The numerator of a fraction is 6 less than its denominator is 3 is added to the numerator and 1 is subtracted from the denominator the fraction is equal to 2/3 find the original fraction
Answers
Given:
✰ The numerator of a fraction is 6 less than its denominator.
✰ If 3 is added to the numerator and 1 is subtracted from the denominator, the fraction is equal to 2/3.
To find:
✠ The original fraction.
Solution:
❖ Let's understand the concept! First we will assume the denominator as x and we know the numerator of a fraction is 6 less than its denominator that means 6 will be substracted from the denominator ( x - 6 ) and after that If 3 is added to the numerator that means sum of numerator by 3 and 1 is subtracted from the denominator - we will reduce/ decrease 1 from denominator, then fraction is equal to 2/3. Thus, we will from one equation and after solving and doing required calculations we can determine the original fraction.
Let's determine it...
Let the denominator of a fraction be x
Let the denominator of a fraction be xthen, the numerator of a fraction be x - 6
According to question,
➤ x - 6 + 3/ x - 1 = 2/3
➤ x - 3/x - 1 = 2/3
By cross-multiplication method,
➤ 3 ( x - 3 ) = 2 ( x - 1 )
➤ 3x - 9 = 2x - 2
➤ 3x - 2x = - 2 + 9
➤ x = 7
∴ The denominator of a fraction = 7
➤ The numerator of a fraction = x - 6
➤ The numerator of a fraction = 7 - 6
➤ The numerator of a fraction = 1
∴ The numerator of a fraction = 1
✭ The original fraction = Numerator/Denominator
✭ The original fraction = 1/7
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