Whole Number Division
* 3 Ways to Represent Division
Symbol
Fraction
Sentence(÷)
1.
3
9 ) 27
=3
27 ÷ 9 = 3
2.
7
8 ) 56
=7
56 ÷ 8 = 7
* Special Division Properties
1.
Dividing by One – the dividend is the quotient
Ex.
33 ÷ 1 = 33
Dividend
2.
Quotient
Zero as the dividend or numerator - the quotient is always zero
Ex.
=0
0·4=0
Use multiplication to check
3.
Zero as the divisor or denominator - the quotient is undefined or meaningless
Ex.
=0
0·0 ≠ 5
Use multiplication to check
=5
5·0≠ 5
Use multiplication to check
= Undefined
5 ÷ 0 = Undefined
Undefined
0) 5
*Mental Division – underline the beginning digits, divide them, and pair up zeros (dancing
zeros) that the divisor and dividend have in common. The zeros (if any)
that are left in the dividend move into the quotient.
Ex. 1)
600
700 ) 420,000
Ex. 2)
3,000 = 6
500
Ex. 3)
400,000 ÷ 8,000 = 50
*Estimating Division-
Ex. 1)
When estimating with division use friendly numbers that divide
easily. Then use mental division strategies to determine the estimate.
35,785 ÷ 9
36,000 ÷ 9 = 4,000
9 divides evenly into 36, so I rounded to 36,000 because it is divisible by 9
Ex. 2)
73,356 ÷ 56
72,000 ÷ 60 = 1,200
6 divides evenly into 72, so I rounded to 72,000 and 60
*Short Division -
Ex. 1)
works best with a one digit divisor… do the division and subtraction in your
head and record what is left with the small number.
510 ÷ 6
85
6  5 130
Ex. 2)
6,786 ÷ 5
13 57
5  6172836
Write remainders as a fraction in simplest form…. Remainder over divisor!