What is the HCF of the reciprocals of \(\frac{3}{4}\), \(\frac{9}{10}\) and \(\frac{15}{16}\)?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\frac{2}{45}\)
For fractions in lowest terms, HCF \(=\displaystyle\frac{\text{HCF of numerators}}{\text{LCM of denominators}}\): the top should be as large as possible and the bottom as small as possible while still dividing every fraction a whole number of times.
Reciprocals: \(\frac{4}{3}\), \(\frac{10}{9}\), \(\frac{16}{15}\)
HCF of numerators 4, 10, 16 \(=2\)
LCM of denominators 3, 9, 15 \(=45\)
HCF \(=\frac{2}{45}\)
The HCF of the reciprocals is \(\frac{2}{45}\).