Long Division Problems with Answers

Example 1) Work out 84 ÷ 3

So we are working out \[ 3 \enclose {longdiv} {84} \]

FIrst step is to work out 8 ÷ 3, which means we need to find how many groups of 3 make 8.

We can get 2 groups of 3 in 8, and 2 x 3 = 6 so this gives us: \[ \begin {array}{l} \quad 2 \\ 3 \enclose {longdiv} {84} \\ \quad \underline{6} \end{array} \]

Next we subtract 6 from 8 to give us: \[ \begin {array}{l} \quad 2 \\ 3 \enclose {longdiv} {84} \\ \quad \underline{6} \\ \quad 2 \end{array} \]

The next step is to bring down the 4 and put it next to the 2 \[ \begin {array}{l} \quad 2 \\ 3 \enclose {longdiv} {84} \\ \quad \underline{6} \\ \quad 24 \end{array} \]

We now have to work out 24 ÷ 3, or how many groups of 3 make 24.

8 groups of 3 make 24. So this gives us: \[ \begin {array}{l} \quad 28 \\ 3 \enclose {longdiv} {84} \\ \quad \underline{6} \\ \quad 24 \\ \quad \underline{24} \end{array} \]

Finally subtract 24 from 24 to give us an answer of 0. \[ \begin {array}{l} \quad 28 \\ 3 \enclose {longdiv} {84} \\ \quad \underline{6} \\ \quad 24 \\ \quad \underline{24} \\ \quad \; \; 0 \end{array} \]

There are no more digits to bring down and we have no remainders, so we have finished.

Answer: 84 ÷ 3 = 28

Example 2) Work out 347 ÷ 4

So we are working out \[ 4 \enclose {longdiv} {347} \]

FIrst step is to work out 3 ÷ 4, which means we need to find how many groups of 4 make 3.

There are 0 groups of 4 in 3, so we keep the 3 in its place and go on to the next digit which is 4.

This gives us: \[ \begin {array}{l} \quad 0 \\ 4 \enclose {longdiv} {347} \end{array} \]

So the next step is to work out 34 ÷ 4, or find how many groups of 4 make 34.

8 groups of 4 make 32. So this gives us: \[ \begin {array}{l} \quad 08 \\ 4 \enclose {longdiv} {347} \\ \quad \underline {32} \end{array} \]

We subtract 32 from 34 to give us an answer of 2. This gives us: \[ \begin {array}{l} \quad 08 \\ 4 \enclose {longdiv} {347} \\ \quad \underline {32} \\ \quad \; \; 2 \end{array} \]

Next we bring the 7 down alongside the 2. \[ \begin {array}{l} \quad 08 \\ 4 \enclose {longdiv} {347} \\ \quad \underline {32} \\ \quad \; \; 27 \end{array} \]

So we need to work out 27 ÷ 4, or find how many 4s make 27.

6 groups of 4 make 24. So this gives us: \[ \begin {array}{l} \quad 086 \\ 4 \enclose {longdiv} {347} \\ \quad \underline {32} \\ \quad \; \; 27 \\ \quad \; \; \underline {24} \end{array} \]

Finally we need to subtract 24 from 27 to give us 3.

There are no more digits to bring down, so we are left with 3 as a remainder. \[ \begin {array}{l} \quad 086r3 \\ 4 \enclose {longdiv} {347} \\ \quad \underline {32} \\ \quad \; \; 27 \\ \quad \; \; \underline {24} \\ \quad \quad 3 \end{array} \]

Answer: 347 ÷ 4 = 86r3

If we wanted the remainder as a fraction, we would have 347 ÷ 4 = 86 ¾

Example 3) Work out 8165 ÷ 12

So we are working out \[ 12 \enclose {longdiv} {8165} \]

FIrst step is to work out 8 ÷ 12, which means we need to find how many groups of 12 make 8.

There are 0 groups of 12 in 8, so we keep the 8 in its place and go on to the next digit which is 1.

This gives us: \[ \begin {array}{l} \quad \; 0 \\ 12 \enclose {longdiv} {8165} \end{array} \]

So the next step is to work out 81 ÷ 12, or find how many groups of 12 make 81.

6 groups of 12 make 72. So this gives us: \[ \begin {array}{l} \quad \; 06 \\ 12 \enclose {longdiv} {8165} \\ \quad \; \, \underline {72} \end{array} \]

6 groups of 12 make 72. So this gives us: \[ \begin {array}{l} \quad \; 06 \\ 12 \enclose {longdiv} {8165} \\ \quad \; \, \underline {72} \\ \qquad 9 \end{array} \]

Next we bring the 6 down alongside the 9. \[ \begin {array}{l} \quad \; 06 \\ 12 \enclose {longdiv} {8165} \\ \quad \; \, \underline {72} \\ \qquad 96 \end{array} \]

So we need to work out 96 ÷ 12, or find how many 12s make 96.

8 groups of 12 make 96. So this gives us: \[ \begin {array}{l} \quad \; 068 \\ 12 \enclose {longdiv} {8165} \\ \quad \; \, \underline {72} \\ \qquad 96 \\ \qquad \underline{96} \end{array} \]

Now we subtract 96 from 96 to give us 0. \[ \begin {array}{l} \quad \; 068 \\ 12 \enclose {longdiv} {8165} \\ \quad \; \, \underline {72} \\ \qquad 96 \\ \qquad \underline{96} \\ \qquad \; \: 0 \end{array} \]

Now we bring down the 5. \[ \begin {array}{l} \quad \; 068 \\ 12 \enclose {longdiv} {8165} \\ \quad \; \, \underline {72} \\ \qquad 96 \\ \qquad \underline{96} \\ \qquad \; \: 05 \end{array} \]

Nexy we need to work out 5 ÷ 12, or how many 12s make 5.

0 groups of 12 make 5, so this gives us: \[ \begin {array}{l} \quad \; 0680 \\ 12 \enclose {longdiv} {8165} \\ \quad \; \, \underline {72} \\ \qquad 96 \\ \qquad \underline{96} \\ \qquad \; \: 05 \\ \qquad \; \: \underline {00} \end{array} \]

Subtracting 0 from 5 gives us 5. There are no more digits to bring down, so 5 is the remainder. \[ \begin {array}{l} \quad \; 0680r5 \\ 12 \enclose {longdiv} {8165} \\ \quad \; \, \underline {72} \\ \qquad 96 \\ \qquad \underline{96} \\ \qquad \; \: 05 \\ \qquad \; \: \underline {00} \\ \qquad \quad 5 \end{array} \]

Answer: 8165 ÷ 12 = 680r5

If we wanted the remainder as a fraction, we would have \[ 8165 \div 12 = 680 {5 \over 12} \]