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Choose between integer, fraction, or mixed number, enter the respective values in the calculator, and calculate the reciprocal in seconds.
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Use our reciprocal calculator to quickly find the reciprocal (multiplicative inverse) of integers, decimals, simple fractions, and mixed fractions. The tool provides step-by-step solutions for easy understanding.
Here’s the process to determine the reciprocal of different types of numbers:
Step 1: Represent the number as a fraction with denominator 1.
Step 2: Swap numerator and denominator.
Example: Find the reciprocal of 24.75
\(\dfrac{24.75}{1} \rightarrow \dfrac{1}{24.75}\)
Convert the decimal to a fraction:
\(\dfrac{1 \times 100}{24.75 \times 100} = \dfrac{100}{2475} = \dfrac{4}{99}\)
Simply swap numerator and denominator:
\(\dfrac{20}{24} \rightarrow \dfrac{24}{20} = 1.2\)
\(\dfrac{24}{20}\) is the reciprocal of \(\dfrac{20}{24}\)
Convert the mixed fraction to an improper fraction, then swap numerator and denominator:
\(3\dfrac{4}{5} = \dfrac{19}{5} \rightarrow \dfrac{5}{19} = 0.263\)
You can compute reciprocals manually as shown, or use our reciprocal calculator for faster and accurate results.
Find the reciprocal of the mixed fraction \(3\dfrac{5}{7}\)
Solution:
Step 1: Convert to improper fraction:
\(3\dfrac{5}{7} = \dfrac{21 + 5}{7} = \dfrac{26}{7}\)
Step 2: Swap numerator and denominator:
\(\dfrac{26}{7} \rightarrow \dfrac{7}{26}\)
Step 3: Verify by multiplying:
\(\dfrac{26}{7} \times \dfrac{7}{26} = 1\)
A negative reciprocal is the reciprocal of a number with a negative sign. This applies to negative integers, fractions, and mixed numbers.
Examples: \(\dfrac{-7}{1}, \dfrac{-4}{3}, -5\dfrac{3}{2}\)
The reciprocal of 1 is itself:
\(\dfrac{1}{1} = 1\), and \(1 \times 1 = 1\)
To divide by a number, multiply the dividend by the reciprocal of the divisor. Essentially, invert the divisor and multiply.
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