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When you want to divide a number into equal parts, you can use the division formula. The symbols (÷) and (/) are used to denote division in mathematics. As a result, the expression “p divided by q” can be written as (p÷q) or (p/q).
The division formula is the formula for dividing, which is one of the four basic operations of arithmetic and is also known as the division rule. The division formula is used to divide a large number into many equal parts in an equal amount of time. For a given value, the division formula can be expressed as follows:
Dividend / Divisor = Quotient
Where,
- The dividend is the number that is to be divided.
- The divisor is the number that is to be divided by two or more.
- The outcome is represented by the quotient.
Division Formula for Verification
Let’s look at how we can check our division answer while using the division formula to see if it is correct. For example, 8 divided by 2 equals 4, and the remainder equals 0. To put it another way, 8=2×4+0. The following is an expression for this method of verification:
Dividend = (Divisor x Quotient) + Remainder
Example
Question 1: A total of 200 chocolates were distributed in an equal distribution among 40 children. What was the total number of chocolates given to each child? This can be calculated by applying the division formula.
Solution: The number of chocolates that were distributed to each child.
The following information is provided: total number of chocolates = 200.
The total number of children is 40.
To calculate chocolates given to each child, divide (total chocolates / total children) by 40 to arrive at a total of 5 chocolates given to each child.
Each child received a box of chocolates worth five dollars.
Question 2: Liza is the mother of four puppies. He purchased 36 chewable bones in order to feed them all equally. How many bones will be given to each puppy?
Solution: Liza currently has a total of four puppies.
The number of bones in the body is 36.
The number of bones required for each puppy is 36/4=9.
Nine bones will be given to each puppy.
Quotient Rule
It is possible to find the derivative or differentiation of an arbitrary function given as a ratio or division of two differentiable functions using the Quotient rule in calculus. That is, when we need to find the derivative of a function of the form: f(x)/g(x), we can use the quotient rule as long as both f(x) and g(x) are differentiable and g(x) is less than zero. In differentiation, the quotient rule is directly related to the product rule and the concept of limits of derivation in differentiation.
In calculus, the quotient rule is a method for determining the derivative of any function given in the form of a quotient produced from the result of the division of two differentiable functions. Simply put, the quotient rule states that, when you subtract the numerator from the denominator, you get a result that is equal to the ratio of the result obtained by subtracting the numerator times the derivative of the denominator from its denominator times the derivative of the numerator to its square denominator.
Quotient Rule Formula
The derivative formula for the quotient rule can be used to calculate the derivative or evaluate the differentiation of the quotient of two functions, respectively. The following is the derivative formula for the quotient rule:
f'(x) = [u(x)/v(x)]’ = [u'(x)/v(x) – u(x)v'(x)] / [v(x)]2
where,
- If f(x) is a function of the form u(x)/v(x), then the derivative of that function is to be calculated.
- In this case, u(x) is a differentiable function that is used to compute the numerator of the function f(x).
- A function u'(x) is a derivation of the function u(x).
- In this case, v(x) is a differentiable function that is used to compute the denominator of the given function f(x).
- A function v'(x) is a derivative of the function v (x).
Conclusion
The division is one of the most important arithmetic operations, ranking second only to addition and subtraction (i.e., Addition, subtraction, multiplication, division). The division operation is used to divide a large number into smaller numbers that are equal in size.
When you want to divide a number into equal parts, you can use the division formula. The symbols (÷) and (/) are used to denote division in mathematics. The division formula is the formula for dividing, which is one of the four basic operations of arithmetic and is also known as the division rule.
Dividend / Divisor = Quotient
The dividend is the number that is to be divided. The divisor is the number that is to be divided by two or more. The outcome is represented by the quotient.
It is possible to find the derivative or differentiation of an arbitrary function given as a ratio or division of two differentiable functions using the Quotient rule in calculus. In differentiation, the quotient rule is directly related to the product rule and the concept of limits of derivation in differentiation.
