All Common Core: 6th Grade Math Resources
Example Questions
Example Question #31 : Fluently Add, Subtract, Multiply, And Divide Multi Digit Decimals: Ccss.Math.Content.6.Ns.B.3
Solve:
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 #32 : Fluently Add, Subtract, Multiply, And Divide Multi Digit Decimals: Ccss.Math.Content.6.Ns.B.3
Solve:
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:
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 #82 : The Number System
Solve:
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.
Example Question #91 : The Number System
Solve:
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:
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:
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?
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.
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?
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.
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?
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.
We can see that Tucson is warmer than New Castle.