The difference of \(1\frac{3}{16}\) and its reciprocal is equal to
2023
The difference of \(1\frac{3}{16}\) and its reciprocal is equal to
Answer: C. \(\frac{105}{304}\) — ConceptA mixed number must first be converted to an improper fraction. For any nonzero fraction \(\frac{a}{b}\), its reciprocal is \(\frac{b}{a}\). To…
- A.
\(\frac{4}{3}\)
- B.
\(\frac{15}{16}\)
- C.
\(\frac{105}{304}\)
- D.
More than one of the above
- E.
None of the above
Show answer & explanation
Correct answer: C
Concept
A mixed number must first be converted to an improper fraction. For any nonzero fraction \(\frac{a}{b}\), its reciprocal is \(\frac{b}{a}\).
To subtract two fractions, use a common denominator and simplify the numerator difference.
Application
Convert the mixed number: \(1\frac{3}{16}=\frac{1\times16+3}{16}=\frac{19}{16}\).
Its reciprocal is \(\frac{16}{19}\).
Subtract using the common denominator 304: \(\frac{19}{16}-\frac{16}{19}=\frac{19\times19-16\times16}{304}\).
Evaluate the numerator: \(\frac{361-256}{304}=\frac{105}{304}\).
Cross-check
The fractions \(\frac{19}{16}\) and \(\frac{16}{19}\) are approximately 1.1875 and 0.8421, so their difference is about 0.3454. Also, \(\frac{105}{304}\approx0.3454\), confirming the exact result.