Question

Simplify $ - \dfrac{8}{9} \times \dfrac{{16}}{{ - 7}}$.

Answer 1

Hint:In order to this question, to simplify the given expression, we will follow the concept of fractional multiplication as the expression is in fraction form. We will follow the various criteria for solving the fractional multiplication.

Complete step by step answer:
For the given expression, we will use the concept of the fraction multiplication in which we will try to first divide the numerator from the denominator, if the numerator is divisible, to make the expression into its simplest form. Or if the numerator is not divisible or cancel out, then we will directly multiply both the numerator by each other and similarly we will multiply both the denominator by each other:

Given expression: $ - \dfrac{8}{9} \times \dfrac{{16}}{{ - 7}}$
In the above expression, first we will cancel out the $( - )$ sign or two negatives always convert into positive, as we know:
$\dfrac{8}{9} \times \dfrac{{16}}{7}$
Now, there is not any condition for division of anything between numerator and denominator. So, we will multiply both the numerators together and similarly denominators together:
$\dfrac{{8 \times 16}}{{9 \times 7}} \\
\Rightarrow \dfrac{{128}}{{63}} \\ $
So, the fractional multiplication of the given expression is $\dfrac{{128}}{{63}}$. And, we can also convert the fractional form into the decimal form: $\dfrac{{128}}{{63}} = 2.031$

Hence, the decimal form is $2.031$.

Note: Properties of the fractional multiplication:-
-The product of the fraction remains the same if the two provided fractional integers are multiplied in either order.
-If the given fractional number is multiplied by $(\dfrac{1}{1})$ , the product remains the same fractional number.
-If a given fractional number is multiplied by 0, the product remains zero.