so:

1150 miles x gallons/46 miles = 25 gallons

Multiplying 25 by $3.90 yields $97.50.

Example Question #1371 : Act Math

If , approximately how many inches are in one meter?

Possible Answers:

Correct answer:

Explanation:

and

Using the factor-label method we get the following equation.

We treat the units as if they are numbers, and can cancel the units from the fractions.

Example Question #1373 : Act Math

You bought a dozen eggs marked at  and received  change from . What is the percent of sales tax?  

Possible Answers:

Correct answer:

Explanation:

Set the equation up as 

 

Solve for , which equals  

or

Therefore the percent sales tax is: 

Example Question #61 : The Number System

Menu 1

Above is the menu at the concession stand at a school carnival. 

David wants to buy some chicken strips for himself and his companions. He wants six strips, his brother Mickey wants five strips, his girlfriend Vickie wants three, and Mickey's girlfriend Jenny wants five. Since the concession stand only sells the strips in orders of four, he has decided to just purchase as many orders as it takes to feed the entire group. How much will he spend on enough orders of strips to satisfy the group?

(No tax is charged, since this is a school event)

Possible Answers:

Correct answer:

Explanation:

The group wants a total of  strips; since 

,

Dave will need to purchase five orders of strips (he cannot purchase a partial order). This will cost him

.

Example Question #1 : How To Solve Arithmetic Word Problems

The menu of a local coffeehouse reads as follows:

Sandy orders some drinks for herself and some friends. She orders three cappuccinos, two iced teas, two cafe lattes, and an espresso. The sales tax is five percent. How much change does she receive back for a twenty-dollar bill?

Possible Answers:

A twenty-dollar bill isn't enough to buy the drinks.

Correct answer:

Explanation:

The three cappuccinos cost: 

The two iced teas cost 

The two cafe lattes cost 

The espresso costs .

Add these amounts to get the cost before tax:

The tax is five percent of  or:

Add both values in order to obtain the total cost after tax.

As a result, the change from a twenty-dollar bill is as follows:

Example Question #11 : 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 42 go into 419

42 can go into 419 nine times times so we write a 9 over the 9 in the dividend:

Next, we multiply 9 and 42 and write that product underneath the 419 and subtract:

Now we bring down the 3 from the dividend to make the 41 into a 413.

Think: how many times can 42 go into 413?

42 can go into 413 nine times so we write a 9 above the 3 in the dividend:

Next, we multiply 9 and 42 and write that product underneath the 413 and subtract:

Now we bring down the 4 from the dividend to make the 35 into a 354.

Think: how many times can 42 go into 354?

42 can go into 354 eight times so we write a 8 above the 4 in the dividend:

Next, we multiply 8 and 42 and write that product underneath the 354 and subtract:

Now we bring down the 8 from the dividend to make the 18 into a 188.

Think: how many times can 42 go into 188?

42 can go into 188 four times so we write a 4 above the 8 in the dividend:

Next, we multiply 4 and 42 and write that product underneath the 188 and subtract:

Notice our remainder is 20 so our answer is 9.984R20.

 

Example Question #62 : 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 88 go into 319

88 can go into 319 three times times so we write a 3 over the 9 in the dividend:

Next, we multiply 3 and 88 and write that product underneath the 319 and subtract:

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

Think: how many times can 88 go into 558?

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

Next, we multiply 6 and 88 and write that product underneath the 558 and subtract:

Now we bring down the 5 from the dividend to make the 30 into a 305.

Think: how many times can 88 go into 305?

88 can go into 305 three times so we write a 3 above the 5 in the dividend:

Next, we multiply 3 and 88 and write that product underneath the 305 and subtract:

Now we bring down the 1 from the dividend to make the 41 into a 411.

Think: how many times can 88 go into 411?

88 can go into 411 four times so we write a 4 above the 1 in the dividend:

Next, we multiply 4 and 88 and write that product underneath the 411 and subtract:

Notice our remainder is 59 so our answer is 3.634R59.

 

Example Question #63 : 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 64 go into 300

64 can go into 300 four times times so we write a 4 over the 0 in the dividend:

Next, we multiply 4 and 64 and write that product underneath the 300 and subtract:

Now we bring down the 2 from the dividend to make the 44 into a 442.

Think: how many times can 64 go into 442?

64 can go into 442 six times so we write a 6 above the 2 in the dividend:

Next, we multiply 6 and 64 and write that product underneath the 442 and subtract:

Now we bring down the 1 from the dividend to make the 58 into a 581.

Think: how many times can 64 go into 581?

64 can go into 581 nine times so we write a 9 above the 1 in the dividend:

Next, we multiply 9 and 64 and write that product underneath the 581 and subtract:

Now we bring down the 6 from the dividend to make the 5 into a 56.

Think: how many times can 64 go into 56?

64 can go into 56 zero so we write a 0 above the 6 in the dividend:

Next, we multiply 0 and 64 and write that product underneath the 56 and subtract:

Notice our remainder is 56 so our answer is 4.690R56.

 

Example Question #64 : 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 82 go into 199

82 can go into 199 two times times so we write a 2 over the 9 in the dividend:

Next, we multiply 2 and 82 and write that product underneath the 199 and subtract:

Now we bring down the 4 from the dividend to make the 35 into a 354.

Think: how many times can 82 go into 354?

82 can go into 354 four times so we write a 4 above the 4 in the dividend:

Next, we multiply 4 and 82 and write that product underneath the 354 and subtract:

Now we bring down the 0 from the dividend to make the 26 into a 260.

Think: how many times can 82 go into 260?

82 can go into 260 three times so we write a 3 above the 0 in the dividend:

Next, we multiply 3 and 82 and write that product underneath the 260 and subtract:

Now we bring down the 2 from the dividend to make the 14 into a 142.

Think: how many times can 82 go into 142?

82 can go into 142 one time so we write a 1 above the 2 in the dividend:

Next, we multiply 1 and 82 and write that product underneath the 142 and subtract:

Notice our remainder is 60 so our answer is 2.431R60.

 

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