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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.
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,
Number | Reciprocal | Number katex is not defined Reciprocal |
---|---|---|
katex is not defined | ![]() 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 | ![]() 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 | ![]() 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 | ![]() 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.
Do you see a pattern?
katex is not defined katex is not definedNot yet? Do you see a pattern now?
katex is not defined katex is not definedYou 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.
How does this apply to 6th grade math?
In order to write the reciprocal of a number:
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DOWNLOAD FREEFind the reciprocal of katex is not defined
2“Flip” the fraction by switching the numerator and denominator.
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 definedThe reciprocal of katex is not defined is katex is not defined
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.
katex is not defined is already a fraction.
“Flip” the fraction by switching the numerator and denominator.
katex is not defined becomes the denominator and katex is not defined becomes the numerator.
Check to make sure the product is katex is not defined.
The reciprocal of katex is not defined is katex is not defined
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.
katex is not defined as an improper fraction is katex is not defined
“Flip” the fraction by switching the numerator and denominator.
katex is not defined becomes the denominator and katex is not defined becomes the numerator.
Check to make sure the product is katex is not defined.
The reciprocal of katex is not defined which is katex is not defined is katex is not defined
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.
katex is not defined is three tenths which is katex is not defined
“Flip” the fraction by switching the numerator and denominator.
katex is not defined becomes the denominator and katex is not defined becomes the numerator.
Check to make sure the product is katex is not defined.
The reciprocal of katex is not defined which is katex is not defined is katex is not defined
katex is not defined
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.
katex is not defined is one and seven tenths which is katex is not defined
katex is not defined as an improper fraction is katex is not defined
“Flip” the fraction by switching the numerator and denominator.
katex is not defined becomes the denominator and katex is not defined becomes the numerator.
Check to make sure the product is katex is not defined.
The reciprocal of katex is not defined is katex is not defined
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.
katex is not defined as an improper fraction is katex is not defined
“Flip” the fraction by switching the numerator and denominator.
katex is not defined becomes the denominator and katex is not defined becomes the numerator.
The reciprocal is a negative number like the original number.
Check to make sure the product is katex is not defined.
The reciprocal of katex is not defined is katex is not defined
1. Find the reciprocal of katex is not defined
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 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 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
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
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
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
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
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.
Finding the reciprocal of a number is flipping the numerator and the denominator so it can be seen as turning the fraction upside down.
The inverse of a number is the reciprocal.
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