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REMAINDERS




Unit Overview

In earlier units, all of the division problems had a quotient with no numbers left over.  Now, we will look at division problems with remainders.

 

Remainders


 

 

Examples of a Division Problem with a Remainder

 

Example 1:  If you divide 13 bananas evenly between Joe and Sally, how many does each one get?

             13 ÷ 2 = ?


Joe and Sally each get 6 bananas, and one is left over.

We write this as:  13 ÷ 2 = 6 R1.


The leftover banana is called the remainder, and is indicated after the letter R. 

Note:  If we didn't want any leftovers, then both could get 6 1/2 bananas.



Example 2:  Here's another way of looking at division and remainder.  How many groups of 2 can we make out of 13 apples?

             13 ÷ 2 = ?

We can make six groups. One apple is left over. 

So, 13 ÷ 2 = 6 R1.



Example 3:  How many groups of 3 can we make out of 20 sheep?


                               20 ÷ 3 = ?

Think:  How many groups of 3 are there in 20?  OR   How many times does 3 fit into 20?

 6 × 3 = 18   and   7 × 3 = 21 (too much)

So, 3 goes into 20 six times.  Since 6 × 3 = 18, and 18 is 2 less than 20, the remainder is 2.

 

You will find the remainder by finding the difference between 20 and 6 × 3 = 18.  20 – 18 = 2. 

So, 20 ÷ 3 = 6 R2.



Example 4:  42 ÷ 8 = ?


Think:  How many times does 8 fit into 42? 

5 × 8 = 40 and 6 × 8 = 48 (too much)

So, 8 goes into 42 five times. And, 5 × 8 is 40. The remainder is the difference between 40 and 42, or 2. 

So, 42 ÷ 8 = 5 R2.



Click on the link to watch the video "Dividing numbers:  Intro to remainders".


 


Student Practice

  Division Worksheet
   
  Division with Remainders Worksheet