2.3 Division of whole numbers  (Page 2/3)

Find $\mathrm{2,}\text{232}÷\text{36}$ .

$\begin{array}{c}\hfill 36\overline{)2232}\end{array}$

Use the first digit of the divisor and the first two digits of the dividend to make the educated guess.

3 goes into 22 at most 7 times.

Try 7: $7\times \text{36}=\text{252}$ which is greater than 223. Reduce the estimate.

Try 6: $6\times \text{36}=\text{216}$ which is less than 223.

$\begin{array}{cc}\text{Multiply:}\hfill & \text{6 × 36 = 216. Write 216 below 223.}\hfill \\ \text{Subtract:}\hfill & \text{223 - 216 = 7. Bring down the 2.}\hfill \end{array}$

Divide 3 into 7 to estimate the number of times 36 goes into 72. The 3 goes into 7 at most 2 times.

Try 2: $2\times \text{36}=\text{72}$ .

Check :

Thus, $\mathrm{2,}\text{232}÷\text{36}=\text{62}$ .

Find $\mathrm{2,}\text{417},\text{228}÷\text{802}$ .

$\begin{array}{c}\hfill 802\overline{)2417228}\end{array}$

First, the educated guess: $\text{24}÷8=3$ . Then $3\times \text{802}=\text{2406}$ , which is less than 2417. Use 3 as the guess. Since $3\times \text{802}=\text{2406}$ , and 2406 has four digits, place the 3 above the fourth digit of the dividend.

Subtract: 2417 - 2406 = 11.
Bring down the 2.

The divisor 802 goes into 112 at most 0 times. Use 0.

$\begin{array}{cc}\text{Multiply:}\hfill & \text{0 × 802 = 0.}\hfill \\ \text{Subtract:}\hfill & \text{112 - 0 = 112.}\hfill \\ \text{Bring down the 2.}\end{array}$

The 8 goes into 11 at most 1 time, and $1\times \text{802}=\text{802}$ , which is less than 1122. Try 1.

Subtract $1122-802=320$
Bring down the 8.

8 goes into 32 at most 4 times.

$4\times \text{802}=\text{3208}$ .

Use 4.

Check:

Thus, $\mathrm{2,}\text{417},\text{228}÷\text{802}=\mathrm{3,}\text{014}$ .

Find $\text{85}÷3$ .

$\left\{\begin{array}{cc}\text{Divide:}\hfill & \text{3 goes into 8 at most 2 times.}\hfill \\ \text{Multiply:}\hfill & \text{2 × 3 = 6. Write 6 below 8.}\hfill \\ \text{Subtract:}\hfill & \text{8 - 6 = 2. Bring down the 5.}\hfill \end{array}\right)$ $\left\{\begin{array}{cc}\text{Divide:}\hfill & \text{3 goes into 25 at most 8 times.}\hfill \\ \text{Multiply:}\hfill & \text{3 × 8 = 24. Write 24 below 25.}\hfill \\ \text{Subtract:}\hfill & \text{25 - 24 = 1.}\hfill \end{array}\right)$

There are no more digits to bring down to continue the process. We are done. One is the remainder.

Check: Multiply 28 and 3, then add 1.

$\begin{array}{c}\hfill 28\\ \hfill \underline{\times \mathrm{ 3}}\\ \hfill 84\\ \hfill \underline{+\mathrm{ 1}}\\ \hfill 85\end{array}$

Thus, $\text{85}÷3=\text{28}\mathrm{R1}$ .

Find $\text{726}÷\text{23}$ .

Check: Multiply 31 by 23, then add 13.

Thus, $\text{726}÷\text{23}=\text{31}R\text{13}$ .