Description:
Divisibility questions ask you to determine if certain numbers or
algebraic terms can be divided evenly by other numbers or algebraic
terms.
Approach:
Divide the larger number by the smaller number on the calculator to see
if the answer is a whole number result. If the result is not a whole
number then the larger number is not divisible by the smaller number.
1) Remainders
When a number is not divisible by another, then dividing the two numbers
produces a remainder.
Determine the remainder by first dividing two numbers on your calculator:
100/7 = 14.285714
Next, determine the whole number result of the denominator (7)
multiplied by the result without the decimal (14).
7 * 14 = 98
Finally, determine the remainder by subtracting the result (98) from
the original numerator (100).
100 - 98 = 2, so our remainder is 2
1-1. Practice:
-
If today is Tuesday, what day will it be 100 days from today?
-
A teacher has 100 pencils which she wants to divide evenly amongst
her 22 students. If she gives each student the most pencils
possible, while still making sure each student receives the same
number of pencils, how many of the 100 pencils are not given to the
students?
2) Algebraic Divisibility
When asked to determine if one algebraic expression is divisible by
another, plug in numbers to make it an arithmetic problem.
For example:
Is x2 + 6x + 9
divisible by x + 3?
Plug in 5 for x and the question becomes is 64 divisible by 8.
2-1. Practice:
Is (4x2 + 12x + 9) divisible by
(2x + 3)?
