Prove that the following rational numbers are equal:
(i) \(-\frac{2}{7}\) and \(-\frac{16}{56}\)
(ii) \(\frac{56}{7}\) and \(8\)
Solution:
Any two rational numbers \(\frac{a}{b}\) and \(\frac{c}{d}\) are said to be equal if .
[Note: Enter the answer in alphabetical order.]
Proof:
(i) \(-\frac{2}{7}\) and \(-\frac{16}{56}\)
\(-2 \times 56\) \(=\) ......(1)
\(7 \times (-16)\) \(=\) ......(2)
Equation (1) Equation (2)
Therefore, \(-\frac{2}{7}\) and \(-\frac{16}{56}\) are .
(ii) \(\frac{56}{7}\) and \(8\)
Proof:
\(\frac{56}{7}\) \(=\) \(\frac{8}{1}\)
\(56 \times 1\) \(=\) ......(1)
\(7 \times 8\) \(=\) ......(2)
Equation (1) Equation (2)
Therefore, \(\frac{56}{7}\) and \(8\) are .