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Class Notes for Division
We usually define the operation division in terms of multiplication. For example, we
know that 2x4 = 8 which we can also write as 2 • 4 = 8 or (2)(4) = 8 we can then reason
if we have 8 items and want to split them into two equal piles there will be 4 items in
each of the two piles . We would write this division problem as 8 ÷ 2 = 4. If we wanted to
take 8 items and divide them into 4 equal piles the division problem would look like this :
8 ÷ 4 = 2.
The vocabulary for the division operation is :
The divisor represents the number of equal groups you are trying to arrange.
The dividend represents the total number items you might have.
The quotient represents the number of items in each of your equal groups.
Multiplication and division are opposite operations. For example,
8x2 =16 and 16 ÷ 2 = 8or16 ÷ 8 = 2. In division to check your answer just multiply the
divisor by the quotient and you answer should be the dividend from your problem.
We often refer to the following combination of facts as a Fact Family or related
24 ÷ 3 = 8
24 ÷ 8 = 3
3× 8 = 24
8 × 3 = 24
Some division patterns you should recognize:
Zero divided by any number is zero . because you take zero items and
try to put them in 5 equal groups you have zero items in each group.
Why? Because any time you take a specific
number of items and divide it up into the same number of groups as you have items there
can only be one item in each group. Therefore we have a pattern that says whenever the
dividend and the divisor are the same the quotient will be 1.
This also makes sense looking at our Fact Family Info:
8 ÷ 8 =1…and…1× 8 = 8
We always say that division by zero is undefined. For example,
8 ÷ 0 = undefined
because there is no number that when multiplied by 0 will yield a product of 8. The zero
product property assures us that when zero is multiplied by any number the product is
number × 0 = 0
Division by a one digit number :
3159 ÷ 7 = ? long division is a process we use to solve this problem .
Intermediate Algorithm 3159 ÷ 7
How many 7s in 3100?
Therefore, the quotient is the sum 400 + 50 + 1, or 451,
and the remainder is 2.
The Standard Algorithm for Division uses the thinking of the algorithm above but does
not write down as many steps .
Definition of an exponent
• We refer to the number that holds the position of x as the base.
• We refer to the number that holds the position of n as the exponent.
For example:. Therefore, 5 is the base and
3 is the exponent.
An unwritten rule for exponents is : the exponent only applies to the number or
variable directly to the left of it unless parentheses are involved. What does that
mean for the following: