Verify each of the following: (i) 3/5 x -5/9 = -5/9 x 3/7 (ii) -8/7 x 13/9 = 13/9 x -8/7

Question

 Verify each of the following:

(i) \(\frac{3}{5}\times\frac{-5}{9} =\frac{-5}{9}\times\frac{3}{7}\)

(ii) \(\frac{-8}{7}\times\frac{13}{9}=\frac{13}{9}\times\frac{-8}{7}\)

(iii) \(\frac{-12}{5}\times\frac{7}{-36}=\frac{7}{-36}\times\frac{-12}{5}\)

(iv) \(-8\times\frac{-13}{12}=\frac{-13}{12}\times(-8)\)

Answer 1

(i)

LHS = \(\frac{3}{7}\times\frac{-5}{9}\)

= \(\frac{3\times-5}{7\times9}\)

= \(\frac{-15}{63}\)

In lowest terms,

\(\frac{-15}{63}= \frac{-15 ÷3}{63 ÷3}=\frac{-5}{21}\)

RHS = \(\frac{-5}{9}\times\frac{3}{7}\)

= \(\frac{-5}{9}\times\frac{3}{7}\)

= \(\frac{-15}{63}\)

In lowest terms,

\(\frac{-15}{63}= \frac{-15 ÷3}{63 ÷3}=\frac{-5}{21}\)

LHS=RHS

(ii)

LHS = \(\frac{-8}{7}\times\frac{13}{9}\)

= \(\frac{-8\times13}{7\times9}\)

= \(\frac{-104}{63}\)

RHS = \(\frac{13}{9}\times\frac{-8}{7}\)

= \(\frac{13\times-8}{9\times7}\)

= \(\frac{-104}{63}\)

LHS=RHS

(iii)

LHS = \(\frac{-12}{5}\times\frac{7}{-36}\)

= \(\frac{-12\times7}{5\times-36}\)

= \(\frac{-84}{-180}= \frac{-84\times-1}{-180\times-1}=\frac{84}{180}\)

In lowest terms,

\(\frac{84}{180}= \frac{84 ÷12}{180 ÷-12}=\frac{7}{15}\)

RHS = \(\frac{7}{-36}\times\frac{-12}{5}\)

= \(\frac{-84}{-180}= \frac{84 ÷12}{180 ÷-12}=\frac{7}{15}\)

In lowest terms,

\(\frac{84}{180}= \frac{84 ÷12}{180 ÷12}=\frac{7}{15}\)

LHS=RHS

(iv)

LHS = \(-8\times\frac{-13}{12}\)

= \(\frac{-8\times-13}{12}\)

= \(\frac{104}{12}\)

In lowest terms,

\(\frac{104}{12}= \frac{104 ÷4}{12 ÷4}=\frac{26}{3}\)

RHS = \(\frac{-13\times-8}{12}\)

= \(\frac{104}{12}\)

In lowest terms,

\(\frac{104}{12}= \frac{104 ÷4}{12 ÷4}=\frac{26}{3}\)

LHS=RHS