Questions: What is the reciprocal of 0.20 and 5^2 / 3 ? A 5 and 3 / 17 B 2 and 3 / 17 C 5 and 17 / 3 D 5 and 3 / 10

What is the reciprocal of 0.20 and 5^2 / 3 ?

A 5 and 3 / 17

B 2 and 3 / 17

C 5 and 17 / 3

D 5 and 3 / 10
Transcript text: 14 What is the reciprocal of 0.20 and $5^{2} / 3$ ? A $\quad 5$ and ${ }^{3} / 17$ B $\quad 2$ and $^{3} / 17$ C $\quad 5$ and ${ }^{17} / 3$ D $\quad 5$ and $^{3} / 10$
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Solution

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Solution Steps

Step 1: Understanding the Problem

The problem asks for the reciprocal of two numbers: 0.20 and 5235 \frac{2}{3}. We need to find the reciprocal of each number and then match our results with the given multiple-choice options.

Step 2: Finding the Reciprocal of 0.20

The reciprocal of a number xx is 1x\frac{1}{x}. For 0.20, the reciprocal is:

10.20=115=5 \frac{1}{0.20} = \frac{1}{\frac{1}{5}} = 5

Step 3: Finding the Reciprocal of 5235 \frac{2}{3}

First, convert the mixed number 5235 \frac{2}{3} to an improper fraction:

523=5×3+23=15+23=173 5 \frac{2}{3} = \frac{5 \times 3 + 2}{3} = \frac{15 + 2}{3} = \frac{17}{3}

The reciprocal of 173\frac{17}{3} is:

1173=317 \frac{1}{\frac{17}{3}} = \frac{3}{17}

Final Answer

The reciprocals are 5 and 317\frac{3}{17}. Therefore, the correct answer is:

A) 5 and 317 \boxed{\text{A) } 5 \text{ and } \frac{3}{17}}

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