Question

How do you solve $ \dfrac{a}{{40}} = \dfrac{3}{{10}} $ ?

Answer 1

Hint: This question is from the rational numbers chapter. Here we need to find the value $ a $ so that it becomes equal to $ \dfrac{3}{{10}} $ .To solve for $ a $ we will use the technique of cross multiplication and isolate $ a $ to find its value. In this we have to perform multiplication and division operation to get the value of $ a $ .

Complete step-by-step answer:
Let us try to solve this question. In this question we need to solve for the value of $ a $ we get a rational number which is equivalent to $ \dfrac{3}{{10}} $ . Here is the definition of rational number for revision, rational numbers are those numbers which can be written in the form $ \dfrac{p}{q} $ such that $ q > 0 $ and where $ p,q $ are natural numbers. To solve for $ a $ we will first do cross multiplication.
We have,
$ \dfrac{a}{{40}} = \dfrac{3}{{10}} $
In cross multiplication we will multiply $ 3 $ with $ 40 $ and $ a $ with $ 10 $ , we get
 $ 10a = 120 $ ---------$ eq(1) $
Now dividing both sides of the equation by $ 10 $ in $ eq(1) $ , we get the value of $ a $ .
 $
  \dfrac{{10a}}{{10}} = \dfrac{{120}}{{10}} \\
  a = 12 \;
  $
Value of $ a $ is $ 12 $ .
 Now let us check if we get the value of $ a $ correct or not. To check the correctness of our value of $ a $ , we will put it in the equation.
So, putting $ a $ $ = 12 $ , we get
 $
  \dfrac{{12}}{{40}} = \dfrac{3}{{10}} \\
  \dfrac{3}{{10}} = \dfrac{3}{{10}} \;
  $
Since L.H.S=R.H.S. So the value of $ a $ is correct. $ $
So, the correct answer is “a = 12”.

Note: In a question in which we have to solve for the value of $ a $ , so given rational numbers become equivalent (equal). We have to perform cross multiplication and isolate the variable whose value we have to find. Interesting fact, a rational number has infinitely many equivalent rational numbers and all integers are rational numbers.