1.5 Divide whole numbers  (Page 4/12)

So far all the division problems have worked out evenly. For example, if we had $24$ cookies and wanted to make bags of $8$ cookies, we would have $3$ bags. But what if there were $28$ cookies and we wanted to make bags of $8?$ Start with the $28$ cookies as shown in [link] .

Try to put the cookies in groups of eight as in [link] .

There are $3$ groups of eight cookies, and $4$ cookies left over. We call the $4$ cookies that are left over the remainder and show it by writing R4 next to the $3.$ (The R stands for remainder.)

To check this division we multiply $3$ times $8$ to get $24,$ and then add the remainder of $4.$

Divide $\mathrm{1,439}÷4.$ Check by multiplying.

Solution

Let's rewrite the problem to set it up for long division.
First we try to divide 4 into 1. Since that won't work, we try 4 into 14. There are 3 fours in 14. We write the 3 over the 4.
Multiply the 3 by 4 and subtract this product from 14.
Now bring down the 3 and repeat these steps. There are 5 fours in 23. Write the 5 over the 3. Multiply the 5 by 4 and subtract this product from 23.
Now bring down the 9 and repeat these steps. There are 9 fours in 39. Write the 9 over the 9. Multiply the 9 by 4 and subtract this product from 39. There are no more numbers to bring down, so we are done. The remainer is 3.
Check by multiplying.

So $\mathrm{1,439}÷4$ is $359$ with a remainder of $3.$ Our answer is correct.

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Divide and then check by multiplying: $\mathrm{1,461}÷13.$

Solution

Let's rewrite the problem to set it up for long division.	$13\overline{)\mathrm{1,461}}$
First we try to divide 13 into 1. Since that won't work, we try 13 into 14. There is 1 thirteen in 14. We write the 1 over the 4.
Multiply the 1 by 13 and subtract this product from 14.
Now bring down the 6 and repeat these steps. There is 1 thirteen in 16. Write the 1 over the 6. Multiply the 1 by 13 and subtract this product from 16.
Now bring down the 1 and repeat these steps. There are 2 thirteens in 31. Write the 2 over the 1. Multiply the 2 by 13 and subtract this product from 31. There are no more numbers to bring down, so we are done. The remainder is 5. $\mathrm{1,462}÷13$ is 112 with a remainder of 5.
Check by multiplying.

Our answer is correct.

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Divide and check by multiplying: $\mathrm{74,521}÷241.$

Solution

Let's rewrite the problem to set it up for long division.	$241\overline{)\mathrm{74,521}}$
First we try to divide 241 into 7. Since that won’t work, we try 241 into 74. That still won’t work, so we try 241 into 745. Since 2 divides into 7 three times, we try 3. Since $3\times 241=723$ , we write the 3 over the 5 in 745. Note that 4 would be too large because $4\times 241=964$ , which is greater than 745.
Multiply the 3 by 241 and subtract this product from 745.
Now bring down the 2 and repeat these steps. 241 does not divide into 222. We write a 0 over the 2 as a placeholder and then continue.
Now bring down the 1 and repeat these steps. Try 9. Since $9\times 241=\mathrm{2,169}$ , we write the 9 over the 1. Multiply the 9 by 241 and subtract this product from 2,221.
There are no more numbers to bring down, so we are finished. The remainder is 52. So $\mathrm{74,521}÷241$ is 309 with a remainder of 52.
Check by multiplying.

Sometimes it might not be obvious how many times the divisor goes into digits of the dividend. We will have to guess and check numbers to find the greatest number that goes into the digits without exceeding them.

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