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Reciprocal: Definition and Example | EDU.COM

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Reciprocal: Definition and Example | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">ReciprocalReciprocal: Definition and ExampleTable of ContentsDefinition of Reciprocal in Mathematics

A reciprocal in mathematics is defined as 1 divided by a given quantity. For any non-zero number xxx, the reciprocal is expressed as 1x\frac{1}{x}x1​, which can also be written as x−1x^{-1}x−1. The fundamental property of reciprocals is that when a number is multiplied by its reciprocal, the product equals 1 (unity). This makes reciprocals essential in division operations, particularly with fractions, as dividing by a number is equivalent to multiplying by its reciprocal.

Reciprocals can be found for various numeric forms, but cannot exist for zero since division by zero is undefined. For natural numbers, the reciprocal is simply 1 divided by that number. For negative numbers, the reciprocal maintains the negative sign, resulting in −1x-\frac{1}{x}−x1​ for a number −x-x−x. For fractions, finding the reciprocal involves interchanging the numerator and denominator, while for mixed fractions and decimals, conversion to improper fractions precedes the interchange.

Examples of Reciprocals in Mathematics Example 1: Finding the Reciprocal of a Whole Number Problem:

What is the reciprocal of 7?

Step-by-step solution: Step 1, recall that the reciprocal of any number xxx is 1x\frac{1}{x}x1​. Step 2, substitute 7 for xxx in the formula: Reciprocal of 7=177 = \frac{1}{7}7=71​ Step 3, therefore, the reciprocal of 7 is 17\frac{1}{7}71​. Example 2: Finding the Reciprocal of a Fraction Problem:

What is the reciprocal of 67\frac{6}{7}76​? Verify your answer.

Step-by-step solution: Step 1, remember that to find the reciprocal of a fraction, we interchange the numerator and denominator. Step 2, we swap the positions of 6 and 7: Reciprocal of 67=76\frac{6}{7} = \frac{7}{6}76​=67​ Step 3, to verify, we multiply the original fraction by its reciprocal: 67×76=6×77×6=4242=1\frac{6}{7} \times \frac{7}{6} = \frac{6 \times 7}{7 \times 6} = \frac{42}{42} = 176​×67​=7×66×7​=4242​=1 Step 4, therefore, the reciprocal of 67\frac{6}{7}76​ is 76\frac{7}{6}67​, and our answer is verified because their product equals 1. Example 3: Pizza Problem with Reciprocals Problem:

A pizza is sliced into 8 pieces. Tom eats 3 slices of the pizza and leaves the rest. Determine the reciprocal of the quantity of the pizza left by Tom.

Step-by-step solution: Step 1, find the number of slices left: Total slices =8= 8=8 Slices Tom ate =3= 3=3 Slices remaining =8−3=5= 8 - 3 = 5=8−3=5 Step 2, express the remaining pizza as a fraction of the whole: Fraction of pizza left =58= \frac{5}{8}=85​ Step 3, find the reciprocal by interchanging the numerator and denominator: Reciprocal of 58\frac{5}{8}85​ = 85\frac{8}{5}58​ Step 4, therefore, the reciprocal of the quantity of pizza left by Tom is 85\frac{8}{5}58​ or 1351\frac{3}{5}153​. Comments(9)PPetLoverGigiNovember 6, 2025This glossary def of reciprocal is great! I've used it to help my students grasp the concept. It's clear and the examples are super useful.

DDJGinaNovember 4, 2025I've used this reciprocal definition with my students. It's clear and really helped them grasp the concept. Great resource!

FFlutistQuinnNovember 4, 2025This glossary page on reciprocals is great! It's helped my students grasp the concept easily. Clear defs and examples are a huge plus.

MCMs. CarterSeptember 17, 2025I’ve used the Reciprocal definition and examples from this page to help my kids with their homework. The step-by-step solutions made it so easy to explain fractions and real-world uses!

MCMs. CarterSeptember 10, 2025I’ve used the reciprocal examples from this page to help my kids understand fractions better. The step-by-step solutions make it so much easier to explain. Great resource for parents and teachers!

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