Questions: What is the reciprocal of 15 2/3 ? A 15 3/2 B 3 2/15 C 45/3 D 3/47

What is the reciprocal of 15 2/3 ? A 15 3/2 B 3 2/15 C 45/3 D 3/47
Transcript text: What is the reciprocal of $15 \frac{2}{3}$ ? A $15 \frac{3}{2}$ B $3 \frac{2}{15}$ C $\quad \frac{45}{3}$ D $\quad \frac{3}{47}$
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Solution

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Solution Steps

Step 1: Convert Mixed Number to Improper Fraction

The given number is \(15 \frac{2}{3}\). First, convert this mixed number to an improper fraction.

\[ 15 \frac{2}{3} = \frac{15 \times 3 + 2}{3} = \frac{45 + 2}{3} = \frac{47}{3} \]

Step 2: Find the Reciprocal

The reciprocal of a fraction \(\frac{a}{b}\) is \(\frac{b}{a}\). Therefore, the reciprocal of \(\frac{47}{3}\) is:

\[ \frac{3}{47} \]

Step 3: Match with the Given Options

Now, compare the reciprocal \(\frac{3}{47}\) with the given options:

  • A: \(15 \frac{3}{2}\)
  • B: \(3 \frac{2}{15}\)
  • C: \(\frac{45}{3}\)
  • D: \(\frac{3}{47}\)

The reciprocal \(\frac{3}{47}\) matches option D.

Final Answer

\[ \boxed{D} \]

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