What does "multiply by the reciprocal" mean?

"Multiplying by the reciprocal" refers to a mathematical process that can be used to divide fractions or mixed numbers. The reciprocal of a number is another number that, when multiplied with the original number, gives a product of 1. Put simply, the reciprocal of a fraction is created by flipping the numerator (the top number) and the denominator (the bottom number). For example, the reciprocal of 3/4 is 4/3.

When you are asked to divide by a fraction, you can instead multiply by the reciprocal of that fraction. This process makes fraction division more straightforward. Here's how to do it step by step:

1. Determine the reciprocal of the divisor (the fraction you are dividing by). If the divisor is a/b, its reciprocal is b/a. 2. Multiply the dividend (the number or fraction you are starting with) by the reciprocal of the divisor. 3. Simplify the result if necessary by reducing the fraction to its lowest terms or by performing any required multiplication.

Let's look at an example: Suppose you want to divide 5 by 1/2. Instead of dividing by 1/2, you would multiply 5 by the reciprocal of 1/2. The reciprocal of 1/2 is 2/1, which is simply 2. So, the operation becomes 5 × 2, which equals 10.