Finding The Reciprocal Of 2/3 – Step By Step Solution

What is the reciprocal of 2 3 ?

The reciprocal of 2 3 is 3 2 .

\text{The reciprocal of }\frac{2}{3} \text{ is }\frac{3}{2}

What Does Reciprocal Mean?

The word reciprocal in mathematics means to find a number when multiplied by the original number will make the product result equal to 1.

Therefore, for this example, solving for x looks something like this:

\frac{2}{3} \ \times \ x = 1

The above formula is showing how to represent finding the reciprocal. To solve the above equation you would do something like this to get x by itself:

\frac{2}{3} \ \times x \ &= 1 \\ \frac{2}{3} \div \frac{2}{3} \times x &= 1 \div \frac{2}{3} \\ x &= 1 \ \times \ \frac{3}{2} \\ x &= \frac{3}{2}

In the stepped solution above you can see how on the second line you divide both sides by the original reciprocal number to get x by itself.

This means on the third line that because you’re dividing by a fraction, you can flip the fraction and multiply it.

And as shown in the fourth and final line because you’re multiplying by 1 whatever the flipped fraction is will be the answer.

This is how you can find the reciprocal step-by-step.

Find Reciprocal By Flipping The Fraction

As demonstrated above, the easiest and fastest way I know to find the reciprocal of a number is to flip the original fraction.

As our original number 2 3 is already a fraction, you only need to swap the two numbers around and you’ve found the reciprocal.

Check Your Reciprocal Answer

To check your reciprocal answer, multiply it by your original number, and if the answer is 1, then you have the correct reciprocal.

Here’s how this would look:

\frac{2}{3} \ \times \ \frac{3}{2} = \frac{2 \times 3}{3 \times 2} = \frac{6}{6} = 1

As both the numerator and the denominator are the same number this fraction simplies to 1, which confirms the reciprocal number is the correct answer.

Finding Reciprocal Of 2 3 Summary

The reciprocal of a number is the number when multiplied by another produces 1.

Therefore in our working example, the reciprocal of 2 3 is 3 2 .