Lesson 6.4 Expressing and
Interpreting Remainders
Math Message:
Three students share 13 sticks of gum. How many
sticks of gum does each student get if they receive
equal shares?
students
sticks
3
students
?
13/3 =
sticks
13
Math Message Follow-Up
• 4 R1 is a correct answer to
the Math Message
problem, but this will not satisfy the three
students who want to know who gets the last
piece of gum.
Draw a picture of the
problem.
1 left over piece of gum
split between 3 people.
• What do the quotient, 4, and remainder, 1,
represent? Should you ignore the remainder?
Mixed Number
• Each student in the group will receive 4
1/3 sticks of gum. Or you can say, 4 1/3
sticks of gum per student.
4 1/3 is a mixed number - it has a whole number
and a fraction.
Can you think of other examples of mixed numbers?
Expressing Remainders
as Fractions or Decimals
• In division number stories, when there is
a remainder, you have to decide:
•
•
What does the remainder represent?
What should I do with the remainder?
Draw a picture on your whiteboard to organize
the information for the problem.
Four brothers are given 35 fruit bars.
They agree to share the bars equally.
How many fruit bars will each boy get?
What does the remainder represent?
3 fruit bars
What should I do with the remainder?
Split it between the brothers.
Write as a mixed number - 8 3/4 fruit bars
the remainder becomes the numerator (top part of fraction) and
the divisor becomes the denominator (bottom part of fraction - think down)
Draw a picture on your whiteboard to organize
the information for the problem.
• Four people split the cost of a $15 present
equally. What is each person’s share? 3 R3
What does the remainder represent?
3 left over dollars
What should I do with the remainder?
Split it between the people.
the remainder becomes the numerator (top part of fraction) and
the divisor becomes the denominator (bottom part of fraction - think down)
$3 3/4, or $3.75
Sometimes you cannot turn a
remainder into a fraction or a decimal
• It is VERY important to identify what the
remainder represents so you can decide
if you should ignore it or round up to the
next whole number.
• It is VERY important to identify what the
remainder represents so you can decide
if you should ignore it or round up to the
next whole number.
Let’s do this problem together.
Three children wish to divide a set of 16 toy cars
equally. What is each child’s share? 5 R 1
Draw a picture on your whiteboard to organize
the information for the problem.
How is this different from
splitting pieces of gum?
The remainder, a toy car, cannot be divided up.
It is a leftover amount - you must ignore it.
The answer would be 5 cars.
•
•
•
•
It is VERY important to identify what the remainder
represents so you can decide if you should
ignore it
or
round up to the next whole number.
Ann has $18 to buy notebooks that cost $4 each. How
many notebooks can she buy? 4 R 2
Draw a picture on your whiteboard to organize
the information for the problem.
Ann can buy four notebooks
and have $2 leftover.
Ann does not have enough money to purchase another
notebook.
Therefore, you must ignore the remainder.
The answer would be 4 notebooks.
•
•
•
•
It is VERY important to identify what the remainder
represents so you can decide if you should
ignore it
or
round up to the next whole number.
Jeffrey has 29 photographs. He can fit 6 photos
on each page of his photo album. How many pages
must he use to hold all 29 photos?4 R5
Draw a picture on your whiteboard to organize
the information for the problem.
Jeffrey needs 4 5/6 pages to
include all 29 photos.
Four pages holds only 24 photos and are not enough.
Jeffrey must use a fifth page to hold the last 5 photos.
You must round up to the next whole number,
from 4 pages to 5 pages to ensure all photos are included.
Partnership Work
• Math Journal page 148 and Math Journal page
149.
REMEMBER:
•What does the
remainder
represent?
•What should I
do with the
remainder?