What is a Quotient in Mathematics?

What is a Quotient

Nowadays, the four basic mathematical operations should be known by every person in the world. Typically, kids begin learning them in first grade. By the time they finish high school, they are expected to have a firm understanding of certain core mathematics concepts. Moreover, classes like Algebra II, Calculus, and Statistics are amongst those completed courses. 

Further, according to the Oxford Advanced Dictionary, the definition of mathematics is the following: 

the science of numbers and shapes. Branches of mathematics include arithmetic, algebra, geometry, and trigonometry.

Oxford Advanced Dictionary

Even though mathematics has many branches, in the core lie the four most basic mathematical operations, which are addition, subtraction, multiplication, and division. It is only natural then that we can effortlessly do the four basic mathematical operations.

Definition of Quotient 

Typically, functions often come as quotients. Moreover, the quotient is the number resulting from the division of one number by another. Or, in other cases, one function is divided by another function. 

For instance, the quotient of 24 divided by 2 is 12. 

Let’s take a look at the following example. 

quotient formula

Moreover, to differentiate a quotient, we can use the quotient rule. 

The Quotient Rule in Calculus 

In short, the quotient rule is a method of finding the derivative of a function. Moreover, the function is the ratio of two differentiable functions. 

Quotient in Mathematics

Moreover, the derivatives of these two functions are as following:

Quotient in Mathematics formula

Further, we have to substitute these results into the given formula.

Quotient in Mathematics formula 2

As you can notice, there are a minus sign and an x in both terms of the numerator. In other words, we can take out a common factor of – x. 

Quotient formula

Lastly, we must cancel the factor of x in the numerator and the denominator. Once we have done that, we will have found the required derivative. 

Here’s Another Example 

Typically, if two functions f (x) andg (x) are differentiable, then the quotient is differentiable.

Quotient example

Following the quotient rule, the derivative of f (x) should be:

Quotient alternative

The First IQ Test 

Now, this is interesting. Did you know that the first intelligence test was developed 116 years ago? In 1904, the French Ministry of Education hired researchers to develop what is now known as the first IQ test. Moreover, the Ministry wanted to distinguish mentally disabled children from intelligent ones. 

Alfred Binet (1857-1911) was a pioneer in various areas of pedagogical and cognitive psychology. Moreover, some of these areas include memory, expertise, movements, suggestibility, visual illusions. On the other hand, Theodore Simon (1873-1961) was a French psychologist who helped Alfred Binet to develop the Binet-Simon scale. 

When it comes to measuring intelligence, the Binet-Simon scale is one of the most widely used scales on the planet. Not only does the test consist of several components including logical reasoning, finding rhyming words, and naming objects, but it also uses the child’s age in determining whether the child is ahead of or lagging other children. 

Also, the formula for this IQ test is not so complicated.

iq test formula

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