Question

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maths assignment

Answer 1

★ Solution (8) :-

Given fractions :

$\sf \leadsto \dfrac{-5}{4} \: ; \: 1 \dfrac{1}{4}$

We can see that the given rational numbers have the same denominator but are of different types. So, first we should convert the second fraction to improper fraction.

$\sf \leadsto 1 \dfrac{1}{4} = \dfrac{5}{4}$

Now, we can locate both rational numbers on the number line.

[Answer in attachment]

★ Solution (9a) :-

$\sf \leadsto \dfrac{x}{25} = \dfrac{-9}{y} = \dfrac{-3}{5} = \dfrac{z}{-75}$

First, we'll find the value of x.

Value of x :-

$\sf \leadsto \dfrac{-3}{5} = \dfrac{x}{25}$

$\sf \leadsto 25(-3) = 5(x)$

$\sf \leadsto -75 = 5x$

$\sf \leadsto 5x = -75$

$\sf \leadsto x = \dfrac{-75}{5}$

$\sf \leadsto x = -15$

Value of y :-

$\sf \leadsto \dfrac{-3}{5} = \dfrac{-9}{y}$

$\sf \leadsto -3(y) = 5(-9)$

$\sf \leadsto -3y = -45$

$\sf \leadsto y = \dfrac{-45}{-3}$

$\sf \leadsto y = 15$

Value of z :-

$\sf \leadsto \dfrac{-3}{5} = \dfrac{z}{-75}$

$\sf \leadsto -75(-3) = 5(z)$

$\sf \leadsto 225 = 5z$

$\sf \leadsto 5z = 225$

$\sf \leadsto z = \dfrac{225}{5}$

$\sf \leadsto z = 45$

★ Solution (9b) :-

$\sf \leadsto \dfrac{x}{-36} = \dfrac{-5}{-9} = \dfrac{25}{y} = \dfrac{z}{-63}$

First, we'll find the value of x.

Value of x :-

$\sf \leadsto \dfrac{-5}{-9} = \dfrac{x}{-36}$

$\sf \leadsto -36(5) = -9(x)$

$\sf \leadsto -180 = -9x$

$\sf \leadsto -9x = -180$

$\sf \leadsto x = \dfrac{-180}{-9}$

$\sf \leadsto x = 20$

Value of y :-

$\sf \leadsto \dfrac{-5}{-9} = {25}{y}$

$\sf \leadsto -5(y) = 25(-9)$

$\sf \leadsto -5y = -225$

$\sf \leadsto y = \dfrac{-225}{-5}$

$\sf \leadsto y = 45$

Value of z :-

$\sf \leadsto \dfrac{-5}{-9} = \dfrac{z}{-63}$

$\sf \leadsto -63(-5) = -9(z)$

$\sf \leadsto 315 = -9z$

$\sf \leadsto -9z = 315$

$\sf \leadsto z = \dfrac{315}{-9}$

$\sf \leadsto z = -35$

Hence solved !!