Introduction
Division is one of the basic operations in mathematics. The basic concept of a division is to find the quotient for a given set of dividend and divisor. We need to examine whether the division is even or not, that is, whether there is a remainder or not.
The operation of division is not only restricted to numbers but also extends to variables and expressions. Here, we will study different types of division problems with only numbers.
The division problems can be of various types depending on the context.
Finding an Average by Division
The average (or arithmetic mean) of a set of items is arrived by dividing the total value of the items by the number of items.
EXAMPLE
What is the average of the set of numbers 22, 24 and 32?
The total value of the items is the sum of all the numbers 22 + 24 + 32, which is 78.
There are 3 items in the given set of numbers.
Therefore, the average of the given set of numbers = 78/3 = 26
Finding an Unit Cost by Division
An unit cost of an item is the total cost for a total number of items divided by the number of items.
EXAMPLE
A fruit vendor displays the price for a bunch of 5 apples as $3.00. What is the unit cost?
Here the unit cost is the price each apple.
If the price for 5 apples is $3.00, then the price for each apple is
3005= 0.60 or 60 cents.
Therefore, the unit cost is 60 cents.
Simplification of Fractions by Division
A fraction is always expressed by reducing it to the lowest possible terms by dividing both the numerator and the denominator by a factor that is common to both.
EXAMPLE
Simplify 18/24
The greatest common factor to both 18 and 24 is 6
18 ÷ 6 = 3 and 24 ÷ 6 = 4
Therefore, 18/24 = 3/4
Finding a Rate by Division
Rate is the measure of a quantity for an unit measure of another quantity when the two quantities are of different units.
EXAMPLE
A car runs 40 miles with a gas of 2 gallons. What is the rate?
Here the rate is the number of miles the car could run for 1 gallon. ( This rate is defined as the mileage)
If the car runs 40 miles for 2 gallons, the number of miles it could run for
1 gallon = 40/2 = 20
Therefore, the rate is 20 gallons per mile.
Finding a Percentage by Division
A percentage can be worked out by dividing one quantity with other and multiplying the fraction with 100.
EXAMPLE
There are 16 girls 40 students in a class. What is the percentage of girl students in the class?
The percentage of girl students in the class = (16/40) x 100 = 40.
So, 40% of the students in the class are girls.
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