Question

By what number should -15/16 be multiplied to get the multiplicative inverse of -32/30

Answer 1

Answer:

1

Step-by-step explanation:

Answer 2

Given: A rational number $\frac{-15}{16}$

To find: A number by which the given number should be multiplied to get multiplicative inverse of $\frac{-32}{30}$

Let: The required number be $x$

Solution: The multiplicative inverse of $\frac{-32}{30}$ is $\frac{-30}{32}$.

So, we need to find a number which when multipllied with $\frac{-15}{16}$ gives $\frac{-30}{32}$ as result.

∴ $\frac{-15}{16} \ * \ x = \frac{-30}{32}$

⇒ $x = \frac{-30}{32} \ * \ \frac{16}{-15} = \frac{2}{2} \ or \ 1$

Verification:

⇒ $\frac{-15}{16} \ * \ \frac{2}{2} = \frac{-30}{32}$

Now, if write 1 instead of $\frac{2}{2}$, it means the same. As we cen see that $\frac{-30}{32}$ is an equivalent fraction of $\frac{-15}{16}$ so we could initially write it as $\frac{-15}{16}$.

⇒ $\frac{-15}{16} \ * \ 1 = \frac{-15}{16} \ i.e. \ (\frac{-30}{32} )$

Hence, the required number is 1.