11. The denominator of a rational number is 2 less than twice the numerator. If numerator and
denominator are increased by 1 each the rational number becomes
4/5
Find the number.
Answers
-6/11 or 6/11 Answer
Step-by-step explanation:
Let denominator = x
So, numerator = 2 - 2x
In the question , if they are increase by 1 then the , denominator = x + 1
numerator = 2 - 2x + 1
(2 - 2x + 1) / x + 1 = 4 /5
= (3 - 2x) / + 1 = 4/5 [ in 2 - 2x + 1 , 2 + 1 = 3.]
= 5(3 - 2x) = 4(x + 1) [cross - multiplication between (3 - 2x) / x + 1 & 4/5.]
= 15 - 10x = 4x + 4
= -10 x - 4x = + 4 - 15 [ +4 x moves yo LHS and becomes -4 x , likewise, +15 moves to RHS and becomes -15. Because x terms cannot be subtracted by non - x terms. ]
= -14 x = -11
Therefore x = -11/-14.
So, now we will substitute the answers.,
denominator = 11/14 and,
numerator = 2 - 2 x 11/14
= 2 - 11/7 [ we divided 14 by 2 which is equal to 7.]
Now, numerator = 3/7
3/7÷11/14 [ as numerator = 3/7 and 11/14 = denominator.]
It can also be written as (3/7)/(11/14).
3/7 x 14/11 [ as we know that in multiplication of rational numbers the second number is reversed .]
= 3/1 x 2/11 = 6/11
THEREFORE , THE NUMBER IS 6/11.
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