Final answer:
The reciprocal of a whole number, pure fraction, mixed number fraction, and pure decimal are 1/number, the inverted fraction, the inverted improper fraction, and a fraction with 1 divided by the number multiplied by its reciprocal respectively. Quickly determining reciprocals is useful for the multiplication and division of fractions.
Step-by-step explanation:
The reciprocal of a number is found by inverting the number so that the numerator becomes the denominator and the denominator becomes the numerator. For example, the reciprocal of a fraction that has a numerator of 15, as in our example, would be 1/15.
Categories of numbers and their reciprocals:
- A) Whole Number: A whole number, such as 299, has a reciprocal that is a pure fraction with the number as the denominator and 1 as the numerator, so the reciprocal of 299 is 1/299.
- B) Pure Fraction: A pure fraction already has a numerator and a denominator. Taking the reciprocal simply involves swapping these, so the reciprocal of ¼ is 4/1, or simply 4.
- C) Mixed Number Fraction: A mixed number, like 3½, is first converted to an improper fraction, and then the reciprocal is taken. The reciprocal of 3½ (= 7/2) is 2/7.
- D) Pure Decimal: A pure decimal can be converted into a fraction and then finding the reciprocal. If we consider a simple decimal like 0.5, which is ½ in fraction form, the reciprocal would be 2.
Important Concepts:
Remember that division of exponentials involves subtracting exponents when dividing like bases, and that dividing by a number is essentially multiplying by its reciprocal. Similarly, Tables of reciprocals can be very handy for quick mental math, especially when these are memorized like multiplication tables. When multiplying fractions, you multiply the top numbers and divide by the bottom numbers, effectively using reciprocals in computation.