What is the value of \(\frac{5}{4}-\frac{8}{3}\)?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(-\frac{17}{12}\)
Fractions with different denominators are first written over the LCM of the denominators. Here the second fraction is larger, so the result is negative.
LCM of 4 and 3 \(=12\)
\(\displaystyle \frac{5}{4}=\frac{15}{12}\) and \(\displaystyle \frac{8}{3}=\frac{32}{12}\)
\(\displaystyle \frac{15}{12}-\frac{32}{12}=\frac{15-32}{12}=-\frac{17}{12}\)
Why the other options are incorrect
Option (1) \(\frac{17}{12}\) — Incorrect. This is \(\frac{8}{3}-\frac{5}{4}\); it drops the minus sign of the result.
Option (3) \(\frac{12}{17}\) — Incorrect. This turns the fraction upside down and also drops the sign.
Option (4) \(-\frac{12}{17}\) — Incorrect. The sign is right, but the fraction is upside down.