Reciprocals

Learning Objectives Define a reciprocal in their own words. Identify the reciprocal of a given fraction. Find the reciprocal of a whole number. Convert a mixed number to an improper fraction to find its reciprocal. Verify that the product of a number and its reciprocal is always 1. Explain the relationship between reciprocals and fraction division. Have you ever heard someone say 'flip it' when talking about fractions? 🔄 Today, we're going to learn about a special 'flip' called a reciprocal! In this lesson, you'll discover what reciprocals are, how to find them for fractions, whole numbers, and even mixed numbers. Understanding reciprocals is super important because it's a key step in dividing fractions, which you'll do a lot in math...

TermDefinitionExample ReciprocalThe reciprocal of a number is what you get when you 'flip' a fraction, swapping its numerator and denominator. When you multiply a number by its reciprocal, the answer is always 1.The reciprocal of $\frac{2}{3}$ is $\frac{3}{2}$. Multiplicative InverseAnother name for a reciprocal. It's the number that, when multiplied by the original number, gives a product of 1.$\frac{1}{5}$ is the multiplicative inverse of 5, because $5 \times \frac{1}{5} = 1$. NumeratorThe top number in a fraction, which tells you how many parts of the whole you have.In the fraction $\frac{3}{4}$, the numerator is 3. DenominatorThe bottom number in a fraction, which tells you how many equal parts the whole is divided into.In the fraction $\frac{3}{4}$, the denominator is...

The Reciprocal Product Rule $a \times \frac{1}{a} = 1$ (for any non-zero number $a$) This rule states that when you multiply any number by its reciprocal, the result is always 1. This is how you can check if you've found the correct reciprocal. Finding the Reciprocal of a Fraction If you have a fraction $\frac{a}{b}$, its reciprocal is $\frac{b}{a}$. To find the reciprocal of a fraction, simply 'flip' the fraction: the numerator becomes the new denominator, and the denominator becomes the new numerator. Finding the Reciprocal of a Whole Number If you have a whole number $n$, first write it as $\frac{n}{1}$. Then, its reciprocal is $\frac{1}{n}$. To find the reciprocal of a whole number, first express it as a fraction with 1 as the denominator. Then, fl...