Question

EXERCISE 1 (E)
1. The product of two rational numbers is -12. If one of the number is -8, find the other,
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Answer 1

Answer:

3/2

Step-by-step explanation:

another number= -12/-8 = 3/2

Answer 2

$\large\sf\underline{Given\::}$

• Product of two numbers is -12

• One of the number is -8

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$\large\sf\underline{To\:find\::}$

• The number whose product with -8 gives us -12.

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$\large\sf\underline{Concept\::}$

Here in the question we are said that the product of two numbers is -12 . One of the number is given as -8 . We are asked to find the other number. In order to do so we would assume the other number to be x and then frame an equation following the question. Solving the equation we would get the other number whose product with -8 gives -12 .

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$\large\sf\underline{Assumption\::}$

Let the other number be x.

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$\large\sf\underline{Solution\::}$

Let frame up an equation :

$\bf\:Assumed\:number\: \times (-8) =(-12)$

$\sf\implies\:x \times (-8) =(-12)$

$\sf\implies\:-8x =-12$

• Now transposing -8 to RHS it goes to the denominator

$\sf\implies\:x =\frac{-12}{-8}$

• Signs gets cancelled out

$\sf\implies\:x =\frac{\cancel{-}12}{\cancel{-}8}$

$\sf\implies\:x =\frac{12}{8}$

• Reducing the fraction to the lower terms

$\sf\implies\:x =\cancel{\frac{12}{8}}$

$\sf\implies\:x =\cancel{\frac{6}{4}}$

$\small{\underline{\boxed{\mathrm\red{{\mathfrak{\implies\:x\:=\:\frac{3}{2}}}}}}}$ ★

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$\large\sf\underline{Verifying\::}$

Let's check if we got the correct number. How would we check!? We just need to substitute the value of x as 3 / 2 in the equation we had framed. Doing so and solving it , if we get LHS = RHS, our answer would be correct.

Our equation : $\sf\:x \times (-8) =(-12)$

• Substituting the value of x

$\sf\rightarrow\:\frac{3}{2} \times (-8) =(-12)$

$\sf\rightarrow\:\frac{3}{2} \times -8=-12$

• Multiplying the numbers

$\sf\rightarrow\:\frac{-24}{2} =-12$

• Reducing the fraction to the lower terms

$\sf\rightarrow\:\cancel{\frac{-24}{2}} =-12$

$\sf\rightarrow\:-12 =-12$

$\bf\rightarrow\:LHS=RHS$

$\bf\color{gray}{Hence\:verified}$ ${\checkmark}$

__________________________

$\dag\:\underline{\sf So\:the\:required\:number\:is\:\frac{3}{2}}$‎

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!! Hope it helps !!