Reading the pieces of Reciprocal
The reciprocal of x is 1/x. Multiplying a nonzero number by its reciprocal gives the multiplicative identity, 1.
A correct reciprocal is reliable for Reciprocal only when its setup matches the relationship.
Math calculator
Reciprocal Calculator
Find the multiplicative inverse of a nonzero number in exact-looking fraction and decimal form. The displayed reciprocal includes enough working to inspect signs and scale.
Reciprocal inputs
Numerical setup
Recognizing a Reciprocal problem
Reciprocals appear when dividing fractions, rearranging formulas, converting rates, and describing inverse variation.
Zero has no reciprocal: no finite number multiplied by zero can equal one. A very small input produces a reciprocal with very large magnitude. If the Reciprocal assumptions do not fit, consider additive inverse.
Working through Reciprocal with numbers
The reciprocal of 8 is 1/8, or 0.125. The reciprocal of −2.5 is −0.4 because the sign remains attached to the inverse.
Checking Reciprocal away from the browser
Place one over the number. For a fraction a/b, interchange numerator and denominator to obtain b/a, retaining the sign.
Reciprocals in rates and units
Units invert with the number. The reciprocal of 5 kilometers per hour is one fifth of an hour per kilometer, which answers a pace question rather than a speed question. Carrying the unit through the inversion prevents those interpretations from being confused.
A second way to verify Reciprocal
Substitute the Reciprocal solution into Nonzero number. This Reciprocal check rejects false Reciprocal branches and forbidden denominators.
Choose an easy Nonzero number value before running Reciprocal. Predict the result, then compare it with the Reciprocal output.
Use Nonzero number as the first Reciprocal checkpoint. Confirm the fixed condition, then anticipate Reciprocal. Repeat Reciprocal without reading the prior answer. If the fixed condition differs, preserve both Reciprocal versions and both values of Reciprocal.
A hand-worked reference for Reciprocal need not duplicate the original numbers. Select an uncomplicated Nonzero number, retain the fixed condition, and estimate Reciprocal. The reference gives the original Reciprocal answer a meaningful scale check.
Validating Reciprocal
Compare the noun in the Reciprocal question with the label Reciprocal. Recheck Nonzero number and the fixed condition if they differ. Correct arithmetic can still produce a related quantity instead of the intended Reciprocal output.
Questions about Reciprocal
Is reciprocal the same as opposite?
No. A reciprocal multiplies to 1; an opposite adds to 0.
What is the reciprocal of 1?
It is 1.
Does a negative number have a negative reciprocal?
Yes.
Why is zero rejected?
Division by zero is undefined.