Making Sense
of Remainders
INTERPRETING THE REMAINDER – MAFS.4.OA.1.A
Interpreting the Remainder
When you solve a division problem with a remainder,
the way you interpret the remainder depends on the
situation and the question.
Ways to Interpret the Remainder

Sometimes you only use the quotient.

Another way is to add 1 to the quotient. Situations when it is
necessary to include all items.

Other times you will only use the remainder.

One way is to write the remainder as a fraction. This often
applies when solving problems using measurement units, like
distances, length and time. Write the remainder as the
numerator and the divisor is the denominator. Remember to
simplify all fractions and use the whole number in your final
answer.
The
annual school relay is on
Saturday. This year 75 students
from 4th grade plan to run the
race. Each relay team can
have up to 8 runners. How
many teams will fourth grade
have this year?
Quotient + 1

Explanation: The numerical answer to the
question is 9 r 3.

However, to ensure that all runners have an
opportunity to participate in the relay, there must
be 10 teams.

There will be 9 teams with 8 runners and 1 team
with 3 runners, making a total of 10 teams.
The
annual school relay is on
Saturday. This year 75 students
from 4th grade plan to run the
race. Each relay team can
have up to 8 runners. How
many runners will make up the
last team? How many runners
are not on a team of 8?
Using Only the Remainder

Explanation: The numerical answer to the
question is 9 r 3.

However, the answer to this question is simply 3.

The remainder 3, reflects the remaining number of
runners, who were unable to make a complete
group of 8.
The
annual school relay is on
Saturday. This year 75 students
from 4th grade plan to run the
race. Each relay team can
have up to 8 runners. How
many teams of 8 will fourth
grade have this year?
Using Only the Quotient

Explanation: The numerical answer to the
question is 9 r 3.

However, the answer the question is 9 teams.

In this case, the remainder is not needed in
answering the question, because the remainder
reflects the number of runners that do not make
up a team of 8.
The
length of the annual relay 75
meters. You have 8 days to
prepare for the relay. If you
plan to run the same exact
amount each day, how far will
you run each day?
Remainder as a Fraction

Explanation: The numerical answer to the
question is 9 r 3.

However, for this question, the remainder must be
interpreted as a fraction to make sure you
account for the total distance/dividend in this
problem.

To express the remainder as a fraction, the
remainder is your numerator and your
denominator is the divisor.

The answer therefore will be, 9 and 3/8 meters
each day.
Interpreting the Remainder
When you solve a division problem with a remainder,
the way you interpret the remainder depends on the
situation and the question.
Ways to Interpret the Remainder

Sometimes you only use the quotient.

Another way is to add 1 to the quotient. Situations when it is
necessary to include all items.

Other times you will only use the remainder.

One way is to write the remainder as a fraction. This often
applies when solving problems using measurement units, like
distances, length and time. Write the remainder as the
numerator and the divisor is the denominator. Remember to
simplify all fractions and use the whole number in your final
answer.