Arithmetic Grade Four

Lesson Fifty-two: Remainders

Take a look at these problems and think about what their answers might be. 

     18 / 5 = 		33 / 10 = 		25 / 8 = 

     39 / 6 = 		42 / 9 = 		24 / 9 =
Sometimes numbers don't divide evenly like the numbers from the last lesson. Sometimes there is something left over after we divide. The left over amount is called the remainder. Let's look at one example real carefully. 

	18 / 5 = ?

   	The largest number that will fit into 18 that is
	a multiple of 5 is 15 (5 x 3). When we subtract
	15 from 18 we get 3. 

	18 / 5 = 3 r3

	This is how we would say this problem out loud: 

	  "18 divided by 5 equals 3 remainder 3."
Here's another example: 

	22 / 7 = ?

	The largest number that will fit into 22 that is
	a multiple of 7 is 21 (7 x 3). When we subtract 
	21 from 22 we get 1.

	22 / 7 = 3 r1

	We say this problem like this:
	  
	   "22 divided by 7 equals 3 remainder 1."
Sometimes all we are interested in knowing is the remainder. Here are three examples where we specify the remainder. 

    18 / 5 has a remainder of 3 (5x3=15, 18-15=3)

    33 / 9 has a remainder of 6 (9x3=27, 33-27=6)

    44 / 5 has a remainder of 4 (4x8=40, 44-40=4)

On this next set of problems you will identify the remainders only.

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