The reciprocal of 3 – 1/5 is

The reciprocal of 3 – 1/5 is

The Correct Answer and Explanation is:

The reciprocal of a number is simply 1 divided by that number. To find the reciprocal of 3−153 – \frac{1}{5}3−51​, we first need to express the given expression as a single fraction.

Step 1: Simplify the expression

Start by converting the mixed number 3−153 – \frac{1}{5}3−51​ into an improper fraction. To do this: 3=1553 = \frac{15}{5}3=515​

So, 3−15=155−15=15−15=1453 – \frac{1}{5} = \frac{15}{5} – \frac{1}{5} = \frac{15 – 1}{5} = \frac{14}{5}3−51​=515​−51​=515−1​=514​

Step 2: Find the reciprocal

Now that we have 145\frac{14}{5}514​, the reciprocal is simply 514\frac{5}{14}145​, as we take the numerator and denominator and swap them.

Step 3: Conclusion

Therefore, the reciprocal of 3−153 – \frac{1}{5}3−51​ is: 514\frac{5}{14}145​

Explanation

The process of finding the reciprocal involves two steps. First, you simplify the given expression if it’s a mixed number or fraction. Then, you take the reciprocal, which is equivalent to taking the inverse of that number. This concept is essential in many areas of mathematics, particularly when dealing with division or solving equations involving fractions. It also comes in handy when you work with rates, proportions, or any context where multiplication by a fraction is required