Question

The sum of 2/−3 and 1/−2 is equal to the product of 4/5 and a number. Find the number

Answer 1

Step-by-step explanation:

Given :-

The sum of 2/−3 and 1/−2 is equal to the product of 4/5 and a number.

To find :-

The number

Solution :-

Given numbers are 2/-3 and 1/-2

2/-3 = -2/3

1/-2 = -1/2

The sum of -2/3 and -1/2

= (-2/3)+(-1/2)

LCM of 3 and 2 = 6

= [(-2×2)+(-1×3)]/6

= [(-4)+(-3)]/6

= (-4-3)/6

= -7/6

The sum of 2/-3 and 1/-2 = -7/6 ------(1)

Let the number be X

The product of X and 4/5

= (4/5)×X

= (4×X)/5

= 4X/5

The product of X and 4/5 = 4X/5 ---------(2)

According to the given problem

The sum of 2/-3 and 1/-2 = The product of X and 4/5

=> (1) = (2)

=> -7/6 = 4X/5

On applying cross multiplication then

=> 4X×6 = -7×5

=> 24X = -35

=> X = -35/24

Therefore, The number = -35/24

Answer :-

The required number is -35/24

Check:-

The number = -35/24

The product of -35/24 and 4/5

= (-35/24)×(4/5)

= (-35×4)/(24×5)

= -7/6

The sum of -2/3 and -1/2 = -7/6

The sum of -2/3 and -1/2 is equal to the product of 4/5 and the given number.

Verified the given relations in the given problem.

Answer 2

Given Data :-

The sum of 2/−3 and 1/−2 is equal to the product of 4/5 and a number.

To Find :

Find the Number. let it be x .

Solution :-

Sum of -2/3 and -1/2

= (-⅔) + (-½)

= (-4 - 3)/6

= -7/6

Then, According to the Question,

Product of a number and 4/5

= x * 4/5

= 4x/5

then, From the Given data

-7/6 = 4x/5

⇒ 5(-7) = 6(4x)

⇒ -35 = 24x

⇒ x = -35/24

FINAL ANSWER :

The Number is -35/24