the numerater of a fractian is 6 less then its denomentar if to is added to bath numeentar and denomentar the fration becouse 3/2 find the frations
Answers
your answer is 8/14
x-6/x
x-6+2/x+2=3/2
x-4/x+2=3/2
2(x-4)=3(x+2)
2x-8=3x+6
x=14
now denominator =14
numerator =14-6=8
so the fraction is 8/14....
hope it helps you
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CORRECT QUESTION :-
★ The numerator of a fraction is 6 less than its denominator, If 2 is added to both numerator and denominator the fraction becomes 3/2. Find the fraction.
TO FIND :-
- The Fraction.
SOLUTION :-
★ Let the Denominator be x.
★ Numerator = x - 6.
∴ Fraction = x - 6/x.
After 2 is added to numerator and denominator,
★ Denominator = x + 2.
★ Numerator = x - 6 + 2 = x - 4.
∴ New Fraction = (x - 4)/(x + 2)
☢ ACCORDING TO QUESTION ☢
→ (x - 4)/(x + 2) = 3/2
By cross multiplication,
→ 2(x - 4) = 3(x + 2)
→ 2x - 8 = 3x + 6
→ 2x - 3x = 6 + 8
→ - x = 14
→ x = -14
∴ The value of x is -14.
★ Numerator = x - 6 = -14 - 6 = -20.
★ Denominator = x = -14.
∴ Fraction = Numerator/Denominator
∴ Fraction = -20/-14
∴ the Required Fraction is -20/-14.
★ VERIFICATION ★
→ (x - 4)/(x + 2) = 3/2
Substitute the values,
→ (-14 - 4)/(-14 + 2) = 3/2
→ -18/-12 = 3/2
→ 18/12 = 3/2
→ 3/2 = 3/2
L.H.S = R.H.S
❏ HENCE VERIFIED.