Question

the sum of the numerator and denominator of a fraction is 10. If the numerator is multiplied by 3 and the denominator by 1/2, the fraction becomes 2/3. Find the fraction.​

Answer 1

Step-by-step explanation:

Let the fraction =\dfrac {x} {y}=

y

x

First condition :

\Rightarrow x+y=2y-3⇒x+y=2y−3

\Rightarrow x-y=-3⇒x−y=−3

Second condition :

\Rightarrow \dfrac {x-1}{y-1}=\dfrac {1}{2}⇒

y−1

x−1

=

2

1

\Rightarrow 2x-2=y-1⇒2x−2=y−1

\Rightarrow 2x-y=1⇒2x−y=1

Subtract two equations ;

\Rightarrow 2x-x=1+3\Rightarrow x=4⇒2x−x=1+3⇒x=4

substitute in above equation

\Rightarrow y=1+8\Rightarrow y=7⇒y=1+8⇒ y=7

\therefore∴ the fraction =\dfrac{4}{7}=

7

4

Answer 2

Answer:

1 / 9

Step-by-step explanation:

LET THE NUMERATOR BE X

LET THE DENOMINATOR BE Y

THEREFORE, THE FRACTION IS X / Y

GIVEN CONDITION:

→ X + Y = 10

NOW,

IF THE NUMERATOR IS MULTIPLIED BY 3,  NUMERATOR BECOMES 3X

IF THE DENOMINATOR IS MULTIPLIED BY 1/2,  DENOMINATOR BECOMES 1/2Y

THEN THE FRACTION IS (3)X / (1/2)Y WHICH IS EQUAL TO 2 / 3

(3)X / (1/2)Y = 2 / 3

SIMPLIFICATION:

THE 2 IN DENOMINATOR GOES TO NUMERATOR SINCE ITS IN 1 / 2

SO IT BECOMES 6X / Y = 2 / 3

CROSS MULTIPLY: BRING BRING 3 WITH 6X AND 2 WITH Y

THEN, 18X = 2Y  i.e.,  9X = Y [DIVIDE BY 2]

SO,  X / Y = 1 / 9

HOPE IT HELPS

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