Question

2. Multiply the additive inverse of -6 2/3 by the multiplicative inverse of 5 1/6. ​

Answer 1

$\sf\huge\bold{Answer:}$

Given :

$\sf \: mixed \: fractions = - 6 \frac{2}{3} ,5 \frac{1}{6}$

To find :

Multiplication of the additive inverse of $\sf - 6 \frac{2}{3}$ by the multiplicative inverse of $\sf \: 5 \frac{1}{6}$.

Solution :

Converting mixed fraction into improper fraction :

$\tt:⟶ - 6 \frac{2}{3} = \frac{3 \times - 6 + 2}{3}$

$= \tt\frac{ - 18+2}{ \: \: \: 3}$

$= \tt\frac{ - 16}{ \: \: \: 3}$

Additive inverse of $→ \tt\frac{ - 16}{ \: \: \: 3}$

$= \tt\frac{ 16}{ \: \: \: 3}$

Converting mixed fraction into improper fraction :

$\tt:⟶5 \frac{1}{6} = \frac{6 \times 5 + 1}{6}$

$\tt = \frac{30 + 1}{6}$

$\tt = \frac{31}{6}$

Multiplicative inverse of $\tt → \frac{31}{6}$

$\tt = \frac{6}{13}$

→ Multiplication of the additive inverse of $\sf - 6 \frac{2}{3}$ by the multiplicative inverse of $\sf \: 5 \frac{1}{6}$.

$= \tt additive\: inverse\: of\: - 6 \frac{2}{3}$ $\tt ×\: multiplicative\: inverse\: of \: 5 \frac{1}{6}$.

$\tt = \frac{16}{3} \times \frac{6}{13}$

$\tt = \frac{6}{3} \times \frac{16}{13}$

$\tt{=}$$\displaystyle{\tt { \cancel{ \frac{6}{3} }} \frac{16}{13} }$

$\tt = 2 \times \frac{16}{13}$

$\tt = \frac{32}{13}$

$\tt\red{ →additive\: inverse\: of\: - 6 \frac{2}{3} ×\: multiplicative\: inverse\: of \: 5 \frac{1}{6} }$$\tt\red{ = \frac{32}{13} }$