Let's consider the following division problem:
We can visualize this division problem by arranging objects into rows with objects in each row.
The bottom row does not contain objects. This tells us that cannot be divided evenly into groups of Nonetheless, we can still solve this division problem:
We have full rows. This tells us that we can create full groups of from
The incomplete row contains the remaining objects.
We write the solution to our division problem as follows:
Note the following:
The number is the whole number part of the division (also called the quotient).
The number is called the remainder.
In words, we'd say " divided by equals remainder "
Given the model above, evaluate
We want to divide by
To solve this division problem, we arrange objects in rows, placing objects in each row.
The number of full rows gives us the whole number part (also called the quotient).
If there is an incomplete row at the end, the number of objects in that row gives us the remainder. If there are no incomplete rows, the remainder equals
We have the following:
full rows. So, the whole number part is
object in the incomplete row. So, the remainder is
Therefore,
Given the model above, $26 \div 4 =$
|
a
|
$6 \,\textrm{R}\,2$ |
|
b
|
$4 \,\textrm{R}\,2$ |
|
c
|
$4 \,\textrm{R}\,6$ |
|
d
|
$2 \,\textrm{R}\,4$ |
|
e
|
$6 \,\textrm{R}\,4$ |
Given the model above, $34 \div 7 =$
|
a
|
$4 \, \textrm{R} \, 6$ |
|
b
|
$6 \, \textrm{R} \, 5$ |
|
c
|
$5 \, \textrm{R} \, 6$ |
|
d
|
$6 \, \textrm{R} \, 4$ |
|
e
|
$5 \, \textrm{R} \, 0$ |
You might wonder what happens to the remainder when a division can be carried out evenly.
Let's consider the following example:
As before, we visualize the division by arranging objects in rows, placing objects in each row:
In our model above, we have the following:
full rows. So, the whole number part (or quotient) equals
There are no incomplete rows. This means that the remainder equals
Therefore, we can write the solution to this division problem as
Since the remainder equals zero, we can drop this part. This gives
Given the model above, find the quotient and remainder of
We want to divide by
To solve this division problem, we arrange objects in rows, placing objects in each row.
The number of full rows gives us the whole number part (also called the quotient).
If there is an incomplete row at the end, the number of objects in that row gives us the remainder. If there are no incomplete rows, the remainder equals
We have the following:
full rows. So, the quotient is
There are no incomplete rows. So, the remainder is
Therefore, which can be written as
Given the model above, what is $24 \div 8?$
|
a
|
$4$ |
|
b
|
$3\,\textrm R \, 7$ |
|
c
|
$4\,\textrm R \, 1$ |
|
d
|
$3\,\textrm R \, 1$ |
|
e
|
$3$ |
Given the model above, what is $24 \div 6?$
|
a
|
$4\, \textrm{R} \, 4$ |
|
b
|
$4\, \textrm{R} \, 0$ |
|
c
|
$6\, \textrm{R} \, 0$ |
|
d
|
$5\, \textrm{R} \, 0$ |
|
e
|
$4\, \textrm{R} \, 1$ |
Complete the diagram above by arranging objects in rows with objects per row, and use this to find
We want to divide by
To solve this division problem, we arrange objects in rows, placing objects in each row.
The number of full rows gives us the whole number part (also called the quotient).
If there is an incomplete row at the end, the number of objects in that row gives us the remainder. If there are no incomplete rows, the remainder equals
We have the following:
full rows. So, the quotient is
object in the incomplete row. So, the remainder is
Therefore,
Complete the diagram above by arranging $20$ objects in rows with $3$ objects per row, and use this to find $20 \div 3.$
|
a
|
$4\,\textrm{R}\,2$ |
|
b
|
$4\,\textrm{R}\,0$ |
|
c
|
$2\,\textrm{R}\,6$ |
|
d
|
$6\,\textrm{R}\,2$ |
|
e
|
$6\,\textrm{R}\,1$ |
Complete the diagram above by arranging $31$ objects in rows with $5$ objects per row, and use this to find $31 \div 5.$
|
a
|
$7 \, \textrm{R} \, 0$ |
|
b
|
$6 \, \textrm{R} \, 1$ |
|
c
|
$6 \, \textrm{R} \, 5$ |
|
d
|
$6 \, \textrm{R} \, 0$ |
|
e
|
$1 \, \textrm{R} \, 7$ |
