Reciprocal math

Here you will learn about reciprocals, including the definition of reciprocal and how to find reciprocals.

Students will first learn about reciprocals in 6th grade math as part of their work in number and operations with fractions when they learn how to divide fractions and extend their knowledge as they work through number systems in middle school.

What is a reciprocal?

The reciprocal of a number is one over that number. When the reciprocal is multiplied by the original number, the product is katex is not defined Reciprocals are also called the multiplicative inverse.

For example,

NumberReciprocalNumber katex is not defined Reciprocal
katex is not defined
Reciprocal table image 1

The numerator of the original
number, katex is not defined becomes the
denominator. The denominator
of the original number , katex is not defined
becomes the numerator.

Reciprocal: katex is not defined

katex is not defined
katex is not defined
Reciprocal table image 2

The numerator of the original
number, katex is not defined becomes the
denominator. The denominator
of the original number , katex is not defined
becomes the numerator.

Reciprocal: katex is not defined

katex is not defined
katex is not defined
Reciprocal table image 3

The numerator of the original
number, katex is not defined becomes the
denominator. The denominator
of the original number , katex is not defined
becomes the numerator.

Reciprocal: katex is not defined or katex is not defined

katex is not defined
katex is not defined
Reciprocal table image 4

The numerator of the original
number, katex is not defined becomes the
denominator. The denominator
of the original number , katex is not defined
becomes the numerator.

Reciprocal: katex is not defined

katex is not defined

To help make sense of a reciprocal, let’s look at visual models.

US reciprocal math image 1

Do you see a pattern?

katex is not defined

katex is not defined

Not yet? Do you see a pattern now?

katex is not defined

katex is not defined

You can think of a reciprocal as writing the number as a fraction and then flipping it so that the numerator becomes the denominator and the denominator becomes the numerator. The numbers are turned upside down.

What is a reciprocal?

What is a reciprocal?

Common Core State Standards

How does this apply to 6th grade math?

  • Grade 6: Number System (6.NS.A.1)
    Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, for example, by using visual fraction models and equations to represent the problem.

How to write the reciprocal of a number

In order to write the reciprocal of a number:

  1. If the number is a whole number, mixed number, or decimal, write it as an improper fraction.
  2. “Flip” the fraction by switching the numerator and denominator.
  3. Check to make sure the product is katex is not defined.

[FREE] Fraction Operations Check for Understanding Quiz (Grade 4 to 6)

[FREE] Fraction Operations Check for Understanding Quiz (Grade 4 to 6)

[FREE] Fraction Operations Check for Understanding Quiz (Grade 4 to 6)

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[FREE] Fraction Operations Check for Understanding Quiz (Grade 4 to 6)

[FREE] Fraction Operations Check for Understanding Quiz (Grade 4 to 6)

[FREE] Fraction Operations Check for Understanding Quiz (Grade 4 to 6)

Use this quiz to check your grade 4 to 6 students’ understanding of fraction operations. 10+ questions with answers covering a range of 4th to 6th grade fraction operations topics to identify areas of strength and support!

DOWNLOAD FREE

Reciprocal maths examples

Example 1: reciprocal of a whole number

Find the reciprocal of katex is not defined

  1. If the number is a whole number, mixed number, or decimal, write it as an improper fraction.

katex is not defined

2“Flip” the fraction by switching the numerator and denominator.

US reciprocal math example 1

katex is not defined becomes the denominator and katex is not defined becomes the numerator.

3Check to make sure the product is katex is not defined.

katex is not defined

The reciprocal of katex is not defined is katex is not defined

Example 2: reciprocal of a fraction number

Find the reciprocal of katex is not defined

If the number is a whole number, mixed number, or decimal, write it as an improper fraction.

“Flip” the fraction by switching the numerator and denominator.

Check to make sure the product is katex is not defined.

Example 3: reciprocal of a mixed number

Find the reciprocal of katex is not defined

If the number is a whole number, mixed number, or decimal, write it as an improper fraction.

“Flip” the fraction by switching the numerator and denominator.

Check to make sure the product is katex is not defined.

Example 4: reciprocal of a decimal number

Find the reciprocal of katex is not defined

If the number is a whole number, mixed number, or decimal, write it as an improper fraction.

“Flip” the fraction by switching the numerator and denominator.

Check to make sure the product is katex is not defined.

Example 5: reciprocal of a decimal greater than 1

Find the reciprocal of katex is not defined

If the number is a whole number, mixed number, or decimal, write it as an improper fraction.

“Flip” the fraction by switching the numerator and denominator.

Check to make sure the product is katex is not defined.

Example 6: reciprocal of a negative number

Find the reciprocal of katex is not defined

If the number is a whole number, mixed number, or decimal, write it as an improper fraction.

“Flip” the fraction by switching the numerator and denominator.

Check to make sure the product is katex is not defined.

Teaching tips for reciprocals

  • Reinforce that the reciprocal is also the multiplicative inverse.

  • Have students discover reciprocal numbers on their own by strategically asking questions such as, “what number multiplied to katex is not defined will give a product of katex is not defined?”

  • When working with reciprocals, have students see that the reciprocal of a unit fraction is a whole number.

  • Although worksheets serve a purpose in the classroom and can help with skill practice and test prep practice, having students discover the mathematical concepts is more meaningful for building long lasting understanding.

Easy mistakes to make

  • Trying to find the reciprocal of zero 
    Zero does not have a reciprocal. This is because we can think about katex is not defined as being katex is not defined When the numerator and the denominator are flipped, it becomes katex is not defined or katex is not defined which is undefined (it does not exist).

  • Forgetting that a whole number can be written as an improper fraction
    Whole numbers can be written as improper fractions. For example, katex is not defined can be written as katex is not defined

Practice reciprocal maths questions

1. Find the reciprocal of katex is not defined

katex is not defined
GCSE Quiz False

katex is not defined
GCSE Quiz False

katex is not defined
GCSE Quiz True

katex is not defined
GCSE Quiz False

Write katex is not defined as an improper fraction.

 

katex is not defined

 

Flip the numerator and the denominator.

 

katex is not defined becomes the denominator and katex is not defined becomes the numerator.

 

The reciprocal of katex is not defined is katex is not defined

2. Find the reciprocal of katex is not defined

katex is not defined
GCSE Quiz False

katex is not defined
GCSE Quiz True

katex is not defined
GCSE Quiz False

katex is not defined
GCSE Quiz False

katex is not defined is already a fraction.

 

Flip the numerator and the denominator.

 

katex is not defined becomes the denominator and katex is not defined becomes the numerator.

 

The reciprocal of katex is not defined is katex is not defined

3. Find the reciprocal of katex is not defined

katex is not defined
GCSE Quiz False

katex is not defined
GCSE Quiz False

katex is not defined
GCSE Quiz False

katex is not defined
GCSE Quiz True

katex is not defined is already in fraction form.

 

Flip the numerator and the denominator.

 

katex is not defined becomes the denominator and katex is not defined becomes the numerator.

 

The reciprocal of katex is not defined is katex is not defined

4. Find the reciprocal of katex is not defined

katex is not defined
GCSE Quiz False

katex is not defined
GCSE Quiz False

katex is not defined
GCSE Quiz True

katex is not defined
GCSE Quiz False

Change katex is not defined to an improper fraction.

 

katex is not defined is katex is not defined

 

Flip the numerator and the denominator.

 

katex is not defined becomes the denominator and katex is not defined becomes the numerator.

 

The reciprocal of katex is not defined is katex is not defined

5. Find the reciprocal of katex is not defined

katex is not defined
GCSE Quiz False

katex is not defined
GCSE Quiz True

katex is not defined
GCSE Quiz False

katex is not defined
GCSE Quiz False

Change katex is not defined to a fraction.

 

katex is not defined

 

Flip the numerator and the denominator.

 

katex is not defined becomes the denominator and katex is not defined becomes the numerator.

 

The reciprocal of katex is not defined is katex is not defined

6. Find the reciprocal of katex is not defined

katex is not defined
GCSE Quiz True

katex is not defined
GCSE Quiz False

katex is not defined
GCSE Quiz False

katex is not defined
GCSE Quiz False

Change katex is not defined to an improper fraction.

 

katex is not defined

 

Flip the numerator and the denominator.

 

katex is not defined becomes the denominator and katex is not defined becomes the numerator.

 

The reciprocal of katex is not defined is katex is not defined

Reciprocals FAQs

Can you find the reciprocal of any real number?

Rational numbers and irrational numbers have reciprocals. The only number that does not have a reciprocal is katex is not defined We can use the formal definition of reciprocals to prove that all numbers have a reciprocal.

By definition, the reciprocal of a number is katex is not defined divided by that number. The product of a number and its reciprocal is katex is not defined

For example, the reciprocal of katex is not defined can be written as katex is not defined or katex is not defined

katex is not defined is an irrational number.

The reciprocal of katex is not defined is katex is not defined or katex is not defined

katex is not defined

The reciprocal of katex is not defined is katex is not defined or katex is not defined which does not exist because you cannot divide by katex is not defined

Can you take a reciprocal of a reciprocal?

Yes, if you take a reciprocal of a reciprocal, you will wind up back at the original given number.

For example, the reciprocal of katex is not defined (written as katex is not defined) is katex is not defined

If you then take the reciprocal of katex is not defined it will be katex is not defined or katex is not defined is the original given number.

Is the reciprocal of a number just turning the fraction upside down?

Finding the reciprocal of a number is flipping the numerator and the denominator so it can be seen as turning the fraction upside down.

What is the inverse of a number?

The inverse of a number is the reciprocal. 

Still stuck?

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