Question

The product of two rational numbers is 5/9 ,if one of the numbers is (-35)/24 ,the second number is *
1 point

Answer 1

Answered 10 months, 1 week ago

Given: One the number = -35/24 and assume another number is P.

The product of two numbers = (-35/24) x P = 5/9 => P = 5x24/(-35x9)

P = -8/21

Hence the another number is P = -8/21.

Answer 2

★ How to do :-

Here, we are given with a rational number that should be multiplied by an other number. We are also given with the answer obtained while multiplying those two fractions. But, we aren't given with the second number that the first number should be multiplied with. We are asked to find the same. To find the answer, we make use of some other concepts such as variables and the transition of numbers from one hand side to the other. While we are using this method, the sign of the appropriate number changes. We can also check out our answer by verification method. So, let's solve!!

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➤ Solution :-

Let the other number be y.

${\tt \leadsto \dfrac{(-35)}{24} \times y = \dfrac{5}{9}}$

Shift the fraction on LHS to RHS.

${\tt \leadsto y = \dfrac{5}{9} \div \dfrac{(-35)}{24}}$

Take the reciprocal of second fraction and multiply both fractions.

${\tt \leadsto y = \dfrac{5}{9} \times \dfrac{24}{(-35)}}$

Write the fraction in lowest form by cancellation method.

${\tt \leadsto y = \dfrac{5 \times \cancel{24}}{\cancel{9} \times (-35)} = \dfrac{5 \times 8}{3 \times (-35)}}$

Now, multiply the remaining numbers.

${\tt \leadsto y = \dfrac{5 \times 8}{3 \times (-35)} = \dfrac{40}{(-105)}}$

Write the obtained fraction in lowest form by cancellation method.

${\tt \leadsto y = \cancel \dfrac{40}{(-105)} = \dfrac{8}{(-21)}}$

Shift the negative sign from denominator to numerator.

${\tt \leadsto y = \dfrac{8}{(-21)} = \dfrac{(-8)}{21}}$

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${\red{\underline{\boxed{\bf So, \: the \: other \: number \: is \: \dfrac{(-8)}{21}.}}}}$

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Verification :-

${\tt \leadsto \dfrac{(-35)}{24} \times y = \dfrac{5}{9}}$

Substitute the value of y.

${\tt \leadsto \dfrac{(-35)}{24} \times \dfrac{(-8)}{21} = \dfrac{5}{9}}$

Write both numerators and denominators in a common fraction.

${\tt \leadsto \dfrac{(-35) \times (-8)}{24 \times 21} = \dfrac{5}{9}}$

Write the numerator and denominator in lowest form.

${\tt \leadsto \dfrac{(-35) \times (-1)}{3 \times 21} = \dfrac{5}{9}}$

Again write the numerators and denominators in lowest form.

${\tt \leadsto \dfrac{(-5) \times (-1)}{3 \times 3} = \dfrac{5}{9}}$

Now, multiply the remaining numbers.

${\tt \leadsto \dfrac{5}{9} = \dfrac{5}{9}}$

So,

${\sf \leadsto LHS = RHS}$