# Creating Reciprocals Worksheets

As we move on to working with fractional values, compound algebraic equations, proportions, and perpendicular lines the concept of reciprocal values becomes extremely helpful to make sense of these things mathematically. In most cases to generate these values, we simply place whole number under 1. In affect we are dividing 1 by our starting value. If we remember back to our definition of a whole number, it is that value over one. As a result, we are just flipping those numbers. The numerator replaces the denominator, and the denominator replaces the numerator. When we are working with fractions, we do the same thing. These worksheets and lessons will help students under what a reciprocal is and how to create them.

### Aligned Standard: 7.NS.A.2a

- Writing Reciprocals Step-by-Step Lesson- Start with an easy fraction and then we give you a mixed number.
- Guided Lesson - See if you can expand all the choices here into mix numbers or whole numbers after determining the reciprocal.
- Guided Lesson Explanation - See if you like the way I wrote the standard explanation. I think it works well.
- Practice Worksheet - This is definitely different, somewhat of an outcast from the other printables here.
- Matching Worksheet - You might need to reduce the fractions in a few areas to determine the final outcome here.

- Answer Keys - These are for all the unlocked materials above.

### Homework Sheets

It sure does start off easy. Then we introduce students to reciprocals of mixed numbers.

- Homework 1 - A reciprocal of a fraction is just when the numerator and denominator switch places.
- Homework 2 - We would just flip the numerator and denominator.
- Homework 3 - See how to set these up.

### Practice Worksheets

By the time students complete these, reciprocals are an automatic skill.

- Practice 1 - A great starter to get you going.
- Practice 2 - Rewrite the mixed number as an improper fraction.
- Practice 3 - Write the reciprocal of the following mixed number.

### Math Skill Quizzes

The first one is simple fractions. Mixed numbers are in numbers two and three.

- Quiz 1 - Write the reciprocal for the following fractions.
- Quiz 2 - Mixed numbers work.
- Quiz 3 - A mix of both skills.

### How Do You Create a Reciprocals?

Have you ever come across reciprocals? If you haven't, let us tell you that reciprocals are the most interesting part of mathematics. In its true essence, reciprocal of a number is when we divide 1 by a value of interest. For example, the reciprocal of the number 8 is 1/8.

If you want to understand reciprocals and know the trick of creating them, let's find out how you can create reciprocals. Follow the instructions to create reciprocals:

To create a reciprocal, simply divide 1 by the given number. If the number is not a whole number and is a fraction, you can create one by flipping the number. This means to switch the positions of the numerator (top number) and denominator (bottom number). What ever value is on top, goes to the bottom. The bottom value goes on top, hence the term flip. For example, the fraction is 2/3; it's reciprocal would be 3/2. The reciprocal of a variable x / (x-1) would be x^{-1/x}; it is simply the upside-down of the variable.

Another form of reciprocal is called flipping a flip; in this form, you create a reciprocal and get the answer, then create the reciprocal of the answer and get it back in its original form. This is called flipping a flip. A reciprocal in its simplest form is also notation. The reciprocal of x is 1/x or x - 1. This is the reciprocal as well as notation of x.

This skill will become very handy when you begin to work with fraction operations. Specifically, when you begin to divide one fraction by another. The only number we cannot do this to is 0. That is because 1/0 is classified as undefined. You may also use this skill in algebra to cross out values in an equation. This is because when you multiply a value by its reciprocal you also get 1. For example, 2,345 x 1/2,345 = 1. Another name for this is the multiplicative inverse.