Question

Fill in the Blanks 4/12 ÷() =-32/18 *​

Answer 1

Answer:

4/12÷x=-32/18

x=-32/18×4/12

x=22/54

x=11/27

Please mark me brainliest

Answer 2

★ How to do :-

Here, we are given with a fraction that should be divided by an other fraction. We are also given with the fraction that will be the answer when we divide the given fraction and an other fraction. But, we aren't given with the other number that the given fraction should be divided with. We are also asked to find the same. To find the value of the second fraction or the missing fraction in this question, we make use of an other concept which is used to find the values of not-given numbers. This method is known as the transposition method. We can find. the value of the missing fraction by the same method. In this method, we transpose the given numbers from one hand side to the other. This method changes the sign of the following fraction. So, let's solve!!

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➤ Solution :-

Let the other number be y.

${\sf \leadsto \dfrac{4}{12} \div y = \dfrac{(-32)}{18}}$

Shift the fraction on LHS to RHS, changing it's sign.

${\sf \leadsto y = \dfrac{4}{12} \div \dfrac{(-32)}{18}}$

Take the reciprocal of second fraction and multiply both fractions.

${\sf \leadsto y = \dfrac{4}{12} \times \dfrac{18}{(-32)}}$

Write the fraction in lowest form by cancellation method.

${\sf \leadsto y =\dfrac{4 \times \cancel{18}}{\cancel{12} \times (-32)} = \dfrac{4 \times 3}{2 \times (-32)}}$

Again write the fraction in lowest form by cancellation method.

${\sf \leadsto y = \dfrac{\cancel{4} \times 3}{2 \times \cancel{(-32)}} = \dfrac{2 \times 3}{2 \times (-16)}}$

Multiply the remaining numbers.

${\sf \leadsto \cancel \dfrac{6}{(-32)} = \dfrac{3}{(-16)}}$

Shift the negative sign on denominator to numerator.

${\sf \leadsto \dfrac{3}{(-16)} = \dfrac{(-3)}{16}}$

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${\red{\underline{\boxed{\bf So, \: the \: other \: number \: is \: \dfrac{(-3)}{16}.}}}}$

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Verification :-

${\sf \leadsto \dfrac{4}{12} \div y = \dfrac{(-32)}{18}}$

Substitute the value of y.

${\sf \leadsto \dfrac{4}{12} \div \dfrac{(-3)}{16} = \dfrac{(-32)}{18}}$

Take the reciprocal of second fraction and multiply both fractions.

${\sf \leadsto \dfrac{4}{12} \times \dfrac{16}{(-3)} = \dfrac{(-32)}{18}}$

Write both numerators with a common denominator.

${\sf \leadsto \dfrac{4 \times 16}{12 \times (-3)} = \dfrac{(-32)}{18}}$

Write the fraction in lowest form.

${\sf \leadsto \dfrac{4 \times 4}{3 \times (-3)} = \dfrac{(-32)}{18}}$

Multiply the remaining numbers.

${\sf \leadsto \dfrac{16}{(-9)} = \dfrac{(-32)}{18}}$

Multiply the fraction on LHS both sides with 2

${\sf \leadsto \dfrac{32}{(-18)} = \dfrac{(-32)}{18}}$

Shift the negative sign on denominator to numerator.

${\sf \leadsto \dfrac{(-32)}{18} = \dfrac{(-32)}{18}}$

So,

${\sf \leadsto LHS = RHS}$

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Hence verified !!