the denominator of a fraction is 7 cm more than the numerator if 1 is added to the numerator and 6 is added the denominator the value of the fraction will be ,1/2 in the numerator and denominator
Answers
Answer:
denominator of a fraction is 7 cm more than the numerator if 1 is added to the numerator and 6 is added the denominator the value of the fraction will be ,1/2 in the numerator and denominator
Answer:
The denominator of a fraction is 7 cm more than the numerator.
If 1 is added to the numerator and 6 is added to the denominator, the value of the fraction becomes 1/2.
\bf \underline{ \underline{\maltese\:To \: find } }
✠Tofind
\sf \implies Original \: fraction = \: ? ⟹Originalfraction=?
\bf \underline{ \underline{\maltese\:Solution } }
✠Solution
\sf Let \: us \: assume \: that, Letusassumethat,
\sf \implies Numerator \: of \: the \: fraction \: be \: x.⟹Numeratorofthefractionbex.
\bf \implies Then, \sf\: the \: denominator \: will \: be \: x+7. ⟹Then,thedenominatorwillbex+7.
\sf According \: to \: question, Accordingtoquestion,
\sf Equation : \bf \red{ \dfrac{x + 1}{(x + 7) + 6} = \dfrac{1}{2} }Equation:
(x+7)+6
x+1
=
2
1
\sf \implies \dfrac{x + 1}{x + 13} = \dfrac{1}{2}⟹
x+13
x+1
=
2
1
\sf Doing \: cross \: multiplication, Doingcrossmultiplication,
\sf \implies (x + 1) \times 2 = (x + 13) \times 1⟹(x+1)×2=(x+13)×1
\sf \implies 2x + 1 = x + 13 ⟹2x+1=x+13
\sf \implies 2x + 1 - x = 13 ⟹2x+1−x=13
\sf \implies x + 2 = 13 ⟹x+2=13
\sf \implies x = 13 - 2 ⟹x=13−2
\sf \implies x = 11⟹x=11
\bf \underline{Now},
Now
,
\sf \implies Numerator \: (x) = \bf 11⟹Numerator(x)=11
\sf \implies Denominator \: (x+7) = \bf (11+7) = 18⟹Denominator(x+7)=(11+7)=18
\bf \underline{Therefore},
Therefore
,
\implies \underline{\boxed{ \sf Original \: fraction = \dfrac{11}{18} }}⟹
Originalfraction=
18
11
━━━━━━━━━━━━━━━━━━━━━━━━━━
\bf \underline{ \underline{\maltese\:Varification } }
✠Varification
To verify the answer just write 11 in place of x.
\sf \implies \dfrac{x + 1}{(x + 7) + 6} = \dfrac{1}{2} ⟹
(x+7)+6
x+1
=
2
1
\sf \implies \dfrac{11+ 1}{(11+ 7) + 6} = \dfrac{1}{2} ⟹
(11+7)+6
11+1
=
2
1
\sf \implies \dfrac{12}{11+13} = \dfrac{1}{2} ⟹
11+13
12
=
2
1
\sf \implies \cancel\dfrac{12}{24} = \dfrac{1}{2} ⟹
24
12
=
2
1
\sf \implies \dfrac{1}{2} = \dfrac{1}{2} ⟹
2
1
=
2
1
Hence Verified!