A fraction bears the same ratio to 1/7 as 3/7 does to 5/9 . Find the fraction?
Answers
Given that:
A fraction has the same ratio to 1/27 as 3/7 does to 5/9.
We need to find the fraction
Solution :
Let the fraction be ‘x’
As per the given condition
x: 1/27=3/7: 5/9
=X x 5/9 = 1/27 x 3/7
=x X 5/9 = 1/63
= X= 1/35
Hence the fraction is 1/35
Let f be the unknown fraction. Since fraction f bears the same ratio to 1/9 as 3/7 does to 5/4, we can write the following proportion:
f/(1/9) = (3/7)/(5/4)
Remember: A proportion is an equation that says that two ratios are equal.
Dividing the two fractions on the right side, we get:
f/(1/9) = (3/7)(4/5)
f/(1/9) = [(3)(4)]/[(7)(5)]
f/(1/9) = 12/35
Now, multiplying both sides by 1/9 to solve for f:
(1/9)[f/(1/9)] = (1/9)(12/35)
Performing cancellation on the right, we get:
[(1/9)/(1/9)]f = (1/3)(4/35)
(1)f = 4/105
f = 4/105 is our desired fraction.
CHECK:
f/(1/9) = (3/7)/(5/4)
(4/105)/(1/9) = (3/7)/(5/4)
(4/105)/(9/1) = (3/7)(4/5)
(4/35)/(3/1) = (3/7)(4/5)
12/35 = 12/35