Question

verify whether the following are true or false : i. (-4/5)÷(-6/5)=(-6/5)÷(-4/5)​

Answer 1

Answer:

false

Step-by-step explanation:

(-4/5)÷(-6/5)=(-6/5)÷(-4/5)

(-4/5) * (5/-6) = (-6/5) * (5/-4)

$\frac{-4*5}{5*-6}$ = $\frac{-6*5}{5*-4}$

2/3 ≠ 3/2

Answer 2

★ How to do :-

Here, we are given with two fraction on LHS and the same two fractions on the RHS of the statement. We are given with two fractions to divide with. They are arranged u. such a way that they are in the form of the commutative property. This property says that when we add two integers we get the same result as we get while we interchange the places of both fractions. The same property can be applied to multiplication of fractions or integers. But, this method cannot be suitable for the subtraction and division of the fractions or integers. In this question, we are given with the division of fractions. So, we can directly say that this statement cannot be possible with the commutative property. But, we should verify that by solving. So, let's solve!!

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➤ Solution :-

${\sf \leadsto \dfrac{(-4)}{5} \div \dfrac{(-6)}{5} \neq \dfrac{(-6)}{5} \div \dfrac{(-4)}{5}}$

Let's solve the LHS and RHS separately.

LHS :-

${\sf \leadsto \dfrac{(-4)}{5} \div \dfrac{(-6)}{5}}$

Take the reciprocal of second fraction and multiply both fractions.

${\sf \leadsto \dfrac{(-4)}{5} \times \dfrac{5}{(-6)}}$

Write the fraction in lowest form by cancellation method.

${\sf \leadsto \dfrac{(-4) \times \cancel{5}}{\cancel{5} \times (-6)} = \dfrac{(-4) \times 1}{1 \times (-6)}}$

Multiply the remaining numbers.

${\sf \leadsto \cancel \dfrac{(-4)}{(-6)} = \dfrac{2}{3}}$

$\:$

RHS :-

${\sf \leadsto \dfrac{(-6)}{5} \div \dfrac{(-4)}{5}}$

Take the reciprocal of second fraction and multiply both fractions.

${\sf \leadsto \dfrac{(-6)}{5} \times \dfrac{5}{(-4)}}$

Write the fraction in lowest form by cancellation method.

${\sf \leadsto \dfrac{(-6) \times \cancel{5}}{\cancel{5} \times (-4)} = \dfrac{(-6) \times 1}{1 \times (-4)}}$

Multiply the remaining numbers.

${\sf \leadsto \cancel \dfrac{(-6)}{(-4)} = \dfrac{3}{2}}$

$\:$

Let's compare the results of both LHS and RHS.

Comparison :-

${\sf \leadsto \dfrac{2}{3} \: and \: \dfrac{3}{2}}$

As we can see that they both aren't equal. So,

${\sf \leadsto \dfrac{2}{3} \neq \dfrac{3}{2}}$

So,

${\sf \leadsto LHS \neq RHS}$

$\:$

Hence verified !!