Question

What number should \[-\dfrac{33}{16}\] be divided by to get \[-\dfrac{11}{4}\]?

Answer 1

Hint: To solve this question we should have the knowledge of solving Linear equations in one variable. We should have good command of the basics of mathematics i.e. addition, subtraction, multiplication, division, etc. We should know how to convert a word problem in the form of linear equations into one variable. Conversion of the problem statement in mathematical form can help us in solving the question accurately.

Complete step-by-step solution:
This question requires the knowledge of solving linear equations in one variable. We should know about variables. Good practice of basic mathematics operations is required. We should know how to apply mathematical operations on all the types of real numbers. The main mathematical operation which this question requires is division. Let us discuss the above concepts one by one.
Division of numbers: Division is one of the basic arithmetic operations in mathematics. For division two numbers are required. In division numerator is divided by denominator. The two numbers behave as numerator and denominator as per the given condition. In simple words division is the number of parts in which the denominator divides the numerator.
For e.g. Perform \[12\] divided by \[3\].
Here, \[12\] is the numerator and \[3\] is the denominator.
\[division=\dfrac{numerator}{deno\min ator}\]
\[\begin{align}
  & \Rightarrow division=\dfrac{12}{3} \\
 & \Rightarrow division=4 \\
\end{align}\]
Linear equations in one variable: The equations consisting of only one variable with index (highest power) \[1\] are known as linear equations in one variable. There is only one variable present in these types of equations. To solve linear equations in one variable we should know basic mathematical rules and operations.
For e.g. \[x-1=0\] is a linear equation in one variable.
By solving we get,
\[x=1\] is the solution of the above linear equation in one variable .
After knowing all the required concepts let us now solve the given question.
We have been given a number \[-\dfrac{33}{16}\]
We have to find that what number should be divided by the given number to get\[-\dfrac{11}{4}\]
From applying the above concepts we can convert the given problem statement into a linear equation in one variable.
Let, \[x\] be the number that we have to find.
Hence, the linear equation in one variable is given by,
\[\dfrac{-\dfrac{33}{16}}{x}=\dfrac{-11}{4}\]
\[\begin{align}
  & \Rightarrow x=\dfrac{-\dfrac{33}{16}}{-\dfrac{11}{4}} \\
 & \Rightarrow x=-\dfrac{33}{16}\times \left( -\dfrac{4}{11} \right) \\
 & \Rightarrow x=\dfrac{3}{4} \\
\end{align}\]
From this we can conclude that the number needed to be divided by \[-\dfrac{33}{16}\] to get \[-\dfrac{11}{4}\] is \[\dfrac{3}{4}\].

Note: This question was simply based on basic mathematics. The concept of linear equations in one variable is the best way to convert these types of problem statements. Even the knowledge of simple division is enough to solve these types of questions. These types of questions are quickly and easily solvable. We can also check the correctness of answers by reverse process i.e. by performing multiplication.