The reciprocal of 5 1/3 is ?
The correct answer and explanation is:
The reciprocal of a number is obtained by flipping the number. For a mixed fraction like 5 1/3, the first step is to convert it into an improper fraction.
Here’s how to do that:
- Multiply the whole number (5) by the denominator of the fractional part (3), which gives 15.
- Add the numerator of the fractional part (1) to this result, giving 16.
- So, 5 1/3 becomes the improper fraction 16/3.
The reciprocal of 16/3 is obtained by swapping the numerator and denominator. Therefore, the reciprocal of 5 1/3 (which is 16/3) is 3/16.
To summarize:
- First, convert the mixed fraction to an improper fraction: 5 1/3 = 16/3.
- Then, find the reciprocal by swapping the numerator and denominator: The reciprocal of 16/3 is 3/16.
Understanding reciprocals is essential in many areas of mathematics, especially in fractions, algebra, and calculus. A reciprocal is often used in division problems, where dividing by a fraction is the same as multiplying by its reciprocal. For example, if you were to divide by 5 1/3, it would be the same as multiplying by 3/16.
It’s also worth noting that the reciprocal of a whole number like 5 would be 1/5. The same principle applies to any number, be it a whole number, fraction, or mixed number: simply flip the fraction to find the reciprocal.