Question

Express $ \dfrac{{15}}{4} + \dfrac{5}{{40}} $ as a decimal without actually dividing ?

Answer 1

Hint: Here in this question, we have + symbol which represents the addition and we have to add the two numbers. The numbers are in the form of fraction. We are going to simplify the sum of two fractions by taking the LCM of the denominators of the fractions such that the value of both the fractions remains unchanged and then add them up. Then, we will represent the sum as a decimal representation.

Complete step-by-step answer:
Here in this question, we have to express the sum of two fractions as a decimal.
As we know, the $ + $ sign indicates the addition. The numbers are in the form of fraction. In fraction we have 3 types: proper fraction, improper fraction and mixed fraction.
In the fraction the numerator is less than the denominator then it is a proper fraction. The numerator is greater than the denominator then it is an improper fraction. The fraction is a combination of the whole number and fraction then it is mixed fraction.
Here in this question both numbers are a proper fraction.
So, we have, $ \dfrac{{15}}{4} + \dfrac{5}{{40}} $
The values of the denominator are not the same so we take LCM for the denominator.
Taking L.C.M. of denominators, we get,
 $ \Rightarrow \dfrac{{15}}{4} + \dfrac{5}{{40}} = \dfrac{{\left( {15 \times 10} \right) + \left( {5 \times 1} \right)}}{{40}} $
Simplifying further, we get,
 $ \Rightarrow \dfrac{{15}}{4} + \dfrac{5}{{40}} = \dfrac{{150 + 5}}{{40}} $
 $ \Rightarrow \dfrac{{15}}{4} + \dfrac{5}{{40}} = \dfrac{{155}}{{40}} $
Now, we know that it is easy to divide a number by powers of ten than to divide by any other number. We also know that we can manipulate the denominator of the fraction to be $ 100 $ . So, we find the equivalent fraction for $ \dfrac{{155}}{{40}} $ with $ 100 $ as denominator by multiplying both numerator and denominator by $ 2.5 $ .
So, we get, \[\dfrac{{155}}{{40}} \times \dfrac{{2.5}}{{2.5}} = \dfrac{{387.5}}{{100}}\]
So, now we have to convert the fraction $ \dfrac{{387.5}}{{100}} $ into decimal form. So, we know that to divide a number by a power of ten, we just have to place a decimal point before the same number of places as there are zeroes in the power of ten.
So, $ \dfrac{{387.5}}{{100}} $ can be represented as $ 3.875 $ in decimal form.
So, the correct answer is “ $ 3.875 $ ”.

Note: While adding the two fractions we need to check the values of the denominator, if both denominators are having the same value then we can add the numerators. Suppose if the fractions have different denominators, we have to take LCM for the denominators and we simplify for further.