Question

Find the reciprocal of\[ - 1.25\].

Answer 1

Hint:To find the reciprocal of the fraction, we invert the fraction. This means that we place the numerator in the denominator and the denominator in the numerator. To get a positive result when multiplying two numbers, the numbers must have the same sign. So, reciprocals must have the same sign.

Complete step by step solution:
Reciprocal basically means reverse of a fraction.

According to the question, we need to find the reciprocal of \[ - 1.25\]which is in the form of decimal.

Hence, dividing the number by 1 will give the same number. So, on dividing the number by 1 we have,

\[\dfrac{{ - 1.25}}{1}\]

Now, to find the reciprocal we need to invert the fraction. Fraction can be inverted by changing the numerator into denominator and vice versa.

Inverting the numerator and denominator we have,
\[\dfrac{1}{{ - 1.25}}\]

Now, multiplying the numerator and denominator by 100 we have,
\[
\Rightarrow \dfrac{{100}}{{ - 125}} \\
\Rightarrow \dfrac{4}{{ - 5}} \\
\]
On simplifying it to the lowest form we have\[\dfrac{4}{{ - 5}} = - 0.8\].

Hence, the reciprocal of \[ - 1.25\]is\[ - 0.8\].

Note: A fraction is divided by reciprocal of itself. It is then multiplied by the original fraction. Whenever we need to find a reciprocal of any number then it has to be inverted. If the number is a fraction then the numerator and denominator can be inverted. If the number is not in a form of fraction then the numbers can be divided by 1 and then it can be inverted. To get an appropriate answer it is important to convert it into the simplest or lowest form which will give a simplified form of answer.