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:

\(\displaystyle {0.73\rightarrow 73}\)

If we move the decimal over two places in the divisor, we must also move the decimal over two places in the dividend: 

\(\displaystyle {3.09705\rightarrow 309.705}\)

The new division problem should look as follows:

\(\displaystyle \ \ \ \ .\\73{\overline{\smash{)}309.705}}\)

*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:

\(\displaystyle \ \ \ \ .\\73{\overline{\smash{)}309.705}}\)

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:

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000} 4.~\phantom{~~0} } \\[-3pt]73\ )309.705\ \end{array}\)

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

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000}4.~\phantom{~~0} } \\[-3pt] 73) \ 309.705\\ \underline{-292\phantom{~000}} \\17\phantom{~000} \end{array}\)

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:

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000}4.2\phantom{00} } \\[-3pt]73) \ 309.705\\ \underline{-292\phantom{~000}} \\ 177\phantom{~00} \end{array}\)

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

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000}4.2 \phantom{00} } \\[-3pt]73) \ 309.705 \\ \underline{-292\phantom{~000}} \\ 177 \phantom{~00} \\ \underline{-146\phantom{~00}} \\31\phantom{~00} \end{array}\)

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:

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000}4.24 \phantom{0} } \\[-3pt]73) \ 309.705 \\ \underline{-292\phantom{~000}} \\ 177\phantom{~00} \\ \underline{-146\phantom{~00}} \\ 310 \phantom{~0} \end{array}\)

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

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000}4.24 \phantom{0} } \\[-3pt]73) \ 309.705 \\ \underline{-292\phantom{~000}} \\ 177\phantom{~00} \\ \underline{-146\phantom{~00}} \\ 310 \phantom{~0} \\ \underline{-292\phantom{~0}} \\18 \phantom{~0} \end{array}\)

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:

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000}4.242 } \\[-3pt]73) \ 309.705 \\ \underline{-292\phantom{~000}} \\ 177\phantom{~00} \\ \underline{-146\phantom{~00}} \\ 310 \phantom{~0} \\ \underline{-292\phantom{~0}} \\185 \phantom{~} \end{array}\)

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

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000}4.242 } \\[-3pt]73) \ 309.705 \\ \underline{-292\phantom{~000}} \\ 177\phantom{~00} \\ \underline{-146\phantom{~00}} \\ 310 \phantom{~0} \\ \underline{-292\phantom{~0}} \\185 \phantom{~} \\ \underline{-146\phantom{~}} \\ 39\phantom{~} \end{array}\)

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

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:

\(\displaystyle {0.8\rightarrow 80}\)

If we move the decimal over two places in the divisor, we must also move the decimal over two places in the dividend: 

\(\displaystyle {2.15805\rightarrow 215.805}\)

The new division problem should look as follows:

\(\displaystyle \ \ \ \ .\\80{\overline{\smash{)}215.805}}\)

*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:

\(\displaystyle \ \ \ \ .\\80{\overline{\smash{)}215.805}}\)

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:

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000} 2.~\phantom{~~0} } \\[-3pt]80\ )215.805\ \end{array}\)

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

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000}2.~\phantom{~~0} } \\[-3pt] 80) \ 215.805\\ \underline{-160\phantom{~000}} \\55\phantom{~000} \end{array}\)

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:

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000}2.6\phantom{00} } \\[-3pt]80) \ 215.805\\ \underline{-160\phantom{~000}} \\ 558\phantom{~00} \end{array}\)

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

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000}2.6 \phantom{00} } \\[-3pt]80) \ 215.805 \\ \underline{-160\phantom{~000}} \\ 558 \phantom{~00} \\ \underline{-480\phantom{~00}} \\78\phantom{~00} \end{array}\)

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:

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000}2.69 \phantom{0} } \\[-3pt]80) \ 215.805 \\ \underline{-160\phantom{~000}} \\ 558\phantom{~00} \\ \underline{-480\phantom{~00}} \\ 780 \phantom{~0} \end{array}\)

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

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000}2.69 \phantom{0} } \\[-3pt]80) \ 215.805 \\ \underline{-160\phantom{~000}} \\ 558\phantom{~00} \\ \underline{-480\phantom{~00}} \\ 780 \phantom{~0} \\ \underline{-720\phantom{~0}} \\60 \phantom{~0} \end{array}\)

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:

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000}2.697 } \\[-3pt]80) \ 215.805 \\ \underline{-160\phantom{~000}} \\ 558\phantom{~00} \\ \underline{-480\phantom{~00}} \\ 780 \phantom{~0} \\ \underline{-720\phantom{~0}} \\605 \phantom{~} \end{array}\)

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

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000}2.697 } \\[-3pt]80) \ 215.805 \\ \underline{-160\phantom{~000}} \\ 558\phantom{~00} \\ \underline{-480\phantom{~00}} \\ 780 \phantom{~0} \\ \underline{-720\phantom{~0}} \\605 \phantom{~} \\ \underline{-560\phantom{~}} \\ 45\phantom{~} \end{array}\)

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

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:

\(\displaystyle {0.52\rightarrow 52}\)

If we move the decimal over two places in the divisor, we must also move the decimal over two places in the dividend: 

\(\displaystyle {4.23445\rightarrow 423.445}\)

The new division problem should look as follows:

\(\displaystyle \ \ \ \ .\\52{\overline{\smash{)}423.445}}\)

*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:

\(\displaystyle \ \ \ \ .\\52{\overline{\smash{)}423.445}}\)

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:

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000} 8.~\phantom{~~0} } \\[-3pt]52\ )423.445\ \end{array}\)

Next, we multiply 8 and 52 and write that product underneath the 423 and subtract:

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000}8.~\phantom{~~0} } \\[-3pt] 52) \ 423.445\\ \underline{-416\phantom{~000}} \\7\phantom{~000} \end{array}\)

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:

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000}8.1\phantom{00} } \\[-3pt]52) \ 423.445\\ \underline{-416\phantom{~000}} \\ 74\phantom{~00} \end{array}\)

Next, we multiply 1 and 52 and write that product underneath the 74 and subtract:

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000}8.1 \phantom{00} } \\[-3pt]52) \ 423.445 \\ \underline{-416\phantom{~000}} \\ 74 \phantom{~00} \\ \underline{-52\phantom{~00}} \\22\phantom{~00} \end{array}\)

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:

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000}8.14 \phantom{0} } \\[-3pt]52) \ 423.445 \\ \underline{-416\phantom{~000}} \\ 74\phantom{~00} \\ \underline{-52\phantom{~00}} \\ 224 \phantom{~0} \end{array}\)

Next, we multiply 4 and 52 and write that product underneath the 224 and subtract:

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000}8.14 \phantom{0} } \\[-3pt]52) \ 423.445 \\ \underline{-416\phantom{~000}} \\ 74\phantom{~00} \\ \underline{-52\phantom{~00}} \\ 224 \phantom{~0} \\ \underline{-208\phantom{~0}} \\16 \phantom{~0} \end{array}\)

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:

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000}8.143 } \\[-3pt]52) \ 423.445 \\ \underline{-416\phantom{~000}} \\ 74\phantom{~00} \\ \underline{-52\phantom{~00}} \\ 224 \phantom{~0} \\ \underline{-208\phantom{~0}} \\165 \phantom{~} \end{array}\)

Next, we multiply 3 and 52 and write that product underneath the 165 and subtract:

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000}8.143 } \\[-3pt]52) \ 423.445 \\ \underline{-416\phantom{~000}} \\ 74\phantom{~00} \\ \underline{-52\phantom{~00}} \\ 224 \phantom{~0} \\ \underline{-208\phantom{~0}} \\165 \phantom{~} \\ \underline{-156\phantom{~}} \\ 9\phantom{~} \end{array}\)

Notice our remainder is 9 so our answer is 8.143R9.

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:

\(\displaystyle {0.75\rightarrow 75}\)

If we move the decimal over two places in the divisor, we must also move the decimal over two places in the dividend: 

\(\displaystyle {2.78249\rightarrow 278.249}\)

The new division problem should look as follows:

\(\displaystyle \ \ \ \ .\\75{\overline{\smash{)}278.249}}\)

*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:

\(\displaystyle \ \ \ \ .\\75{\overline{\smash{)}278.249}}\)

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:

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000} 3.~\phantom{~~0} } \\[-3pt]75\ )278.249\ \end{array}\)

Next, we multiply 3 and 75 and write that product underneath the 278 and subtract:

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000}3.~\phantom{~~0} } \\[-3pt] 75) \ 278.249\\ \underline{-225\phantom{~000}} \\53\phantom{~000} \end{array}\)

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:

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000}3.7\phantom{00} } \\[-3pt]75) \ 278.249\\ \underline{-225\phantom{~000}} \\ 532\phantom{~00} \end{array}\)

Next, we multiply 7 and 75 and write that product underneath the 532 and subtract:

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000}3.7 \phantom{00} } \\[-3pt]75) \ 278.249 \\ \underline{-225\phantom{~000}} \\ 532 \phantom{~00} \\ \underline{-525\phantom{~00}} \\7\phantom{~00} \end{array}\)

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:

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000}3.70 \phantom{0} } \\[-3pt]75) \ 278.249 \\ \underline{-225\phantom{~000}} \\ 532\phantom{~00} \\ \underline{-525\phantom{~00}} \\ 74 \phantom{~0} \end{array}\)

Next, we multiply 0 and 75 and write that product underneath the 74 and subtract:

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000}3.70 \phantom{0} } \\[-3pt]75) \ 278.249 \\ \underline{-225\phantom{~000}} \\ 532\phantom{~00} \\ \underline{-525\phantom{~00}} \\ 74 \phantom{~0} \\ \underline{-0\phantom{~0}} \\74 \phantom{~0} \end{array}\)

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:

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000}3.709 } \\[-3pt]75) \ 278.249 \\ \underline{-225\phantom{~000}} \\ 532\phantom{~00} \\ \underline{-525\phantom{~00}} \\ 74 \phantom{~0} \\ \underline{-0\phantom{~0}} \\749 \phantom{~} \end{array}\)

Next, we multiply 9 and 75 and write that product underneath the 749 and subtract:

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000}3.709 } \\[-3pt]75) \ 278.249 \\ \underline{-225\phantom{~000}} \\ 532\phantom{~00} \\ \underline{-525\phantom{~00}} \\ 74 \phantom{~0} \\ \underline{-0\phantom{~0}} \\749 \phantom{~} \\ \underline{-675\phantom{~}} \\ 74\phantom{~} \end{array}\)

Notice our remainder is 74 so our answer is 3.709R74.

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:

\(\displaystyle {0.43\rightarrow 43}\)

If we move the decimal over two places in the divisor, we must also move the decimal over two places in the dividend: 

\(\displaystyle {2.38293\rightarrow 238.293}\)

The new division problem should look as follows:

\(\displaystyle \ \ \ \ .\\43{\overline{\smash{)}238.293}}\)

*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:

\(\displaystyle \ \ \ \ .\\43{\overline{\smash{)}238.293}}\)

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:

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000} 5.~\phantom{~~0} } \\[-3pt]43\ )238.293\ \end{array}\)

Next, we multiply 5 and 43 and write that product underneath the 238 and subtract:

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000}5.~\phantom{~~0} } \\[-3pt] 43) \ 238.293\\ \underline{-215\phantom{~000}} \\23\phantom{~000} \end{array}\)

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:

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000}5.5\phantom{00} } \\[-3pt]43) \ 238.293\\ \underline{-215\phantom{~000}} \\ 232\phantom{~00} \end{array}\)

Next, we multiply 5 and 43 and write that product underneath the 232 and subtract:

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000}5.5 \phantom{00} } \\[-3pt]43) \ 238.293 \\ \underline{-215\phantom{~000}} \\ 232 \phantom{~00} \\ \underline{-215\phantom{~00}} \\17\phantom{~00} \end{array}\)

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:

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000}5.54 \phantom{0} } \\[-3pt]43) \ 238.293 \\ \underline{-215\phantom{~000}} \\ 232\phantom{~00} \\ \underline{-215\phantom{~00}} \\ 179 \phantom{~0} \end{array}\)

Next, we multiply 4 and 43 and write that product underneath the 179 and subtract:

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000}5.54 \phantom{0} } \\[-3pt]43) \ 238.293 \\ \underline{-215\phantom{~000}} \\ 232\phantom{~00} \\ \underline{-215\phantom{~00}} \\ 179 \phantom{~0} \\ \underline{-172\phantom{~0}} \\7 \phantom{~0} \end{array}\)

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:

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000}5.541 } \\[-3pt]43) \ 238.293 \\ \underline{-215\phantom{~000}} \\ 232\phantom{~00} \\ \underline{-215\phantom{~00}} \\ 179 \phantom{~0} \\ \underline{-172\phantom{~0}} \\73 \phantom{~} \end{array}\)

Next, we multiply 1 and 43 and write that product underneath the 73 and subtract:

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000}5.541 } \\[-3pt]43) \ 238.293 \\ \underline{-215\phantom{~000}} \\ 232\phantom{~00} \\ \underline{-215\phantom{~00}} \\ 179 \phantom{~0} \\ \underline{-172\phantom{~0}} \\73 \phantom{~} \\ \underline{-43\phantom{~}} \\ 30\phantom{~} \end{array}\)

Notice our remainder is 30 so our answer is 5.541R30.

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:

\(\displaystyle {0.78\rightarrow 78}\)

If we move the decimal over two places in the divisor, we must also move the decimal over two places in the dividend: 

\(\displaystyle {4.40648\rightarrow 440.648}\)

The new division problem should look as follows:

\(\displaystyle \ \ \ \ .\\78{\overline{\smash{)}440.648}}\)

*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:

\(\displaystyle \ \ \ \ .\\78{\overline{\smash{)}440.648}}\)

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:

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000} 5.~\phantom{~~0} } \\[-3pt]78\ )440.648\ \end{array}\)

Next, we multiply 5 and 78 and write that product underneath the 440 and subtract:

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000}5.~\phantom{~~0} } \\[-3pt] 78) \ 440.648\\ \underline{-390\phantom{~000}} \\50\phantom{~000} \end{array}\)

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:

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000}5.6\phantom{00} } \\[-3pt]78) \ 440.648\\ \underline{-390\phantom{~000}} \\ 506\phantom{~00} \end{array}\)

Next, we multiply 6 and 78 and write that product underneath the 506 and subtract:

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000}5.6 \phantom{00} } \\[-3pt]78) \ 440.648 \\ \underline{-390\phantom{~000}} \\ 506 \phantom{~00} \\ \underline{-468\phantom{~00}} \\38\phantom{~00} \end{array}\)

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:

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000}5.64 \phantom{0} } \\[-3pt]78) \ 440.648 \\ \underline{-390\phantom{~000}} \\ 506\phantom{~00} \\ \underline{-468\phantom{~00}} \\ 384 \phantom{~0} \end{array}\)

Next, we multiply 4 and 78 and write that product underneath the 384 and subtract:

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000}5.64 \phantom{0} } \\[-3pt]78) \ 440.648 \\ \underline{-390\phantom{~000}} \\ 506\phantom{~00} \\ \underline{-468\phantom{~00}} \\ 384 \phantom{~0} \\ \underline{-312\phantom{~0}} \\72 \phantom{~0} \end{array}\)

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:

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000}5.649 } \\[-3pt]78) \ 440.648 \\ \underline{-390\phantom{~000}} \\ 506\phantom{~00} \\ \underline{-468\phantom{~00}} \\ 384 \phantom{~0} \\ \underline{-312\phantom{~0}} \\728 \phantom{~} \end{array}\)

Next, we multiply 9 and 78 and write that product underneath the 728 and subtract:

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000}5.649 } \\[-3pt]78) \ 440.648 \\ \underline{-390\phantom{~000}} \\ 506\phantom{~00} \\ \underline{-468\phantom{~00}} \\ 384 \phantom{~0} \\ \underline{-312\phantom{~0}} \\728 \phantom{~} \\ \underline{-702\phantom{~}} \\ 26\phantom{~} \end{array}\)

Notice our remainder is 26 so our answer is 5.649R26.

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:

\(\displaystyle {0.69\rightarrow 69}\)

If we move the decimal over two places in the divisor, we must also move the decimal over two places in the dividend: 

\(\displaystyle {4.54439\rightarrow 454.439}\)

The new division problem should look as follows:

\(\displaystyle \ \ \ \ .\\69{\overline{\smash{)}454.439}}\)

*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:

\(\displaystyle \ \ \ \ .\\69{\overline{\smash{)}454.439}}\)

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:

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000} 6.~\phantom{~~0} } \\[-3pt]69\ )454.439\ \end{array}\)

Next, we multiply 6 and 69 and write that product underneath the 454 and subtract:

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000}6.~\phantom{~~0} } \\[-3pt] 69) \ 454.439\\ \underline{-414\phantom{~000}} \\40\phantom{~000} \end{array}\)

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:

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000}6.5\phantom{00} } \\[-3pt]69) \ 454.439\\ \underline{-414\phantom{~000}} \\ 404\phantom{~00} \end{array}\)

Next, we multiply 5 and 69 and write that product underneath the 404 and subtract:

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000}6.5 \phantom{00} } \\[-3pt]69) \ 454.439 \\ \underline{-414\phantom{~000}} \\ 404 \phantom{~00} \\ \underline{-345\phantom{~00}} \\59\phantom{~00} \end{array}\)

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:

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000}6.58 \phantom{0} } \\[-3pt]69) \ 454.439 \\ \underline{-414\phantom{~000}} \\ 404\phantom{~00} \\ \underline{-345\phantom{~00}} \\ 593 \phantom{~0} \end{array}\)

Next, we multiply 8 and 69 and write that product underneath the 593 and subtract:

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000}6.58 \phantom{0} } \\[-3pt]69) \ 454.439 \\ \underline{-414\phantom{~000}} \\ 404\phantom{~00} \\ \underline{-345\phantom{~00}} \\ 593 \phantom{~0} \\ \underline{-552\phantom{~0}} \\41 \phantom{~0} \end{array}\)

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:

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000}6.586 } \\[-3pt]69) \ 454.439 \\ \underline{-414\phantom{~000}} \\ 404\phantom{~00} \\ \underline{-345\phantom{~00}} \\ 593 \phantom{~0} \\ \underline{-552\phantom{~0}} \\419 \phantom{~} \end{array}\)

Next, we multiply 6 and 69 and write that product underneath the 419 and subtract:

\(\displaystyle \begin{array}{rl} \underline{ \phantom{000}6.586 } \\[-3pt]69) \ 454.439 \\ \underline{-414\phantom{~000}} \\ 404\phantom{~00} \\ \underline{-345\phantom{~00}} \\ 593 \phantom{~0} \\ \underline{-552\phantom{~0}} \\419 \phantom{~} \\ \underline{-414\phantom{~}} \\ 5\phantom{~} \end{array}\)

Notice our remainder is 5 so our answer is 6.586R5.

There are several ways that we could solve this problem. First, we can say that the temperature in New Castle is \(\displaystyle 23^\circ F\) below zero and in Tucson it is \(\displaystyle 65^\circ F\) above zero; therefore we can say:

\(\displaystyle 23+65=88^\circ F\)

Also, we can solve this problem by using a number line. New Castle’s temperature is \(\displaystyle 23\) units away from zero and Tucson’s is \(\displaystyle 65\) units away.  

We can see that Tucson is \(\displaystyle 88^\circ F\) warmer than New Castle.

There are several ways that we could solve this problem. First, we can say that the temperature in New Castle is \(\displaystyle 27^\circ F\) below zero and in Tucson it is \(\displaystyle 70^\circ F\) above zero; therefore we can say:

\(\displaystyle 27+70=97^\circ F\)

Also, we can solve this problem by using a number line. New Castle’s temperature is \(\displaystyle 27\) units away from zero and Tucson’s is \(\displaystyle 70\) units away.  

We can see that Tucson is \(\displaystyle 97^\circ F\) warmer than New Castle.

There are several ways that we could solve this problem. First, we can say that the temperature in New Castle is \(\displaystyle 31^\circ F\) below zero and in Tucson it is \(\displaystyle 75^\circ F\) above zero; therefore we can say:

\(\displaystyle 31+75=106^\circ F\)

Also, we can solve this problem by using a number line. New Castle’s temperature is \(\displaystyle 31\) units away from zero and Tucson’s is \(\displaystyle 75\) units away.  

We can see that Tucson is \(\displaystyle 106^\circ F\) warmer than New Castle.