It's important to interpret quotients and remainders when they arise in real-life problems.
Consider the following situation:
There are students in a class. The teacher divided this class into groups of As a result, there were several fully-filled groups and one incomplete group.
Let's answer the following questions:
- How many fully-filled groups were there?
- How many students were in the incomplete group?
- How many groups were there in total?
Since the class was divided into groups of let's start by dividing by
Let's now answer our questions by interpreting this result:
The quotient of our division is This means that there were fully-filled groups.
The remainder of our division is This means that there were students in the incomplete group.
Since we have fully-filled groups and incomplete group, there were groups in total.
Let's see some more examples.
Olivia has beads and would like to make bracelets. If each bracelet should have the same number of beads, and Olivia wants to use as many beads as possible, how many beads will be left over after she has finished making bracelets?
To find the number of beads that will be left over, we need to divide by This means that beads will be left over after Olivia has finished making bracelets.
Howard has $57$ apples that he would like to pack into bags. If each bag must contain exactly $8$ apples, how many apples will be left over after he has finished packing?
|
a
|
$7$ |
|
b
|
$3$ |
|
c
|
$4$ |
|
d
|
$1$ |
|
e
|
$5$ |
George bought $34$ cans of soda that he packed into boxes. Each box can contain a maximum of $6$ cans. How many cans of soda are in the final box if all boxes except the last are full?
|
a
|
$1$ |
|
b
|
$4$ |
|
c
|
$6$ |
|
d
|
$7$ |
|
e
|
$5$ |
Dorothy has of potatoes she would like to pack into bags. One bag holds a maximum of of potatoes. How many bags will Dorothy fill completely if all but one are filled?
To find the number of bags needed, we first need to divide by This means that Dorothy will fill bags, and she will need one more bag for the extra of potatoes.
Therefore, Dorothy will fill bags completely.
There are $39$ people in a group. They would like to rent some cars for a trip. Each car can fit exactly $5$ people. If all the cars are fully filled except one of them, how many fully-filled cars will there be?
|
a
|
$5$ |
|
b
|
$8$ |
|
c
|
$7$ |
|
d
|
$6$ |
|
e
|
$4$ |
Maria has baked $28$ cupcakes for a bake sale and wants to pack them all into boxes. If one box holds a maximum of $3$ cupcakes and she wants to use as few boxes as possible, how many boxes will Maria fill completely?
|
a
|
$9$ |
|
b
|
$1$ |
|
c
|
$12$ |
|
d
|
$10$ |
|
e
|
$8$ |
Monica has made ounces of jam that she plans to scoop into jars. If one jar holds a maximum of ounces of jam, how many jars does Monica need?
To find out the number of jars Monica requires, we first need to divide by This means that Monica will fill full jars, and she will need one more jar for the remaining ounces.
Therefore, Monica needs jars in total.
A group of $47$ people would like to rent some cars for a trip. If each car can fit $5$ people, how many cars should the group rent?
|
a
|
$9$ |
|
b
|
$5$ |
|
c
|
$12$ |
|
d
|
$10$ |
|
e
|
$11$ |
Emma has $48$ beads and would like to put them into bags. If each bag can fit a maximum of $10$ beads and she wants to use as few bags as possible, how many bags will Emma need?
|
a
|
$5$ |
|
b
|
$4$ |
|
c
|
$6$ |
|
d
|
$10$ |
|
e
|
$8$ |