When Division is Not Exact
This is a complete lesson with teaching and exercises about the concept of remainder in division (when division is not exact), meant for third grade. It starts out by explaining the idea of a remainder using the example of sharing bananas. First, students work with visual examples, writing division sentences with remainders. Then the lesson explains how to find the remainder by multiplying and subtracting to find the difference (without a visual help).
The leftover banana is called the remainder, and is indicated after the letter R. (If we didn't want any leftovers, then both could get 6 1/2 bananas.) 
1. Fill in the blanks.
a. 14 bananas divided among 3 people

b. 14 carrots divided among 5 people


c.
8 scissors divided among 5 people

d.
3 apples divided among 5 people means we cannot share them equally. So, no one gets any apples. All 3 are left over.


e.
___ rams divided among 6 people

f.
___ camels divided between 2 people


2. Divide the dots into groups and write a division sentence.










3. Divide and indicate the remainders.
a. 7 ÷ 2 = _____, R ____ 1 ÷ 2 = _____, R ____ 
b. 3 ÷ 4 = _____, R ____ 11 ÷ 2 = _____, R ____ 
c. 18 ÷ 5 = _____, R ____ 7 ÷ 6 = _____, R ____ 
You will find the remainder by finding the difference between 20 and 6 × 3 = 18. 

Example. 42 ÷ 8 = ?
Think: How many times does 8 fit into 42? 5 ×
8 = 40 and 6 × 8 = 48. 
4. Practice some more!
a. 13 ÷ 5 = ____, R ____ 14 ÷ 5 = ____, R ____ 
b. 5 ÷ 8 = ____, R _____ 25 ÷ 8 = ____, R _____ 
c. 47 ÷ 6 = ____, R _____ 50 ÷ 6 = ____, R _____ 
d. 13 ÷ 2 = ____, R ____ 13 ÷ 5 = ____, R ____ 
e. 54 ÷ 8 = ____, R ____ 67 ÷ 8 = ____, R ____ 
f. 57 ÷ 7 = ____, R _____ 39 ÷ 9 = ____, R _____ 
5. Divide. What patterns do you notice?
a. 21 ÷ 2 = _____, R ____ 22 ÷ 2 = _____, R ____ 23 ÷ 2 = _____, R ____ 24 ÷ 2 = _____, R ____ 25 ÷ 2 = _____, R ____ 26 ÷ 2 = _____, R ____ 27 ÷ 2 = _____, R ____ 28 ÷ 2 = _____, R ____ 29 ÷ 2 = _____, R ____ 30 ÷ 2 = _____, R ____ 
b. 21 ÷ 3 = _____, R ____ 22 ÷ 3 = _____, R ____ 23 ÷ 3 = _____, R ____ 24 ÷ 3 = _____, R ____ 25 ÷ 3 = _____, R ____ 26 ÷ 3 = _____, R ____ 27 ÷ 3 = _____, R ____ 28 ÷ 3 = _____, R ____ 29 ÷ 3 = _____, R ____ 30 ÷ 3 = _____, R ____ 
c. 21 ÷ 4 = _____, R ____ 22 ÷ 4 = _____, R ____ 23 ÷ 4 = _____, R ____ 24 ÷ 4 = _____, R ____ 25 ÷ 4 = _____, R ____ 26 ÷ 4 = _____, R ____ 27 ÷ 4 = _____, R ____ 28 ÷ 4 = _____, R ____ 29 ÷ 4 = _____, R ____ 30 ÷ 4 = _____, R ____ 
This lesson is taken from Maria Miller's book Math Mammoth Multiplication 1, and posted at www.HomeschoolMath.net with permission from the author. Copyright © Maria Miller.
Math Mammoth Division 1
A selfteaching worktext for 3rd grade that covers division concept, division & multiplication fact families, word problems, division facts, remainder, zero and one in division, and more.Download ($3.70). Also available as a printed copy.