A reciprocal can be very easy to work out, as all you need to do is to divide the number you are finding the reciprocal of into 1. Just use the formula:
Reciprocal = 1 ÷ your number
Let’s take a look at some examples. It will be easier to leave your answers as fractions in most cases rather than decimals.
Find the reciprocal of 7.
So all you need to do is divide this number into 1.
1÷7 = 1/7 (or 0.143 to 3sf)
Find the reciprocal of 12.
1÷12 = 1/12 (or 0.083)
Find the reciprocal of 2/3
1 ÷ 2/3 = 3/2 (or 1.5)
Notice when you find the reciprocal of a fraction, the fraction gets turned around (inverted). That is, the numerator becomes the denominator, and the denominator becomes the numerator. This is the effect of dividing a number into 1! Check out my dividing fraction page if you need more help on this.
Find the reciprocal of 8/7.
1 ÷ 8/7 = 7/8 (or 0.875)
Again, just invert the fraction.
Find the reciprocal of 0.6.
1 ÷ 0.6 = 1.6r
In this last example it might be easier to change 0.6 to a fraction first (this is 6/10 or 3/5).
So 1 ÷ 3/5 = 5/3
Find the reciprocal of -4
1 ÷ -4 = -1/4 (or -0.25)
To summarise what a reciprocal is, all you need to do is divide the number into 1. It sounds a lot harder than what it actually is. It’s much easier to work with fractions when taking reciprocals, as you are less likely that you will need to use a calculator.
Reciprocals can be useful when integrating, or when finding the gradient of a perpendicular line.