Another method to divide numbers by two-digit numbers is to use box models.
Let's see how to use a box model by finding the value of
We start by writing our division in the following way. We place the dividend in a box and the divisor to the left of the box.
We want to find how many times goes into But instead of trying to figure this out in a single step, let's break this problem up into a series of simpler steps.
In our first step, we will pick a multiple of that is easy to compute and is fairly large but no larger than We will choose the multiple because we can compute quickly and the result is no larger than
To organize our work so far, we write above the box and subtract from inside the box.
The result of the subtraction is This indicates that if we take a total of times, then it will fit into with left over.
Now, we repeat the process with a dividend of instead of To start the next round, we write in a new box to the right.
Again, we are looking for a multiple of that is easy to compute and is no larger than We will choose the multiple because we can compute quickly and the result is no larger than
As before, we write above the box and subtract from inside the box.
We get , so the division is done.
To find the quotient all we need to do is add the numbers on top of the boxes:
Therefore,
Brian's mother made muffins to be sent to a birthday party. She wants to pack them in boxes containing muffins each. Use the box model below to find out how many boxes she will need in total to pack all the muffins.
To find out the number of boxes Brian's mother will need, we have to divide by
We write our division this way:
Since is less than , we subtract from
Next, we bring to the right.
Finally, since , we subtract from
We get , so the division is done.
The quotient is the sum of the numbers on top of the boxes:
Therefore,
This means that Brian's mom will need boxes to pack all the muffins.
A total of $195$ people are employed by Mega-Chicken, which has $15$ locations, each with the same number of employees. Use the area model below to determine how many employees work in each shop.
|
a
|
$15$ |
|
b
|
$17$ |
|
c
|
$21$ |
|
d
|
$19$ |
|
e
|
$13$ |
Use the box model below to find the value of $450 \div 25.$
|
a
|
$18$ |
|
b
|
$14$ |
|
c
|
$16$ |
|
d
|
$20$ |
|
e
|
$19$ |
Use the box model below to find the quotient and the remainder of
We write our division this way:
Since is less than , we subtract from
Next, we bring to the right.
Again, since is less than , we subtract from
Next, we bring to the right.
Finally, since is less than , we subtract from
We can't subtract any further since is less than Hence, is the remainder.
The quotient is the sum of the numbers on top of the boxes:
Therefore,
Gina traveled a distance of $272$ miles from Piqua to Chicago. The car consumed $17$ gallons of fuel in total during the trip. Use the box model below to find the distance the car traveled for each gallon of fuel.
|
a
|
$26$ miles |
|
b
|
$24$ miles |
|
c
|
$14$ miles |
|
d
|
$19$ miles |
|
e
|
$16$ miles |
Use the box model below to find the quotient and the remainder of $334 \div 15.$
|
a
|
$21 \,\text{R}\, 11$ |
|
b
|
$22 \,\text{R}\, 8$ |
|
c
|
$21 \,\text{R}\, 8$ |
|
d
|
$22 \,\text{R}\, 2$ |
|
e
|
$22 \,\text{R}\, 4$ |
Use the box model below to find the quotient of
We write our division this way:
Since is less than , we subtract from
Next, we bring to the right.
Since is less than , we subtract from
Next, we bring to the right.
Finally, since , we subtract from
We get , so the division is done.
The quotient is the sum of the numbers on top of the boxes:
Therefore,
Use the box model below to find the quotient of $2,352 \div 42.$
|
a
|
$50$ |
|
b
|
$48$ |
|
c
|
$59$ |
|
d
|
$56$ |
|
e
|
$58$ |
Use the box model below to find the quotient of $1,856 \div 32.$
|
a
|
$60$ |
|
b
|
$58$ |
|
c
|
$57$ |
|
d
|
$56$ |
|
e
|
$59$ |