What is the reciprocal of 1.25? Give your answer as a fraction in its simplest form.
There are a couple of ways to approach this problem. If we firstly look at the definition of the reciprocal, this states that the reciprocal of a number is one divided by the number. This means that, in our case, the reciprocal of 1.25 is one divided by 1.25.
As our denominator is a decimal, we need to find an equivalent fraction where the numerator and denominator are both integers or whole numbers. Remember that, with fractions, whatever you do to the top you must do to the bottom. In this case, we’re going to multiply the numerator by four and the denominator by four. One multiplied by four is equal to four, and 1.25 multiplied by four is equal to five. Therefore, our fraction could be rewritten as four-fifths or four over five. The reciprocal of 1.25 is four-fifths.
An alternative method would be to rewrite 1.25 as a fraction. Well, 0.25 is the same as a quarter. Therefore, 1.25 is equal to one and a quarter. In the diagrams, we’ve shaded one and a quarter. This is the same as five-quarters. 1.25 is equal to five-quarters or five over four. In order to work out the reciprocal of this fraction, five-quarters, we flip the fraction upside down. In this case, five-quarters flipped upside down is four-fifths. So the reciprocal of 1.25 using this method is also four-fifths.